2006-09-01
Aerospace Applications, AIAA-Paper 96-2355, New Orleans, 1996 2. V.A.Bityurin, A.N.Bocharov, J.Lineberry, MHD Aerospace Applications, Invited Lecture ...Paper 2003- 4303, Orlando, FL 8. V.A.Bityurin, Prospective of MHD Interaction in Hypersonic and Propulsion Technologies, In: von Karman Series : Lectures ...Efforts in MHD AeoSpace Applications, In: von Karman Series : Lectures , Introduction of Magneto-Fluid Dynamics for AeroSpace Applications, von Karman
Birzvalk, Yu.
1978-01-01
The shunting ratio and the local shunting ratio, pertaining to currents induced by a magnetic field in a flow channel, are properly defined and systematically reviewed on the basis of the Lagrange criterion. Their definition is based on the energy balance and related to dimensionless parameters characterizing an MHD flow, these parameters evolving from the Hartmann number and the hydrodynamic Reynolds number as well as the magnetic Reynolds number, and the Lundquist number. These shunting ratios, of current density in the core of a stream (uniform) or equivalent mean current density to the short-circuit (maximum) current density, are given here for a slot channel with nonconducting or conducting walls, for a conduction channel with heavy side rails, and for an MHD-flow around bodies. 5 references, 1 figure.
Bloom, M. H.
1980-01-01
The aim of this program is to contribute to certain facets of the development of the MHD/coal power system, and particularly the CDIF of DOE with regard to its flow train. Consideration is given specifically to the electrical power take-off, the diagnostic and instrumentation systems, the combustor and MHD channel technology, and electrode alternatives. Within the constraints of the program, high priorities were assigned to the problems of power take-off and the related characteristics of the MHD channel, and to the establishment of a non-intrusive, laser-based diagnostic system. The next priority was given to the combustor modeling and to a significantly improved analysis of particle combustion. Separate abstracts were prepared for nine of the ten papers included. One paper was previously included in the data base. (WHK)
Hodograph method in MHD orthogonal fluid flows
P. V. Nguyen
1992-01-01
Full Text Available Equations for steady plane MHD orthogonal flows of a viscous incompressible fluid of finite electrical conductivity are recast in the hodograph plane by using the Legendre transform function of the streamfunction. Three examples are studied to illustrate the developed theory. Solutions and geometries for these examples are determined.
MHD squeezing flow between two infinite plates
Umar Khan
2014-03-01
Full Text Available Magneto hydrodynamic (MHD squeezing flow of a viscous fluid has been discussed. Conservation laws combined with similarity transformations have been used to formulate the flow mathematically that leads to a highly nonlinear ordinary differential equation. Analytical solution to the resulting differential equation is determined by employing Variation of Parameters Method (VPM. Runge–Kutta order-4 method is also used to solve the same problem for the sake of comparison. It is found that solution using VPM reduces the computational work yet maintains a very high level of accuracy. The influence of different parameters is also discussed and demonstrated graphically.
Drag reduction in turbulent MHD pipe flows
Orlandi, P.
1996-01-01
This is a preliminary study devoted to verifying whether or not direct simulations of turbulent Magneto-Hydro-Dynamic (MHD) flows in liquid metals reproduce experimental observations of drag reduction. Two different cases have been simulated by a finite difference scheme which is second order accurate in space and time. In the first case, an external azimuthal magnetic field is imposed. In this case, the magnetic field acts on the mean axial velocity and complete laminarization of the flow at N(sub a) = 30 has been achieved. In the second case, an axial magnetic field is imposed which affects only fluctuating velocities, and thus the action is less efficient. This second case is more practical, but comparison between numerical and experimental results is only qualitative.
Resonant interactions of perturbations in MHD flows
Sagalakov, A.M.; Shtern, V.N.
1977-01-17
The nonlinear theory of hydrodynamic stability differentiates three types of interactions: deformation of the initial velocity profile by Reynolds stress pulsations, multiplication of harmonics, and the resonant interaction of harmonics with dissimilar wave numbers and frequencies. This article analyzes an approach considering the first and third of these non-linear mechanisms, producing an acceptable approximation of the averaged characteristics of a developing pulsation movement, particularly the averaged turbulent velocity profile. The approach consists in analysis of triharmonic oscillations, the parameters of which satisfy the resonant relationships. A model of a triharmonic pulsation mode is studied which is applicable to MHD flows. It is shown in particular how a magnetic field transverse to the flow plane suppresses the resonant interaction of three-dimensional perturbations. This agrees with experimental studies on two-dimensional turbulence conducted earlier. 11 references, 3 figures.
Magnetorotational Instability of Dissipative MHD Flows
HERRON, ISOM H
2010-07-10
Executive summary Two important general problems of interest in plasma physics that may be addressed successfully by Magnetohydrodynamics (MHD) are: (1) Find magnetic field configurations capable of confining a plasma in equilibrium. (2) Study the stability properties of each such an equilibrium. It is often found that the length scale of many instabilities and waves that are able to grow or propagate in a system, are comparable with plasma size, such as in magnetically confined thermonuclear plasmas or in astrophysical accretion disks. Thus MHD is able to provide a good description of such large-scale disturbances. The Magnetorotational instability (MRI) is one particular instance of a potential instability. The project involved theoretical work on fundamental aspects of plasma physics. Researchers at the Princeton Plasma Physics Laboratory (PPPL) began to perform a series of liquid metal Couette flow experiments between rotating cylinders. Their purpose was to produce MRI, which they had predicted theoretically 2002, but was only observed in the laboratory since this project began. The personnel on the project consisted of three persons: (1) The PI, who was partially supported on the budget during each of four summers 2005-2008. (2) Two graduate research assistants, who worked consecutively on the project throughout the years 2005-2009. As a result, the first student, Fritzner Soliman, obtained an M.S. degree in 2006; the second student, Pablo Suarez obtained the Ph.D. degree in 2009. The work was in collaboration with scientists in Princeton, periodic trips were made by the PI as part of the project. There were 4 peer-reviewed publications and one book produced.
Local conservative regularizations of compressible MHD and neutral flows
Krishnaswami, Govind S; Thyagaraja, Anantanarayanan
2016-01-01
Ideal systems like MHD and Euler flow may develop singularities in vorticity (w = curl v). Viscosity and resistivity provide dissipative regularizations of the singularities. In this paper we propose a minimal, local, conservative, nonlinear, dispersive regularization of compressible flow and ideal MHD, in analogy with the KdV regularization of the 1D kinematic wave equation. This work extends and significantly generalizes earlier work on incompressible Euler and ideal MHD. It involves a micro-scale cutoff length lambda which is a function of density, unlike in the incompressible case. In MHD, it can be taken to be of order the electron collisionless skin depth c/omega_pe. Our regularization preserves the symmetries of the original systems, and with appropriate boundary conditions, leads to associated conservation laws. Energy and enstrophy are subject to a priori bounds determined by initial data in contrast to the unregularized systems. A Hamiltonian and Poisson bracket formulation is developed and applied ...
MHD Flows in Compact Astrophysical Objects Accretion, Winds and Jets
Beskin, Vasily S
2010-01-01
Accretion flows, winds and jets of compact astrophysical objects and stars are generally described within the framework of hydrodynamical and magnetohydrodynamical (MHD) flows. Analytical analysis of the problem provides profound physical insights, which are essential for interpreting and understanding the results of numerical simulations. Providing such a physical understanding of MHD Flows in Compact Astrophysical Objects is the main goal of this book, which is an updated translation of a successful Russian graduate textbook. The book provides the first detailed introduction into the method of the Grad-Shafranov equation, describing analytically the very broad class of hydrodynamical and MHD flows. It starts with the classical examples of hydrodynamical accretion onto relativistic and nonrelativistic objects. The force-free limit of the Grad-Shafranov equation allows us to analyze in detail the physics of the magnetospheres of radio pulsars and black holes, including the Blandford-Znajek process of energy e...
Motion stability of a suspended particle in a MHD flow
Shvarts, I.A.
1977-07-01
An examination is made of the motion instability of a suspended particle in a plane-parallel laminar flow with a velocity profile U(y,A) where A is certain parameter. An expression was obtained for the critical Reynolds number Re = ..cap alpha../delta/U/delta y/:the coefficient ..cap alpha.. is associated with dimensions and form of the particle. The results of the common theory are used for studying the motion instability of suspended spherical particle in Couette--Hartmann MHD flows. At large Hartmann numbers Re*/Ha was shown to be constant. This agrees well with experimental data on the hydrodynamic stability of the MHD flow itself. A definite correlation also takes place between Re/sub kr/(Ha) of a MHD flow and the Reynolds numbers that determine the stability of suspended particles when the Hartmann numbers are small. Thus, in a number of cases it is possible to examine the hydrodynamic stability of a MHD flow by the motion stability of solid particles introduced into the flow. 8 references, 2 illustrations.
Performance and flow characteristics of MHD seawater thruster
Doss, E.D.
1990-01-01
The main goal of the research is to investigate the effects of strong magnetic fields on the electrical and flow fields inside MHD thrusters. The results of this study is important in the assessment of the feasibility of MHD seawater propulsion for the Navy. To accomplish this goal a three-dimensional fluid flow computer model has been developed and applied to study the concept of MHD seawater propulsion. The effects of strong magnetic fields on the current and electric fields inside the MHD thruster and their interaction with the flow fields, particularly those in the boundary layers, have been investigated. The results of the three-dimensional computations indicate that the velocity profiles are flatter over the sidewalls of the thruster walls in comparison to the velocity profiles over the electrode walls. These nonuniformities in the flow fields give rise to nonuniform distribution of the skin friction along the walls of the thrusters, where higher values are predicted over the sidewalls relative to those over the electrode walls. Also, a parametric study has been performed using the three-dimensional MHD flow model to analyze the performance of continuous electrode seawater thrusters under different operating parameters. The effects of these parameters on the fluid flow characteristics, and on the thruster efficiency have been investigated. Those parameters include the magnetic field (10--20 T), thruster diameter, surface roughness, flow velocity, and the electric load factor. The results show also that the thruster performance improves with the strength of the magnetic field and thruster diameter, and the efficiency decreases with the flow velocity and surface roughness.
Buoyancy induced MHD transient mass transfer flow with thermal radiation
N. Ahmed
2016-09-01
Full Text Available The problem of a transient MHD free convective mass transfer flow past an infinite vertical porous plate in presence of thermal radiation is studied. The fluid is considered to be a gray, absorbing-emitting radiating but non-scattered medium. Analytical solutions of the equations governing the flow problem are obtained. The effects of mass transfer, suction, radiation and the applied magnetic field on the flow and transport characteristics are discussed through graphs.
Nonlinear Terms of MHD Equations for Homogeneous Magnetized Shear Flow
Dimitrov, Z D; Hristov, T S; Mishonov, T M
2011-01-01
We have derived the full set of MHD equations for incompressible shear flow of a magnetized fluid and considered their solution in the wave-vector space. The linearized equations give the famous amplification of slow magnetosonic waves and describe the magnetorotational instability. The nonlinear terms in our analysis are responsible for the creation of turbulence and self-sustained spectral density of the MHD (Alfven and pseudo-Alfven) waves. Perspectives for numerical simulations of weak turbulence and calculation of the effective viscosity of accretion disks are shortly discussed in k-space.
Model problem of MHD flow in a lithium blanket
Cherepanov, V.Y.
1978-01-01
A model problem is considered for a feasibility study concerning controlled MHD flow in the blanket of a Tokamak nuclear reactor. The fundamental equations for the steady flow of an incompressible viscous fluid in a uniform transverse magnetic field are solved in rectangular coordinates, in the zero-induction approximation and with negligible induced currents. A numerical solution obtained for a set of appropriate boundary constraints establishes the conditions under which no stagnation zones will be formed.
Hot self-similar relativistic MHD flows
Zakamska, Nadia L; Blandford, Roger D
2008-01-01
We consider axisymmetric relativistic jets with a toroidal magnetic field and an ultrarelativistic equation of state, with the goal of studying the lateral structure of jets whose pressure is matched to the pressure of the medium through which they propagate. We find all self-similar steady-state solutions of the relativistic MHD equations for this setup. One of the solutions is the case of a parabolic jet being accelerated by the pressure gradient as it propagates through a medium with pressure declining as p(z)\\propto z^{-2}. As the jet material expands due to internal pressure gradients, it runs into the ambient medium resulting in a pile-up of material along the jet boundary, while the magnetic field acts to produce a magnetic pinch along the axis of the jet. Such jets can be in a lateral pressure equilibrium only if their opening angle \\theta_j at distance z is smaller than about 1/\\gamma, where \\gamma is the characteristic bulk Lorentz-factor at this distance; otherwise, different parts of the jet canno...
Galkowski, A. [Institute of Atomic Energy, Otwock-Swierk (Poland)
1994-12-31
Non-linear ideal MHD equilibria in axisymmetric system with flows are examined, both in 1st and 2nd ellipticity regions. Evidence of the bifurcation of solutions is provided and numerical solutions of several problems in a tokamak geometry are given, exhibiting bifurcation phenomena. Relaxation of plasma in the presence of zero-order flows is studied in a realistic toroidal geometry. The field aligned flow allows equilibria with finite pressure gradient but with homogeneous temperature distribution. Numerical calculations have been performed for the 1st and 2nd ellipticity regimes of the extended Grad-Shafranov-Schlueter equation. Numerical technique, alternative to the well-known Grad`s ADM methods has been proposed to deal with slow adiabatic evolution of toroidal plasma with flows. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. (author). 178 refs, 37 figs, 5 tabs.
MHD-flow in slotted channels with conducting walls
Evtushenko, I.A.; Kirillov, I.R. [D.V. Efremov Scientific Research Institute of Electrophysical Apparatus, St. Petersburg (Russian Federation); Reed, C.B. [Argonne National Lab., Chicago, IL (United States)
1994-07-01
A review of experimental results is presented for magnetohydrodynamic (MHD) flow in rectangular channels with conducting walls and high aspect ratios (longer side parallel to the applied magnetic field), which are called slotted channels. The slotted channel concept was conceived at Efremov Institute as a method for reducing MHD pressure drop in liquid metal cooled blanket design. The experiments conducted by the authors were aimed at studying both fully developed MHD-flow, and the effect of a magnetic field on the hydrodynamics of 3-D flows in slotted channels. Tests were carried out on five models of the slotted geometry. A good agreement between test and theoretical results for the pressure drop in slotted channels was demonstrated. Application of a {open_quotes}one-electrode movable probe{close_quotes} for velocity measurement permitted measurement of the M-shape velocity profiles in the slotted channels. Suppression of 3-D inertial effects in slotted channels of complex geometry was demonstrated based on potential distribution data.
Yankova, Krasimira
2015-01-01
Accretion is one of the most important problems of astrophysics concerning the transfer of matter and the transformation of energy into space. Process represents a falling of the substance on a cosmic object from the surrounding area and is a powerful gravitational mechanism for the production of radiation. Accretion disc effectively converts the mass of the substance by viscous friction and released potential energy transformed into radiation by particle collisions. Accretion onto compact object shows high energy efficiency and temporal variability in a broad class of observational data in all ranges. In the disks of these objects are developed a series instabilities and structures that govern the distribution of the energy. They are expressed in many variety non-stationary phenomena that we observe. That is why we propose generalized model of magnetized accretion disk with advection, which preserves the nonlinearity of the problem. We study interaction of the plasmas flow with the magnetic field, and how this affects the self-organizing disk. The aim of the work is to describe the accretion flow in detail, in his quality of the open astrophysical system, to investigate the evolution and to reveal the mechanisms of the structuring the disk-corona system for to interpret correctly the high energy behavior of such sources.
Zhang, Xiujie; Pan, Chuanjie; Xu, Zengyu
2016-12-01
Numerical and experimental investigation results on the magnetohydrodynamics (MHD) film flows along flat and curved bottom surfaces are summarized in this study. A simplified modeling has been developed to study the liquid metal MHD film state, which has been validated by the existing experimental results. Numerical results on how the inlet velocity (V), the chute width (W) and the inlet film thickness (d0) affect the MHD film flow state are obtained. MHD stability analysis results are also provided in this study. The results show that strong magnetic fields make the stable V decrease several times compared to the case with no magnetic field, especially small radial magnetic fields (Bn) will have a significant impact on the MHD film flow state. Based on the above numerical and MHD stability analysis results flow control methods are proposed for flat and curved MHD film flows. For curved film flow we firstly proposed a new multi-layers MHD film flow system with a solid metal mesh to get the stable MHD film flows along the curved bottom surface. Experiments on flat and curved MHD film flows are also carried out and some firstly observed results are achieved. supported by the National Magnetic Confinement Fusion Science Program of China (Nos. 2014GB125003 and 2013GB114002), National Natural Science Foundation of China (No. 11105044)
MHD simulation studies of z-pinch shear flow stabilization
Paraschiv, I.; Bauer, B. S.; Sotnikov, V. I.; Makhin, V.; Siemon, R. E.
2003-10-01
The development of the m=0 instability in a z-pinch in the presence of sheared plasma flows is investigated with the aid of a two-dimensional magnetohydrodynamic (MHD) simulation code (MHRDR). The linear growth rates are compared to the results obtained by solving the ideal MHD linearized equations [1] and to the results obtained using a 3D hybrid simulation code [2]. The instability development is followed into the nonlinear regime where its growth and saturation are examined. [1] V.I. Sotnikov, I. Paraschiv, V. Makhin, B.S. Bauer, J.-N. Leboeuf, and J.M. Dawson, "Linear analysis of sheared flow stabilization of global magnetohydrodynamic instabilities based on the Hall fluid mode", Phys. Plasmas 9, 913 (2002). [2] V.I. Sotnikov, V. Makhin, B.S. Bauer, P. Hellinger, P. Travnicek, V. Fiala, J.-N. Leboeuf, "Hybrid Simulations of Current-Carrying Instabilities in Z-pinch Plasmas with Sheared Axial Flow", AIP Conference Proceedings, Volume 651, Dense Z-Pinches: 5th International Conference on Dense Z-Pinches, edited by J. Davis et al., page 396, June 2002.
MHD Effect of Liquid Metal Film Flows as Plasma-Facing Components
ZHANG Xiujie; XU Zengyu; PAN Chuanjie
2008-01-01
Stability of liquid metal film flow under gradient magnetic field is investigated. Three dimensional numerical simulations on magnetohydrodynamics (MHD) effect of free surface film flow were carried out, with emphasis on the film thickness variation and its surface stability. Three different MHD phenomena of film flow were observed in the experiment, namely, retardant, rivulet and flat film flow. From our experiment and numerical simulation it can be concluded that flat film flow is a good choice for plasma-facing components (PFCs)
Flow stabilization of the ideal MHD resistive wall mode^1
Smith, S. P.; Jardin, S. C.; Freidberg, J. P.; Guazzotto, L.
2009-05-01
We demonstrate for the first time in a numerical calculation that for a typical circular cylindrical equilibrium, the ideal MHD resistive wall mode (RWM) can be completely stabilized by bulk equilibrium plasma flow, V, for a window of wall locations without introducing additional dissipation into the system. The stabilization is due to a resonance between the RWM and the Doppler shifted ideal MHD sound continuum. Our numerical approach introduces^2 u=φξ+ iV .∇ξ and the perturbed wall current^3 as variables, such that the eigenvalue, φ, only appears linearly in the linearized stability equations, which allows for the use of standard eigenvalue solvers. The wall current is related to the plasma displacement at the boundary by a Green's function. With the introduction of the resistive wall, we find that it is essential that the finite element grid be highly localized around the resonance radius where the parallel displacement, ξ, becomes singular. We present numerical convergence studies demonstrating that this singular behavior can be approached in a limiting sense. We also report on progress toward extending this calculation to an axisymmetric toroidal geometry. ^1Work supported by a DOE FES fellowship through ORISE and ORAU. ^2L.Guazzotto, J.P Freidberg, and R. Betti, Phys.Plasmas 15, 072503 (2008). ^3S.P. Smith and S. C. Jardin, Phys. Plasmas 15, 080701 (2008).
MHD Simulations of the Plasma Flow in the Magnetic Nozzle
Smith, T. E. R.; Keidar, M.; Sankaran, K.; olzin, K. A.
2013-01-01
The magnetohydrodynamic (MHD) flow of plasma through a magnetic nozzle is simulated by solving the governing equations for the plasma flow in the presence of an static magnetic field representing the applied nozzle. This work will numerically investigate the flow and behavior of the plasma as the inlet plasma conditions and magnetic nozzle field strength are varied. The MHD simulations are useful for addressing issues such as plasma detachment and to can be used to gain insight into the physical processes present in plasma flows found in thrusters that use magnetic nozzles. In the model, the MHD equations for a plasma, with separate temperatures calculated for the electrons and ions, are integrated over a finite cell volume with flux through each face computed for each of the conserved variables (mass, momentum, magnetic flux, energy) [1]. Stokes theorem is used to convert the area integrals over the faces of each cell into line integrals around the boundaries of each face. The state of the plasma is described using models of the ionization level, ratio of specific heats, thermal conductivity, and plasma resistivity. Anisotropies in current conduction due to Hall effect are included, and the system is closed using a real-gas equation of state to describe the relationship between the plasma density, temperature, and pressure.A separate magnetostatic solver is used to calculate the applied magnetic field, which is assumed constant for these calculations. The total magnetic field is obtained through superposition of the solution for the applied magnetic field and the self-consistently computed induced magnetic fields that arise as the flowing plasma reacts to the presence of the applied field. A solution for the applied magnetic field is represented in Fig. 1 (from Ref. [2]), exhibiting the classic converging-diverging field pattern. Previous research was able to demonstrate effects such as back-emf at a super-Alfvenic flow, which significantly alters the shape of the
Analysis on MHD Stability of Free Surface Jet flow in a Gradient Magnetic Fields
许增裕; 康伟山; 潘传杰
2004-01-01
The simplified modeling for analysis on MHD stability of free surface jet flow in a gradient magnetic fields is based on the theoretical and experimental results on channel liquid metal MHD flow, especially, the results of MHD flow velocity distribution in cross-section of channels (rectangular duct and circular pipe), and the expected results from the modeling are well agreed with the recent experimental data obtained. It is the first modeling which can efficiently explain the experimental results of liquid-metal free surface jet flow.
Wall functions for numerical modeling of laminar MHD flows
Widlund, O
2003-01-01
general wall function treatment is presented for the numerical modeling of laminar magnetohydrodynamic (MHD) flows. The wall function expressions are derived analytically from the steady-state momentum and electric potential equations, making use only of local variables of the numerical solution. No assumptions are made regarding the orientation of the magnetic field relative to the wall, nor of the magnitude of the Hartmann number, or the wall conductivity. The wall functions are used for defining implicit boundary conditions for velocity and electric potential, and for computing mass flow and electrical currents in near wall-cells. The wall function treatment was validated in a finite volume formulation, and compared with an analytic solution for a fully developed channel flow in a transverse magnetic field. For the case with insulating walls, a uniform 20 x 20 grid, and Hartmann numbers Ha = [10,30,100], the accuracy of pressure drop and wall shear stress predictions was [1.1%,1.6%,0.5%], respectively. Com...
Exact solutions for MHD flow of couple stress fluid with heat transfer
Najeeb Alam Khan
2016-01-01
Full Text Available This paper aims at presenting exact solutions for MHD flow of couple stress fluid with heat transfer. The governing partial differential equations (PDEs for an incompressible MHD flow of couple stress fluid are reduced to ordinary differential equations by employing wave parameter. The methodology is implemented for linearizing the flow equations without extra transformation and restrictive assumptions. Comparison is made with the result obtained previously.
MHD coal-fired flow facility. Annual technical progress report, October 1979-September 1980
Alstatt, M.C.; Attig, R.C.; Brosnan, D.A.
1981-03-01
The University of Tennessee Space Institute (UTSI) reports on significant activity, task status, planned research, testing, development, and conclusions for the Magnetohydrodynamics (MHD) Coal-Fired Flow Faclity (CFFF) and the Energy Conversion Facility (ECF).
MHD biconvective flow of Powell Eyring nanofluid over stretched surface
Naseem, Faiza; Shafiq, Anum; Zhao, Lifeng; Naseem, Anum
2017-06-01
The present work is focused on behavioral characteristics of gyrotactic microorganisms to describe their role in heat and mass transfer in the presence of magnetohydrodynamic (MHD) forces in Powell-Eyring nanofluids. Implications concerning stretching sheet with respect to velocity, temperature, nanoparticle concentration and motile microorganism density were explored to highlight influential parameters. Aim of utilizing microorganisms was primarily to stabilize the nanoparticle suspension due to bioconvection generated by the combined effects of buoyancy forces and magnetic field. Influence of Newtonian heating was also analyzed by taking into account thermophoretic mechanism and Brownian motion effects to insinuate series solutions mediated by homotopy analysis method (HAM). Mathematical model captured the boundary layer regime that explicitly involved contemporary non linear partial differential equations converted into the ordinary differential equations. To depict nanofluid flow characteristics, pertinent parameters namely bioconvection Lewis number Lb, traditional Lewis number Le, bioconvection Péclet number Pe, buoyancy ratio parameter Nr, bioconvection Rayleigh number Rb, thermophoresis parameter Nt, Hartmann number M, Grashof number Gr, and Eckert number Ec were computed and analyzed. Results revealed evidence of hydromagnetic bioconvection for microorganism which was represented by graphs and tables. Our findings further show a significant effect of Newtonian heating over a stretching plate by examining the coefficient values of skin friction, local Nusselt number and the local density number. Comparison was made between Newtonian fluid and Powell-Eyring fluid on velocity field and temperature field. Results are compared of with contemporary studies and our findings are found in excellent agreement with these studies.
Unsteady MHD free convective flow past a vertical porous plate ...
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2000 Mathematics subject classification: 76 W 05. Keywords: Free ... the design of MHD generators and accelerators, underground water energy storage system etc. ... In many works on plasma physics, the Hall effect is disregarded. But if the.
Simulation of three-dimensional nonideal MHD flow at high magnetic Reynolds number
无
2010-01-01
A conservative TVD scheme is adopted to solve the equations governing the three-dimensional flow of a nonideal compressible conducting fluid in a magnetic field.The eight-wave equations for magnetohydrodynamics(MHD) are proved to be a non-strict hyperbolic system,therefore it is difficult to develop its eigenstructure.Powell developed a new set of equations which cannot be numerically simulated by conservative TVD scheme directly due to its non-conservative form.A conservative TVD scheme augmented with a new set of eigenvectors is proposed in the paper.To validate this scheme,1-D MHD shock tube,unsteady MHD Rayleigh problem and steady MHD Hartmann problem for different flow conditions are simulated.The simulated results are in good agreement with the existing analytical results.So this scheme can be used to effectively simulate high-conductivity fluids such as cosmic MHD problem and hypersonic MHD flow over a blunt body,etc.
MHD Advanced Power Train Phase I, Final Report, Volume 7
A. R. Jones
1985-08-01
This appendix provides additional data in support of the MHD/Steam Power Plant Analyses reported in report Volume 5. The data is in the form of 3PA/SUMARY computer code printouts. The order of presentation in all four cases is as follows: (1) Overall Performance; (2) Component/Subsystem Information; (3) Plant Cost Accounts Summary; and (4) Plant Costing Details and Cost of Electricity.
Characterization of the three-dimensional supersonic flow for the MHD generator
LU HaoYu; LEE ChunHian; DONG HaiTao
2009-01-01
A numerical procedure based on a five-wave MHD model associated with non-ideal, low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy condi-tioned scheme for solving the non-homogeneous Navier-Stokes equations, in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode, where the local adverse pressure gradient is large, and the core of the flow field is characterized as a 2-D flow due to the Hartmann ef-fects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases, and even induce an eddy current. Induced eddy cur-rent was also found in the different cross-sections along the axial direction, all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section, which, in turn, induces the corner eddy current at the cor-ner. A numerical parametric study was also performed, and the computed performance parameters for the MHD generator suggest that, in order to enhance the performance of MHD generator, the magnetic interaction parameter should be elevated.
Characterization of the three-dimensional supersonic flow for the MHD generator
LEE; ChunHian
2009-01-01
A numerical procedure based on a five-wave MHD model associated with non-ideal,low magnetic Reynolds number MHD flows was developed in the present study for analyzing the flow fields in the MHD generator of a MHD bypass scramjet. The numerical procedure is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations,in conjunction with an SOR method for solving the elliptic equation governing the electrical potential. It was found that a separation would take place near the downstream edge of the second electrode,where the local adverse pressure gradient is large,and the core of the flow field is characterized as a 2-D flow due to the Hartmann effects along the direction of the magnetic field. The electric current lines would be increasingly distorted as the magnetic interactive parameter increases,and even induce an eddy current. Induced eddy current was also found in the different cross-sections along the axial direction,all of these would definitely deteriorate the performance of the MHD generator. The cross-sectional M-shape velocity profile found along the axial direction between the insulating walls is responsible for the formation of the vortex flow at the corner of the insulator cross-section,which,in turn,induces the corner eddy current at the corner. A numerical parametric study was also performed,and the computed performance parameters for the MHD generator suggest that,in order to enhance the performance of MHD generator,the magnetic interaction parameter should be elevated.
Jones, A.R.
1985-08-01
This System Design Description and Specification provides the basis for the design of the magnetohydrodynamic (MHD) Power Train (PT) for a nominal 200 MWe early commercial tiHD/Steam Power Plant. This document has been developed under Task 2, Conceptual Design, of Contract DE-AC22-83PC60575 and is to be used by the project as the controlling and coordinating documentation during future design efforts. Modification and revision of this specification will occur as the design matures, and tiie-Westinghouse MHD Project Manager will be the focal point for maintaining this document and issuing periodic revisions. This document is intended to delineate the power train and-power train components requirements and assumptions that properly reflect the MHD/Steam Power Plant in the PT design. The parameters discussed in this document have been established through system calculations as well as through constraints set by technology and by limitations on materials, cost, physical processes associated with MHD, and the expected operating data for the plant. The specifications listed in this document have precedence over all referenced documents. Where this specification appears to conflict with the requirements of a reference document, such conflicts should be brought to the attention of the Westinghouse MHD Project Manager for resolution.
Simulation of three-dimensional nonideal MHD flow at low magnetic Reynolds number
LU HaoYu; LEE ChunHian
2009-01-01
A numerical procedure based on a five-wave model associated with non-ideal,low magnetic Reynolds number magnetohydrodynamic(MHD)flows was developed.It is composed of an entropy conditioned scheme for solving the non-homogeneous Navier-Stokes equations,in conjunction with an SOR method for solving the elliptic equation governing the electrical potential of flow field.To validate the developed procedure,two different test cases were used which included MHD Rayleigh problem and MHD Hartmann problem.The simulations were performed under the assumption of low magnetic Reynolds number.The simulated results were found to be in good agreement with the closed form analytical solutions deduced in the present study,showing that the present algorithm could simulate engineering MHD flow at low magnetic Reynolds number effectively.In the end,a flow field between a pair of segmented electrodes in a three dimensional MHD channel was simulated using the present algorithm with and without including Hall effects.Without the introduction of Hall effects,no distortion was observed in the current and potential lines.By taking the Hall effects into account,the potential lines distorted and clustered at the upstream and downstream edges of the cathode and anode,respectively.
On computations for thermal radiation in MHD channel flow with heat and mass transfer.
Hayat, T; Awais, M; Alsaedi, A; Safdar, Ambreen
2014-01-01
This study examines the simultaneous effects of heat and mass transfer on the three-dimensional boundary layer flow of viscous fluid between two infinite parallel plates. Magnetohydrodynamic (MHD) and thermal radiation effects are present. The governing problems are first modeled and then solved by homotopy analysis method (HAM). Influence of several embedded parameters on the velocity, concentration and temperature fields are described.
MHD flow of a viscous fluid on a nonlinear porous shrinking sheet with homotopy analysis method
S. Nadeem; Anwar Hussain
2009-01-01
The present paper investigates the magnetohydrodynamic (MHD) flow of a viscous fluid towards a nonlinear porous shrinking sheet. The governing equations are simplified by similarity transformations. The reduced problem is then solved by the homotopy analysis method. The pertinent parameters appearing in the problem are discussed graphically and presented in tables. It is found that the shrinking solutions exist in the presence of MHD. It is also observed from the tables that the solutions for f"(0) with different values of parameters are convergent.
MHD and heat transfer benchmark problems for liquid metal flow in rectangular ducts. Final paper
Sidorenkov, S.I. [D.V. Efremov Scientific Research Inst. of Electrophysical Apparatus, St. Petersburg (Russian Federation); Hua, T.Q. [Argonne National Lab., IL (United States); Araseki, Hideo [Central Research Inst. of Electric Power Industry, Tokyo (Japan)
1994-07-01
Liquid metal cooling systems of a self-cooled blanket in a tokamak reactor will likely include channels of rectangular cross section where liquid metal is circulated in the presence of strong magnetic fields. MHD pressure drop, velocity distribution and heat transfer characteristics are important issues in the engineering design considerations. Computer codes for the reliable solution of three-dimensional MHD flow problems are needed for fusion relevant conditions. This paper describes four benchmark problems to validate magnetohydrodynamic (MHD) and heat transfer computer codes. The problems include rectangular duct geometry with uniform and nonuniform magnetic fields, with and without surface heat flux, and various rectangular cross sections. Two of the problems are based on experiments. Participants in this benchmarking activity come from three countries: The Russian Federation, The United States, and Japan. The solution methods to the problems are described. Results from the different computer codes are presented and compared.
Enhanced MHD transport in astrophysical accretion flows: turbulence, winds and jets
Dobbie, Peter B; Bicknell, Geoffrey V; Salmeron, Raquel
2009-01-01
Astrophysical accretion is arguably the most prevalent physical process in the Universe; it occurs during the birth and death of individual stars and plays a pivotal role in the evolution of entire galaxies. Accretion onto a black hole, in particular, is also the most efficient mechanism known in nature, converting up to 40% of accreting rest mass energy into spectacular forms such as high-energy (X-ray and gamma-ray) emission and relativistic jets. Whilst magnetic fields are thought to be ultimately responsible for these phenomena, our understanding of the microphysics of MHD turbulence in accretion flows as well as large-scale MHD outflows remains far from complete. We present a new theoretical model for astrophysical disk accretion which considers enhanced vertical transport of momentum and energy by MHD winds and jets, as well as transport resulting from MHD turbulence. We also describe new global, 3D simulations that we are currently developing to investigate the extent to which non-ideal MHD effects may...
COUETTE FLOW PROBLEM FOR AN UNSTEADY MHD THIRD-GRADE FLUID WITH HALL CURRENTS
Muhammad Azram
2014-12-01
Full Text Available ABSTRACT: In this work, we analyze Coutte flow problem for an unsteady mangneto-hydrodynamic (MHD third-grade fluid in the presence of a pressure gradient and Hall currnts. Existing literature on the topic shows that the effecs of Hall current on Coutte flow of an unsteady MHD third-grade fluid with a prssure gradient has not yet been investigated. The arising non-linear problem is solved by the homotopy analysis method (HAM and the convergence of the obtained complex series solution is carefully analyzed. The effects of pressure number, Hartmann number and Hall parameter on unsteady velocity are discussed via analysis of plots. ABSTRAK: Kajian dijalan untuk menganalisa masalah aliran Coutte bagi bendalir MHD gred ketiga dan arus Hall. Bagi topik ini kesan arus Hall terhadap aliran Couette dalam bendalir MHD gred ketiga tak mantap dengan kecerunan tekanan, belum pernah dikaji selidik. Masalah tak linear berbangkit diselesaikan dengan kaedah analisis homotopi (HAM dan ketumpuan solusi rangkaian kompleks dianalisa dengan teliti. Kesan nilai tekanan, nombor Hartmann dan parameter Hall terhadap halaju tak mantap diperbincangkan melalui plot yang dianalisis.KEYWORDS: Cuette; flow; hall currents; unsteady; third-grade fluid; HAM
Numerical study for MHD peristaltic flow in a rotating frame.
Hayat, T; Zahir, Hina; Tanveer, Anum; Alsaedi, A
2016-12-01
The aim of present investigation is to model and analyze the magnetohydrodynamic (MHD) peristaltic transport of Prandtl fluid in a channel with flexible walls. The whole system consisting of fluid and channel are in a rotating frame of reference with uniform angular velocity. Viscous dissipation in thermal equation is not ignored. The channel boundaries satisfy the convective conditions in terms of temperature. The arising complicated problems are reduced in solvable form using large wavelength and small Reynolds number assumptions. Numerical solution for axial and secondary velocities, temperature and heat transfer coefficient are presented. Main emphasis is given to the outcome of rotation and material parameters of Prandtl fluid on the physical quantities of interest.
MHD Flow Visualization of Magnetopause and Polar Cusps Vortices
Collado-Vega, Y. M.; Kessel, R. L.; Shao, X.; Boller, R. A.
2007-01-01
Detailed analysis of Wind, Geotail, and Cluster data shows how magnetopause boundary and polar cusps vortices associated with high speed streams can be a carrier of energy flux to the Earth's magnetosphere. For our analysis time interval, March 29 . - April 5 2002, the Interplanetary Magnetic Field (IMF) is primarily northward and MHD simulations of vortices along the flanks within nine hours of the time interval suggest that a Kelvin Helmholtz (KH) instability is likely present. Vortices were classified by solar wind input provided by the Wind satellite located 70-80 RE upstream from Earth. We present statistics for a total of 304 vortices found near the ecliptic plane on the magnetopause flanks, 273 with northward IMF and 31 with southward IMF. The vortices generated under northward IMF were more driven into the dawnside than into the duskside, being substantially more ordered on the duskside. Most of the vortices were large in scale, up to 10 RE, and with a rotation axis closely aligned with the Z(sub GSE) direction. They rotated preferentially clockwise on the dawnside, and. counter-clockwise on the duskside. Those generated under southward IMF were less ordered, fewer in number, and also smaller in diameter. Significant vortex activity occurred on the nightside region of the magnetosphere for these southward cases in contrast to the northward IMF cases on which most of the activity was driven onto the magnetopause flanks. Magnetopause crossings seen by the Geotail spacecraft for the time interval were analyzed and compared with the MHD simulation to validate our results. Vortices over the polar cusps are also being analyzed and the simulation results will be compared to the multi-point measurements of the four Cluster satellites.
MHD Flow Towards a Permeable Surface with Prescribed Wall Heat Flux
Anuar Ishak; Roslinda Nazar; Ioan Pop
2009-01-01
The steady magnetohydrodynamic (MHD) mixed convection flow towards a vertical permeable surface with prescribed heat flux is investigated. The governing partial differential equations are transformed into a system of ordinary differential equations, which is then solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analysed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for the assisting flow, besides the solutions usually reported in the literature for the opposing flow.
Endoscope effects on MHD peristaltic flow of a power-law fluid
T. Hayat
2006-01-01
Full Text Available To understand the influence of an inserted endoscope and magnetohydrodynamic (MHD power-law fluid on peristaltic motion, an attempt has been made for flow through tubes. The magnetic field of uniform strength is applied in the transverse direction to the flow. The analysis has been performed under long wavelength at low-Reynolds number assumption. The velocity fields and axial pressure gradient have been evaluated analytically. Numerical results are also presented and discussed.
DNS of MHD turbulent flow via the HELIOS supercomputer system at IFERC-CSC
Satake, Shin-ichi; Kimura, Masato; Yoshimori, Hajime; Kunugi, Tomoaki; Takase, Kazuyuki
2014-06-01
The simulation plays an important role to estimate characteristics of cooling in a blanket for such high heating plasma in ITER-BA. An objective of this study is to perform large -scale direct numerical simulation (DNS) on heat transfer of magneto hydro dynamic (MHD) turbulent flow on coolant materials assumed from Flibe to lithium. The coolant flow conditions in ITER-BA are assumed to be Reynolds number and Hartmann number of a higher order. The maximum target of the DNS assumed by this study based on the result of the benchmark of Helios at IFERC-CSC for Project cycle 1 is 116 TB (2048 nodes). Moreover, we tested visualization by ParaView to visualize directly the large-scale computational result. If this large-scale DNS becomes possible, an essential understanding and modelling of a MHD turbulent flow and a design of nuclear fusion reactor contributes greatly.
DIPAK SARMA
2012-12-01
Full Text Available A steady two dimensional MHD convective flow of an incompressible viscous and electrically conducting fluid past a continuously moving porous vertical plate with Soret and Dufour effects is analyzed. A magnetic field of uniform strength is assumed to be applied transversely to the direction of the main flow. The solutions for thevelocity field, temperature and concentrations are performed for a wide range of the governing flow parameters viz the Soret number, Prandtl number, Schmidt number, Grashof number for heat transfer, Dufour number, Solutal Grashof number and Hartmann number. The effects of these flow parameters on the velocity, temperature, concentration, skin friction coefficient and Sherwood number are discussed graphically.
Realistic Modeling of Fast MHD Wave Trains in Coronal Active Regions
Ofman, Leon; Sun, Xudong
2017-08-01
Motivated by recent SDO/AIA observations we have developed realistic modeling of quasi-periodic, fast-mode propagating MHD wave trains (QFPs) using 3D MHD model initiated with potential magnetic field extrapolated from the solar coronal boundary. Localized quasi-periodic pulsations associated with C-class flares that drive the waves (as deduced from observations) are modeled with transverse periodic displacement of magnetic field at the lower coronal boundary. The modeled propagating speed and the form of the wave expansions matches the observed fast MHD waves speed >1000 km/s and topology. We study the parametric dependence of the amplitude, propagation, and damping of the waves for a range of key model parameters, such as the background temperature, density, and the location of the flaring site within the active region. We investigate the interaction of multiple QFP wave trains excited by adjacent flaring sources. We use the model results to synthesize EUV intensities in multiple AIA channels and obtain the model parameters that best reproduce the properties of observed QFPs, such as the recent DEM analysis. We discuss the implications of our modeling results for the seismological application of QFPs for the diagnostic of the active region field, flare pulsations, end estimate the energy flux carried by the waves.
Physical Model Development and Benchmarking for MHD Flows in Blanket Design
Ramakanth Munipalli; P.-Y.Huang; C.Chandler; C.Rowell; M.-J.Ni; N.Morley; S.Smolentsev; M.Abdou
2008-06-05
An advanced simulation environment to model incompressible MHD flows relevant to blanket conditions in fusion reactors has been developed at HyPerComp in research collaboration with TEXCEL. The goals of this phase-II project are two-fold: The first is the incorporation of crucial physical phenomena such as induced magnetic field modeling, and extending the capabilities beyond fluid flow prediction to model heat transfer with natural convection and mass transfer including tritium transport and permeation. The second is the design of a sequence of benchmark tests to establish code competence for several classes of physical phenomena in isolation as well as in select (termed here as “canonical”,) combinations. No previous attempts to develop such a comprehensive MHD modeling capability exist in the literature, and this study represents essentially uncharted territory. During the course of this Phase-II project, a significant breakthrough was achieved in modeling liquid metal flows at high Hartmann numbers. We developed a unique mathematical technique to accurately compute the fluid flow in complex geometries at extremely high Hartmann numbers (10,000 and greater), thus extending the state of the art of liquid metal MHD modeling relevant to fusion reactors at the present time. These developments have been published in noted international journals. A sequence of theoretical and experimental results was used to verify and validate the results obtained. The code was applied to a complete DCLL module simulation study with promising results.
A Resistive MHD Simulation of the Shear Flow Effects on the Structure of Reconnection Layer
SUN Xiaoxia; WANG Chunhua; LIN Yu; WANG Xiaogang
2007-01-01
By using a one-dimensional resistive magnetohydrodynamic (MHD) model, the Rie-mann problem is solved numerically for the structure of the reconnection layer under a sheared flow along the anti-parallel magnetic field components. The simulation is carried out for general cases with symmetric or asymmetric plasma densities and magnetic fields on the two sides of the initial current sheet, and cases with or without a guide magnetic field, as in various space and fusion plasmas. The generation of MHD discontinuities in the reconnection layer is discussed, including time-dependent intermediate shocks, intermediate shocks, slow shocks, slow expansion waves, and the contact discontinuity. It is shown that the structure of the reconnection layer is significantly affected by the presence of the shear flow. For an initial symmetric current sheet, the symmetry condition is altered due to the shear flow. For cases with an asymmetric initial current sheet, as at the Earth's magnetopause, the strengths of MHD discontinuities change significantly with the shear flow speed. Moreover, the general results for the reconnection layers in the outflow regions on either side of the X line are discussed systematically for the first time.
Buoyancy Effect on MHD Flow Past a Permeable Bed
S. Venkataramana
1986-10-01
Full Text Available In this paper, the effect of buoyancy force on the parallel flows bounded above by a rigid permeable plate which may be moving or stationary and below, by a permeable bed has been investigated. To discuss the solution, the flow region is divided into two zones. In Zone 1, the flow is laminar and is governed by the Navier-Stokes equations from the impermeable upper rigid plate to the permeable bed. In Zone 2, the flow is governed by the Darcy law in the permeable bed below the nominal surface. The expressions for velocity and temparature distributions, Slip velocity, slip temperature, mass flow rate and the rates of heat transfer coefficients are obtained. The effects of magnetic, porous, slip and buoyancy parameters and Biot number on the above physical quantities are investigated. The thickness of the boundary layer in Zone 2 has been evaluated.
Analytical description of stationary ideal MHD flows with constant total pressure
Golovin, Sergey V
2009-01-01
Incompressible stationary flows of ideal plasma are observed. By introduction of curvilinear system of coordinates in which streamlines and magnetic force lines form a family of coordinate surfaces, MHD equations are partially integrated and brought to a certain convenient form. It is demonstrated that the admissible group of Bogoyavlenskij's symmetry transformations performs as a scaling transformation for the curvilinear coordinates. Analytic description of stationary flows with constant total pressure is given. It is shown, that contact magnetic surfaces of such flows are translational surfaces, i.e. are swept out by translating one curve rigidly along another curve. Explicit examples of solutions with constant total pressure possessing a significant functional arbitrariness are given.
MHD non-Newtonian micropolar fluid flow and heat transfer in channel with stretching walls
M. ASHRAF; N. JAMEEL; K. ALI
2013-01-01
A study is presented for magnetohydrodynamics (MHD) flow and heat trans-fer characteristics of a viscous incompressible electrically conducting micropolar fluid in a channel with stretching walls. The micropolar model introduced by Eringen is used to describe the working fluid. The transformed self similar ordinary differential equations together with the associated boundary conditions are solved numerically by an algorithm based on quasi-linearization and multilevel discretization. The effects of some physical parameters on the flow and heat transfer are discussed and presented through tables and graphs. The present investigations may be beneficial in the flow and thermal control of polymeric processing.
MHD Casson nanofluid flow past a wedge with Newtonian heating
Ahmad, Kartini; Hanouf, Zahir; Ishak, Anuar
2017-02-01
The problem of steady Casson nanofluid flow past a wedge is studied in this paper. The presence of magnetic field along with Newtonian heating at the surface is considered. The governing partial differential equations are first transformed into a set of nonlinear ordinary differential equations by similarity transformations, before being solved numerically using the Keller-box method. The effects of the wedge angle Ω from 0° (horizontal plate) to 180° (vertical plate) as well as of as the magnetic parameter M on the non-Newtonian fluid flow and heat transfer characteristics are investigated. It is found that the surface temperature is slightly higher for the flow over a horizontal plate compared to that over a vertical plate. It is also found that the magnetic field decreases the surface temperature but increases the skin friction. The flow of a Newtonian fluid is found to give higher skin friction as compared to that of Casson fluid.
On soft stability loss in rotating turbulent MHD flows
Kapusta, Arkady [Center for MHD Studies, Ben-Gurion University of the Negev PO Box 653, Beer-Sheva 84105 (Israel); Mikhailovich, Boris, E-mail: borismic@bgu.ac.il [Department of Mechanical Engineering, Ben-Gurion University of the Negev PO Box 653, Beer-Sheva 84105 (Israel)
2014-08-01
The problem of the stability of turbulent flows of liquid metal in a cylindrical cavity against small velocity disturbances under the action of a rotating magnetic field (RMF) has been studied. The flow is considered in the induction-free approximation using the ‘external’ friction model. A system of dimensionless equations is examined in cylindrical coordinates. The results of computations performed on the basis of this mathematical model using the exchange of stabilities principle have shown a good consistency between the critical values of computed and experimental Reynolds numbers. (paper)
MHD and heat transfer benchmark problems for liquid metal flow in rectangular ducts
Sidorenkov, S.I. [D.V. Efremov Scientific Research Inst. of Electrophysical Apparatus, St. Petersburg (Russian Federation); Hua, T.Q. [Argonne National Lab., IL (United States); Araseki, H. [Central Research Inst. of Electric Power Industry, Tokoyo (Japan)
1994-12-31
Liquid metal cooling systems of a self-cooled blanket in a tokamak reactor will likely include channels of rectangular cross section where liquid metal is circulated in the presence of strong magnetic fields. MHD pressure drop, velocity distribution and heat transfer characteristics are important issues in the engineering design considerations. Computer codes for the reliable solution of three-dimensional MHD flow problems are needed for fusion relevant conditions. Argonne National Laboratory and The Efremov Institute have jointly defined several benchmark problems for code validation. The problems, described in this paper, are based on two series of rectangular duct experiments conducted at ANL; one of the series is a joint ANL/Efremov experiment. The geometries consist of variation of aspect ratio and wall thickness (thus wall conductance ratio). The transverse magnetic fields are uniform and nonuniform in the axial direction.
Ideal MHD Ballooning modes, shear flow and the stable continuum
Taylor, J B
2012-01-01
There is a well established theory of Ballooning modes in a toroidal plasma. The cornerstone of this is a local eigenvalue lambda on each magnetic surface - which also depends on the ballooning phase angle k. In stationary plasmas lambda(k) is required only near its maximum, but in rotating plasmas its average over k is required. Unfortunately in many case lambda(k) does not exist for some range of k, because the spectrum there contains only a stable continuum. This limits the application of the theory, and raises the important question of whether this "stable interval" gives rise to significant damping. This question is re-examined using a new, simplified, model - which leads to the conclusion that there is no appreciable damping at small shear flow. In particular, therefore, a small shear flow should not affect Ballooning mode stability boundaries.
Hall Effects on MHD Flow Through a Porous Straight Channel
N. Bhaskara Reddy
1982-10-01
Full Text Available The effect of Hall currents on the flow of a viscous incompressible slightly conducting fluid through a porous straight channel under a uniform transverse magnetic field is considered. The pressure gradient is taken as constant quantity and the case of steady flow is obtained by taking the time since the start of the motion to be infinite. Skin friction, temperature distribution and coefficients of heat transfer at both the plates have been evaluated. The effects of Hall parameter, magnetic parameter and Reynolds number on the above physical quantities have been investigated. Velocity distribution when the pressure gradient (i varies linearly with time, and (ii decreases exponentially with time has also been evaluated.
Resonant behaviour of MHD waves on magnetic flux tubes. III - Effect of equilibrium flow
Goossens, Marcel; Hollweg, Joseph V.; Sakurai, Takashi
1992-01-01
The Hollweg et al. (1990) analysis of MHD surface waves in a stationary equilibrium is extended. The conservation laws and jump conditions at Alfven and slow resonance points obtained by Sakurai et al. (1990) are generalized to include an equilibrium flow, and the assumption that the Eulerian perturbation of total pressure is constant is recovered as the special case of the conservation law for an equilibrium with straight magnetic field lines and flow along the magnetic field lines. It is shown that the conclusions formulated by Hollweg et al. are still valid for the straight cylindrical case. The effect of curvature is examined.
MHD Flow of an Oldroyd-B Fluid through a Porous Space Induced by Sawtooth Pulses
Masood Khan; Zeeshan
2011-01-01
@@ We investigate the unsteady magnetohydrodynamic (MHD) flow of an Oldroyd-B fluid through a porous space inducedby sawtooth pulses.The fluid is assumed to be electrically conducting in the presence of a transverse uniform magnetic field.The porous space is taken into account using modified Darcy's law for the Oldroyd-B fluid.Exact solutions of the governing problem are obtained by using the Laplace transform method.The effects of the magnetic parameter, the permeability of the porous space and the elasticity parameter of the fluid are studied on the flow characteristics.
Heat transfer in MHD flow due to a linearly stretching sheet with induced magnetic field
El-Mistikawy, Tarek M A
2016-01-01
The full MHD problem of the flow and heat transfer due to a linearly stretching sheet in the presence of a transverse magnetic field is put in a self-similar form. Traditionally ignored physical processes such as induced magnetic field, viscous dissipation, Joule heating, and work shear are included and their importance is established. Cases of prescribed surface temperature, prescribed heat flux, surface feed (injection or suction), velocity slip, and thermal slip are also considered. The problem is shown to admit self similarity. Sample numerical solutions are obtained for chosen combinations of the flow parameters.
NATURAL CONVECTION IN MHD TRANSIENT FLOW PAST AN ACCELERATED VERTICAL PLATE WITH HEAT SINK
N. AHMED
2014-09-01
Full Text Available The problem of an MHD heat and mass transfer flow past an accelerated infinite vertical plate in a porous medium in presence of chemical reaction, thermal diffusion and first order heat sink is studied. A magnetic field of uniform strength is assumed to be applied normal to the field directed to the fluid region. The resulting system of equations governing the fluid motion is solved by adopting Laplace Transform technique in closed form. The effects of the physical parameters involved in the problem on the flow and the transport characteristics are studied graphs.
Numerical Solution of Boundary Layer MHD Flow with Viscous Dissipation
S. R. Mishra
2014-01-01
Full Text Available The present paper deals with a steady two-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a shrinking sheet in the presence of uniform transverse magnetic field with viscous dissipation. Using suitable similarity transformations the governing partial differential equations are transformed into ordinary differential equations and then solved numerically by fourth-order Runge-Kutta method with shooting technique. Results for velocity and temperature profiles for different values of the governing parameters have been discussed in detail with graphical representation. The numerical evaluation of skin friction and Nusselt number are also given in this paper.
Power, W. H.
1980-05-01
The purpose of this study was to investigate combustor reactant mixing with swirling oxidizer flow. The combustor configuration that was considered was designed to simulate a 4 lbm/sec mas flow pulverized coal combustor being tested in The University of Tennessee Space Institute MHD Facility. A one-fourth dimensionally scaled combustor model was developed for isothermal flow testing. A comparison was made of cold flow tests using 3 swirler designs with a base case oxidizer injector design of perforated plated which demonstrated acceptable performance in the 4 lbm/sec MHD combustor. The three swirlers that were evaluated were designed to allow a wide range of swirl intensity to be investigated. The design criterion of the swirler was the swirl number which has been related to swirler geometry. The results of the study showed that the swirlers that were tested fell short of the mixing characteristics displayed with the perforated plate base case oxidizer injector. Test data obtained with the cold flow model established that the actual swirl numbers of two of the swirlers were much lower than the design swirl numbers. Recirculation zones were defined for all configurations that were tested, and a comparison of velocity profiles was made for the configurations.
Heat Transfer in MHD Squeezing Flow using Brinkman Model
Satish Chandra RAJVANSHI
2014-01-01
Full Text Available This study investigates squeezing flow of viscous incompressible fluid in a highly permeable medium between 2 parallel, permeable, unsteadily rotating plates in the presence of a magnetic field and radiation. The plates at time t* are separated by a distance H(1-at*1/2. Using a similarity transformation, the governing equations have been transformed into a system of non-linear ordinary differential equations. The resulting equations have been solved numerically by a shooting method. Graphs are presented to depict the temperature and heat transfer profiles. The results show a decline in the temperature profiles under the effect of enhanced radiation.doi:10.14456/WJST.2014.68
Benyo, Theresa L.
2011-01-01
Flow matching has been successfully achieved for an MHD energy bypass system on a supersonic turbojet engine. The Numerical Propulsion System Simulation (NPSS) environment helped perform a thermodynamic cycle analysis to properly match the flows from an inlet employing a MHD energy bypass system (consisting of an MHD generator and MHD accelerator) on a supersonic turbojet engine. Working with various operating conditions (such as the applied magnetic field, MHD generator length and flow conductivity), interfacing studies were conducted between the MHD generator, the turbojet engine, and the MHD accelerator. This paper briefly describes the NPSS environment used in this analysis. This paper further describes the analysis of a supersonic turbojet engine with an MHD generator/accelerator energy bypass system. Results from this study have shown that using MHD energy bypass in the flow path of a supersonic turbojet engine increases the useful Mach number operating range from 0 to 3.0 Mach (not using MHD) to a range of 0 to 7.0 Mach with specific net thrust range of 740 N-s/kg (at ambient Mach = 3.25) to 70 N-s/kg (at ambient Mach = 7). These results were achieved with an applied magnetic field of 2.5 Tesla and conductivity levels in a range from 2 mhos/m (ambient Mach = 7) to 5.5 mhos/m (ambient Mach = 3.5) for an MHD generator length of 3 m.
MHD Coal Fired Flow Facility. Quarterly technical progress report, July-September 1980
Altstatt, M. C.; Attig, R. C.; Brosnan, D. A.
1980-11-01
Significant activity, task status, planned research, testing, development, and conclusions for the Magnetohydrodynamics (MHD) Coal-Fired Flow Facility (CFFF) and the Energy Conversion Facility (ECF) are described. On Task 1, the first phase of the downstream quench system was completed. On Task 2, all three combustor sections were completed, hydrotested, ASME code stamped, and delivered to UTSI. The nozzle was also delivered. Fabrication of support stands and cooling water manifolds for the combustor and vitiation heater were completed, heat transfer and thermal stress analysis, along with design development, were conducted on the generator and radiant furnace and secondary combustor installation progressed as planned. Under Task 3 an Elemental Analyzer and Atomic Absorption Spectrophotometer/Graphite Furnace were received and installed, sites were prepared for two air monitoring stations, phytoplankton analysis began, and foliage and soil sampling was conducted using all study plots. Some 288 soil samples were combined to make 72 samples which were analyzed. Also, approval was granted to dispose of MHD flyash and slag at the Franklin County landfill. Task 4 effort consisted of completing all component test plans, and establishing the capability of displaying experimental data in graphical format. Under Task 7, a preliminary testing program for critical monitoring of the local current and voltage non-uniformities in the generator electrodes was outlined, electrode metal wear characteristics were documented, boron nitride/refrasil composite interelectrode sealing was improved, and several refractories for downstream MHD applications were evaluated with promising results.
LI Yiwen; LI Yinghong; LU Haoyu; ZHU Tao; ZHANG Bailing; CHEN Feng; ZHAO Xiaohu
2011-01-01
This paper presents a preliminary experimental investigation on magnetohydrodynamic (MHD) power generation using seeded supersonic argon flow as working fluid.Helium and argon are used as driver and driven gas respectively in a shock tunnel.Equilibrium contact surface operating mode is used to obtain high temperature gas,and the conductivity is obtained by adding seed K2CO3 powder into the driven section.Under the conditions of nozzle inlet total pressure being 0.32 MPa,total temperature 6 504 K,magnetic field density about 0.5 T and nozzle outlet velocity 1 959 m/s,induction voltage and short-circuit current of the segmentation MHD power generation channel are measured,and the experimental results agree with theoretical calculations; the average conductivity is about 20 S/m calculated from characteristics of voltage and current.When load factor is 0.5,the maximum power density of the MHD power generation channel reaches 4.797 1 MW/m3,and the maximum enthalpy extraction rate is 0.34%.Finally,the principle and method of indirect testing for gas state parameters are derived and analyzed.
2D stationary resistive MHD flows: borderline to magnetic reconnection solutions
Nickeler, D H; Nickeler, Dieter H.; Fahr, Hans-Joerg
2005-01-01
We present the basic equations for stationary, incompressible resistive MHD flows in two dimensions. This leads to a system of differential equations for two flux functions, one elliptic partial differential equation (Grad-Shafranov-like) for the magnetic flux function and one for the stream function of the flow. In these equations two potentials appear: one potential is a generalized pressure. The second potential couples the magnetic and the flow shear components of the system. With the restriction to flux or at least line conserving flows one has to solve a modified Ohm's law. For the two dimensional case these are two coupled differential equations, which represent the borderline between the resistive but flux conserving (or line conserving) case, and that of reconnective solutions. We discuss some simplified solutions of these equations.
Pressure Gradient Influence on MHD Flow for Generalized Burgers’ Fluid with Slip Condition
Ghada H. Ibraheem,
2014-07-01
Full Text Available This paper presents a research for magnetohydrodynamic (MHD flow of an incompressible generalized Burgers' fluid including by an accelerating plate and flowing under the action of pressure gradient. Where the no – slip assumption between the wall and the fluid is no longer valid. The fractional calculus approach is introduced to establish the constitutive relationship of the generalized Burgers' fluid. By using the discrete Laplace transform of the sequential fractional derivatives, a closed form solutions for the velocity and shear stress are obtained in terms of Fox H- function for the following two problems: (i flow due to a constant pressure gradient, and (ii flow due to due to a sinusoidal pressure gradient. The solutions for no – slip condition and no magnetic field, can be derived as special cases of our solutions. Furthermore, the effects of various parameters on the velocity distribution characteristics are analyzed and discussed in detail. Comparison between the two cases is also made.
The variational multiscale element free Galerkin method for MHD flows at high Hartmann numbers
Zhang, Lin; Ouyang, Jie; Zhang, Xiaohua
2013-04-01
The aim of the paper is the development of an efficient numerical algorithm for the solution of magnetohydrodynamics (MHD) flow problems with either fully insulating walls or partially insulating and partially conducting walls. Toward this, we first extend the influence domain of the shape function for the element free Galerkin (EFG) method to have arbitrary shape. When the influence factor approaches 1, we find that the EFG shape function almost has the Delta property at the node (i.e. the value of the EFG shape function of the node is nearly equal to 1 at the position of this node) as well as the property of slices in the influence domain of the node (i.e. the EFG shape function in the influence domain of the node is nearly constructed by different functions defined in different slices). Therefore, for MHD flow problems at high Hartmann numbers we follow the idea of the variational multiscale finite element method (VMFEM) to combine the EFG method with the variational multiscale (VM) method, namely the variational multiscale element free Galerkin (VMEFG) method is proposed. Subsequently, in order to validate the proposed method, we compare the obtained approximate solutions with the exact solutions for some problems where such exact solutions are known. Finally, several benchmark problems of MHD flows are simulated and the numerical results indicate that the VMEFG method is stable at moderate and high values of Hartmann number. Another important feature of this method is that the stabilization parameter has appeared naturally via the solution of the fine scale problem. Meanwhile, because this proposed method is a type of meshless method, it can avoid the need for meshing, a very demanding task for complicated geometry problems.
Three-Dimensional MHD Models of Waves and Flows in Coronal Active Region Loops
Ofman, L.; Wang, T.; Davila, J. M.
2011-12-01
Recent observations show that slow magnetosonic waves are present in active region loops, and are often associated with subsonic up-flows of coronal material. In order to study the relation between up-flows and waves we develop a 3D MHD model of an idealized bi-polar active region with flows in coronal loops. The model is initiated with a dipole magnetic field and gravitationally stratified isothermal atmosphere. To model the effects of flares, coronal material is injected in small-scale regions at the base of the model active region. The up-flows have sub-sonic speeds of ˜100 km/s and are steady or periodic, producing higher density loops by filling magnetic flux-tubes with injected material. We find that the up-flows produce fast and slow magnetosonic waves that propagate in the coronal loops. We perform a parametric study of up-flow magnitude and periodicity, and the relation with the resulting waves. As expected, we find that the up-flow speed decreases with loop height due to the diverge of the flux tubes, while the slow magnetosonic speed is independent of height. When the amplitude of the driving pulses is increased above the sound speed, we find that slow shocks are produced in the loops. Using the results of the 3D MHD model we show that observed slow magnetosonic waves in active region loops can be driven by impulsive flare-produced up-flows at the transition region/corona interface of active regions.
Pantellini, Filippo; Griton, Léa
2016-10-01
The spatial structure of a steady state plasma flow is shaped by the standing modes with local phase velocity exactly opposite to the flow velocity. The general procedure of finding the wave vectors of all possible standing MHD modes in any given point of a stationary flow requires numerically solving an algebraic equation. We present the graphical procedure (already mentioned by some authors in the 1960's) along with the exact solution for the Alfvén mode and approximate analytic solutions for both fast and slow modes. The technique can be used to identify MHD modes in space and laboratory plasmas as well as in numerical simulations.
Thin film flow in MHD third grade fluid on a vertical belt with temperature dependent viscosity.
Taza Gul
Full Text Available In this work, we have carried out the influence of temperature dependent viscosity on thin film flow of a magnetohydrodynamic (MHD third grade fluid past a vertical belt. The governing coupled non-linear differential equations with appropriate boundary conditions are solved analytically by using Adomian Decomposition Method (ADM. In order to make comparison, the governing problem has also been solved by using Optimal Homotopy Asymptotic Method (OHAM. The physical characteristics of the problem have been well discussed in graphs for several parameter of interest.
Thin film flow in MHD third grade fluid on a vertical belt with temperature dependent viscosity.
Gul, Taza; Islam, Saed; Shah, Rehan Ali; Khan, Ilyas; Shafie, Sharidan
2014-01-01
In this work, we have carried out the influence of temperature dependent viscosity on thin film flow of a magnetohydrodynamic (MHD) third grade fluid past a vertical belt. The governing coupled non-linear differential equations with appropriate boundary conditions are solved analytically by using Adomian Decomposition Method (ADM). In order to make comparison, the governing problem has also been solved by using Optimal Homotopy Asymptotic Method (OHAM). The physical characteristics of the problem have been well discussed in graphs for several parameter of interest.
Golovin, Sergey V., E-mail: sergey@hydro.nsc.r [Lavrentyev Institute of Hydrodynamics SB RAS, 630090 Novosibirsk (Russian Federation); Department of Mechanics and Mathematics, Novosibirsk State University, 630090 Novosibirsk (Russian Federation)
2011-01-17
Equations of magnetohydrodynamics (MHD) in the natural curvilinear system of coordinates where trajectories and magnetic lines play a role of coordinate curves are reduced to the non-linear vector wave equation coupled with the incompressibility condition in the form of the generalized Cauchy integral. The symmetry group of obtained equation, equivalence transformation, and group classification with respect to the constitutive equation are calculated. New exact solutions with functional arbitrariness describing non-stationary incompressible flows with constant total pressure are given by explicit formulae. The corresponding magnetic surfaces have the shape of deformed nested cylinders, tori, or knotted tubes.
On the MHD flow of fractional generalized Burgers' fluid with modified Darcy's law
T. Hayat; M. Khan; S. Asghar
2007-01-01
This work is concerned with applying the fractional calculus approach to the magnetohydrodynamic(MHD) pipe flow of a fractional generalized Burgers' fluid in a porous space by using modified Darcy's relationship. The fluid is electrically conducting in the presence of a constant applied magnetic field in the transverse direction. Exact solution for the velocity distribution is developed with the help of Fourier transform for fractional calculus. The solutions for a Navier-Stokes, second grade, Maxwell, Oldroyd-B and Burgers' fluids appear as the limiting cases of the present analysis.
Jahan, Shah; Sakidin, Hamzah; Nazar, Roslinda Mohd
2016-11-01
The behavior of magnetohydrodynamics (MHD) flow of viscous fluid near the stagnation point over a stretching cylinder with variable thermal conductivity is analyzed. Thermal conductivity is assumed to be linearly related with temperature. The joule heating effects due to magnetic field is also encountered here. Analytical solutions are developed for both momentum and energy equations by using the homotopy analysis method (HAM). The variations of different parameters on the velocity and temperature distributions along with the skin friction coefficient and local Nusselt number are displayed graphically. Numerical values for the skin friction coefficient are calculated and discussed
An Optimal Homotopy Asymptotic Approach Applied to Nonlinear MHD Jeffery-Hamel Flow
Vasile Marinca
2011-01-01
Full Text Available A simple and effective procedure is employed to propose a new analytic approximate solution for nonlinear MHD Jeffery-Hamel flow. This technique called the Optimal Homotopy Asymptotic Method (OHAM does not depend upon any small/large parameters and provides us with a convenient way to control the convergence of the solution. The examples given in this paper lead to the conclusion that the accuracy of the obtained results is growing along with increasing the number of constants in the auxiliary function, which are determined using a computer technique. The results obtained through the proposed method are in very good agreement with the numerical results.
Large- and small-scale turbulent spectra in MHD and atmospheric flows
O. G. Chkhetiani
2006-01-01
Full Text Available In the present review we discuss certain studies of large- and small-scale turbulent spectra in MHD and atmospheric flows performed by S. S. Moiseev and his co-authors during the last years of his life and continued by his co-authors after he passed away. It is shown that many ideas developed in these works have not lost their novelty and urgency until now, and can form the basis of future studies in this field.
MHD Coal-Fired Flow Facility. Quarterly technical progress report, April-June 1980
Altstatt, M. C.; Attig, R. C.; Baucum, W. E.
1980-07-31
Significant activity, task status, planned research, testing, development, and conclusions for the Magnetohydrodynamics (MHD) Coal-Fired Flow Facility (CFFF) and the Energy Conversion Facility (ECF), formerly the Research and Development Laboratory, are reported. CFFF Bid Package construction is now virtually complete. The remaining construction effort is being conducted by UTSI. On the quench system, another Task 1 effort, the cyclone was erected on schedule. On Tasks 2 through 6, vitiation heater and nozzle fabrication were completed, an investigation of a fish kill (in no way attributable to CFFF operations) in Woods Reservoir was conducted, major preparation for ambient air quality monitoring was made, a broadband data acquisition system for enabling broadband data to be correlated with all general performance data was selected, a Coriolis effect coal flow meter was installed at the CFFF. On Task 7, an analytical model of the coal flow combustor configuration was prepared, MHD generator testing which, in part, involved continued materials evaluation and the heat transfer characteristics of capped and uncapped electrodes was conducted, agglomerator utilization was studied, and development of a laser velocimeter system was nearly completed.
Chemical reaction and heat source effects on MHD oscillatory flow in an irregular channel
P.V. Satya Narayana
2016-12-01
Full Text Available This paper investigates the effect of heat and mass transfer on MHD oscillatory flow in an asymmetric wavy channel with chemical reaction and heat source. The unsteadiness in the flow is due to an oscillatory pressure gradient across the ends of the channel. A magnetic field of uniform strength is applied in the direction perpendicular to the channel. However, the induced magnetic field is neglected due to the assumption of small magnetic Reynolds number. The temperature difference of the channel is also assumed high enough to induce heat transfer due to radiation. The governing equations are solved analytically by regular perturbation method. The analytical results are evaluated numerically and then are presented graphically to discuss the effects of different parameters entering into the problem. It is observed that the heat transport of a system is more increased in oscillatory flow than in ordinary conduction.
Analytical description of stationary ideal MHD flows with constant total pressure
Golovin, Sergey V., E-mail: sergey@hydro.nsc.r [Lavrentyev Institute of Hydrodynamics SB RAS, 630090 Novosibirsk (Russian Federation); Department of Mechanics and Mathematics, Novosibirsk State University, 630090 Novosibirsk (Russian Federation)
2010-02-01
Incompressible stationary flows of ideal plasma are studied. By introduction of curvilinear system of coordinates in which streamlines and magnetic force lines form a family of coordinate surfaces, MHD equations are partially integrated and brought to a certain convenient form. It is demonstrated that the admissible group of Bogoyavlenskij's symmetry transformations (Bogoyavlenskij, 2001 ) performs as a scaling transformation (the scaling factor is an arbitrary function of one variable) for the curvilinear coordinates. Analytic description of stationary flows with constant total pressure is given. It is shown, that contact magnetic surfaces of such flows are translational surfaces, i.e. are swept out by translating one curve rigidly along another curve. Examples of solutions with constant total pressure possessing an arbitrariness in one function of two variables and three functions of one variable are given.
Dual solutions in MHD stagnation-point flow of Prandtl fluid impinging on shrinking sheet
N.S.AKBAR; Z.H.KHAN; R.U.HAQ; S.NADEEM
2014-01-01
The present article investigates the dual nature of the solution of the magneto-hydrodynamic (MHD) stagnation-point flow of a Prandtl fluid model towards a shrinking surface. The self-similar nonlinear ordinary differential equations are solved numerically by the shooting method. It is found that the dual solutions of the flow exist for cer-tain values of the velocity ratio parameter. The special case of the first branch solutions (the classical Newtonian fluid model) is compared with the present numerical results of stretching flow. The results are found to be in good agreement. It is also shown that the boundary layer thickness for the second solution is thicker than that for the first solution.
Ahmed, Rubel; Rana, B. M. Jewel; Ahmmed, S. F.
2017-06-01
Temperature dependent viscosity and thermal conducting heat and mass transfer flow with chemical reaction and periodic magnetic field past an isothermal oscillating cylinder have been considered. The partial dimensionless equations governing the flow have been solved numerically by applying explicit finite difference method with the help Compaq visual 6.6a. The obtained outcome of this inquisition has been discussed for different values of well-known flow parameters with different time steps and oscillation angle. The effect of chemical reaction and periodic MHD parameters on the velocity field, temperature field and concentration field, skin-friction, Nusselt number and Sherwood number have been studied and results are presented by graphically. The novelty of the present problem is to study the streamlines by taking into account periodic magnetic field.
2D-simulation of stationary MHD flows in the ducts of rectangular cross-section
Khalzov, Ivan; Ilgisonis, Victor
2005-10-01
The numerical code for a calculation of 2D stationary MHD flows of incompressible conducting viscous fluids (liquid metals) in straight and circular ducts of rectangular cross-section is developed. The flows are driven by the electrical current perpendicular both to the duct axis and to the external magnetic field. The code generalizes the well-known iterative Gauss-Seidel method for the case of systems of elliptic equations. The algorithm developed allows us to carry out the calculations of stationary flows in a wide range of Hartmann (Ha=110^3) and Reynolds (Re=110^6) numbers. The numerical results are presented for the experimental device, which is under construction in Russia.
Nature and dynamics of overreflection of Alfven waves in MHD shear flows
Gogichaishvili, D; Chanishvili, R; Lominadze, J
2014-01-01
Our goal is to gain new insights into the physics of wave overreflection phenomenon in MHD nonuniform/shear flows changing the existing trend/approach of the phenomenon study. The performed analysis allows to separate from each other different physical processes, grasp their interplay and, by this way, construct the basic physics of the overreflection in incompressible MHD flows with linear shear of mean velocity, ${\\bf U}_0=(Sy,0,0)$, that contain two different types of Alfv${\\rm \\acute{e}}$n waves. These waves are reduced to pseudo- and shear shear-Alfv${\\rm \\acute{e}}$n waves when wavenumber along $Z$-axis equals zero (i.e., when $k_z=0$). Therefore, for simplicity, we labelled these waves as: P-Alfv${\\rm \\acute{e}}$n and S-Alfv${\\rm \\acute{e}}$n waves (P-AWs and S-AWs). We show that: (1) the linear coupling of counter-propagating waves determines the overreflection, (2) counter-propagating P-AWs are coupled with each other, while counter-propagating S-AWs are not coupled with each other, but are asymmetri...
MHD flow of tangent hyperbolic fluid over a stretching cylinder: Using Keller box method
Malik, M.Y.; Salahuddin, T., E-mail: taimoor_salahuddin@yahoo.com; Hussain, Arif; Bilal, S.
2015-12-01
A numerical solution of MHD flow of tangent hyperbolic fluid model over a stretching cylinder is obtained in this paper. The governing boundary layer equation of tangent hyperbolic fluid is converted into an ordinary differential equation using similarity transformations, which is then solved numerically by applying the implicit finite difference Keller box method. The effects of various parameters on velocity profiles are analyzed and discussed in detail. The values of skin friction coefficient are tabulated and plotted in order to understand the flow behavior near the surface of the cylinder. For validity of the model a comparison of the present work with the literature has been made. - Highlights: • Non-Newtonian (tangent hyperbolic) fluid is taken by using boundary layer approximation. • MHD effects are assumed. • To solve the highly non-linear equations by numerical approach (Keller box Method). • Keller box method is one of the best computational methods capable of solving different engineering problems in fluid mechanics. • Keller box method is an implicit method and has truncation error of order h{sup 2}.
MHD Spectroscopic Study of the Stabilizing Effect of Plasma Flow on the Resistive Wall Mode
Reimerdes, H.; Garofalo, A. M.; Navratil, G. A.; Chu, M. S.; Jackson, G. L.; Jensen, T. H.; La Haye, R. J.; Scoville, J. T.; Strait, E. J.; Edgell, D. H.; Jayakumar, R. J.; Okabayashi, M.
2003-10-01
MHD Spectroscopic Study of the Stabilizing Effect of Plasma Flow on the Resistive Wall Mode,* H. Reimerdes, A.M. Garofalo, G.A. Navratil, Columbia U, M.S. Chu, G.L. Jackson, T.H. Jensen, R.J. La Haye, J.T. Scoville, E.J. Strait, GA, D.H. Edgell, FAR-TECH, Inc., R.J. Jayakumar, LLNL, M. Okabayashi, PPPL - Resistive wall mode (RWM) stabilization by plasma rotation has been under study for the last decade. Dissipation caused by an interaction between the quasi-static magnetic perturbation and a near-sonic plasma flow alters the RWM stability [Bondeson, Phys. Rev. Lett. 72, 2709 (1994)]. To probe the RWM stability in DIII-D, we extend the technique of MHD spectroscopy, which was previously applied at frequencies above 10 kHz [Fasoli, et al., Phys. Rev. Lett. 75, 645 (1995)], to frequencies of a few Hz. Internal coils generate a rotating magnetic field, whose spatial structure largely overlaps with the RWM structure. The plasma response, measured as the perturbed field at the wall, is rigid and peaks when the external field rotates at a fraction of the inverse wall time in the direction of the plasma rotation, which is in good agreement with a single mode model [Garofalo, et al., Phys. Plasmas 9, 4573 (2002)]. This measurement is used to determine the contribution of the proposed dissipation mechanisms to the stabilization of the RWM.
MHD Boundary Layer Slip Flow and Heat Transfer over a Flat Plate
Krishnendu Bhattacharyya; Swati Mukhopadhyay; G.C.Layek
2011-01-01
An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented. A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method. In the boundary slip condition no local similarity occurs. Velocity and temperature distributions within the boundary layer are presented. Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate.%@@ An analysis of magnetohydrodynamic (MHD) boundary layer flow and heat transfer over a flat plate with slip condition at the boundary is presented.A complete self-similar set of equations are obtained from the governing equations using similarity transformations and are solved by a shooting method.In the boundary slip condition no local similarity occurs.Velocity and temperature distributions within the boundary layer are presented.Our analysis reveals that the increase of magnetic and slip parameters reduce the boundary layer thickness and also enhance the heat transfer from the plate.
Benyo, Theresa L.
2010-01-01
Preliminary flow matching has been demonstrated for a MHD energy bypass system on a supersonic turbojet engine. The Numerical Propulsion System Simulation (NPSS) environment was used to perform a thermodynamic cycle analysis to properly match the flows from an inlet to a MHD generator and from the exit of a supersonic turbojet to a MHD accelerator. Working with various operating conditions such as the enthalpy extraction ratio and isentropic efficiency of the MHD generator and MHD accelerator, interfacing studies were conducted between the pre-ionizers, the MHD generator, the turbojet engine, and the MHD accelerator. This paper briefly describes the NPSS environment used in this analysis and describes the NPSS analysis of a supersonic turbojet engine with a MHD generator/accelerator energy bypass system. Results from this study have shown that using MHD energy bypass in the flow path of a supersonic turbojet engine increases the useful Mach number operating range from 0 to 3.0 Mach (not using MHD) to an explored and desired range of 0 to 7.0 Mach.
Radiation Effects on MHD Stagnation-Point Flow in a Nanofluid
Mohammad Eftekhari Yazdi
2013-05-01
Full Text Available In this study, the two-dimensional Magnetohydrodynamic (MHD boundary layer of stagnation-point flow in a nanofluid in the presence of thermal radiation is investigated. Using a similarity transform, the Navier-Stokes equations are reduced to a set of nonlinear ordinary differential equations. The similarity equations are solved numerically for three types of nanoparticles, namely copper (Cu, alumina (Al2O3 and titania (TiO2 in water as the base fluid. The skin-friction coefficient and Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters are presented graphically and discussed. Effects of the nanoparticle volume fraction on the flow and heat transfer characteristics are thoroughly examined.
Magnetohydrodynamic (MHD) flow of Cu-water nanofluid due to a rotating disk with partial slip
Hayat, Tasawar [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia); Rashid, Madiha; Imtiaz, Maria, E-mail: mi-qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Alsaedi, Ahmed [Nonlinear Analysis and Applied Mathematics Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
2015-06-15
This paper investigates MHD steady flow of viscous nanofluid due to a rotating disk. Water is treated as a base fluid and copper as nanoparticle. Nanofluid fills the porous medium. Effects of partial slip, viscous dissipation and thermal radiation are also considered. Similarity transformations reduce the nonlinear partial differential equations to ordinary differential equations. Flow and heat transfer characteristics are computed by HAM solutions. Also computations for skin friction coefficient and Nusselt number are presented and examined for pertinent parameters. It is noted that higher velocity slip parameter decreases the radial and azimuthal velocities while temperature decreases for larger values of the thermal slip parameter. Also the rate of heat transfer enhances when the nanoparticle volume fraction increases.
P. LOGANATHAN,
2010-11-01
Full Text Available The numerical study of effects of thermal conductivity on unsteady MHD free convective flow over an isothermal semi infinite vertical plate is presented. It is assumed that the thermal conductivity of the fluid as a linear function of temperature. A magnetic field is applied transversely to the direction of the flow. The boundary layer equations of continuity, momentum and energy equations are transformed into non-linear coupled equations and then solved using implicit finite-difference method of Crank-Nicholson type. A parametric study is performed to illustrate the influence of thermal conductivity, magnetic parameter and Prandtl number on the velocity and temperature profiles. In addition, the local and average skin friction, Nusselt number at the plate are shown graphically for both air and water. An analysis of the results obtained shows that the flowfield is influenced appreciably by the strength of magnetic field, thermal conductivity at the wall of the plate.
MHD flow of dusty nanofluid over a stretching surface with volume fraction of dust particles
Sandeep Naramgari
2016-06-01
Full Text Available In this study we analyzed the momentum and heat transfer behavior of MHD nanofluid embedded with conducting dust particles past a stretching surface in the presence of volume fraction of dust particles. The governing equations of the flow and heat transfer are transformed into nonlinear ordinary differential equations by using similarity transformation and then solved numerically using Runge–Kutta based shooting technique. The effect of non-dimensional governing parameters on velocity and temperature profiles of the flow are discussed and presented through graphs. Additionally friction factor and the Nusselt number have also been computed. Under some special conditions, numerical results obtained by the present study were compared with the existed studies. The result of the present study proves to be highly satisfactory. The results indicate that an increase in the interaction between the fluid and particle phase enhances the heat transfer rate and reduces the friction factor.
Momentum and Heat Transfer in MHD Axisymmetric Stagnation-Point Flow over a Shrinking Sheet
T. R. Mahapatra
2013-01-01
Full Text Available In this paper we present a mathematical analysis for the magneto hydrodynamic (MHD axi-symmetric stagnation-point flow and heat transfer over a shrinking sheet which shrinks axi-symmetrically in its own plane. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then these equations are solved numerically by shooting technique. Thermal conductivity is assumed to vary linearly with the temperature. Temperature profiles are obtained for two different types of heating process namely (i the sheet with prescribed surface temperature (PST and (ii the sheet with prescribed surface heat flux (PHF. The effects of various physical parameters on the flow and heat transfer characteristics are presented graphically and discussed.
Damping of Linear Nonadiabatic MHD Waves in a Flowing Prominence Medium
Nagendra Kumar
2014-01-01
Full Text Available We study the effect of shear flow on the time damping of linear nonadiabatic magnetoacoustic waves in a solar prominence. We consider a homogeneous, isothermal, and unbounded medium permeated by a uniform magnetic field. The adiabaticity is removed by including the optically thin radiative losses, thermal conduction, and heating term in energy equation. We present a local theory of MHD waves to obtain a dispersion relation. The dispersion relation is solved numerically to study the time damping of these waves. It is found that flow influences the damping time and damping per period of both the slow and fast waves significantly. Damping time and damping per period of slow waves are very much higher than the damping time and damping per period of fast waves.
M.S Uddin
2011-01-01
Full Text Available The paper is concerned to find the distribution of the chemically reactant solute in the MHD flow of an electrically conducting viscous incompressible fluid over a stretching surface. The first order chemical reaction and the variable solute distribution along the surface are taken into consideration. The governing partial differential equations along with appropriate boundary conditions for flow field and reactive solute are transformed into a set of non-linear self-similar ordinary differential equations by using scaling group of transformations. An exact analytic solution is obtained for the velocity field. Using this velocity field, we obtain numerical solution for the reactant concentration field. It reveals from the study that the values of concentration profile enhances with the increase of the magnetic field and decreases with increase of Schmidt number as well as the reaction rate parameter. Most importantly, when the solute distribution along the surface increases then the concentration profile decreases.
Radiation Effect on Mhd Heat and Mass Transfer Flow over a Shrinking Sheet with Mass Suction
patkar ramesh
2014-01-01
Full Text Available A numerical analysis has been carried out to study the effects radiation and heat source/sink on the steady two dimensional magnetohydrodynamic (MHD boundary layer flow of heat and mass transfer past a shrinking sheet with wall mass suction. In the dynamic system, a uniform magnetic field acts normal to the plane of flow. The governing partial differential equations are transformed into self-similar equations are solved by employing finite difference using the quasilinearization technique. From the analysis it is found that the velocity inside the boundary layer increases with increase of wall mass suction and magnetic field and accordingly the thickness of the momentum boundary layer decreases. The temperature decreases with Hartmann number, Prandtl number, and heat sink parameter and the temperature increases with heat source parameter, radiation parameter. The concentration decreases with an increase of Hartmann number, mass suction parameter, Schmidt number, chemical reaction parameter.
MHD mixed convection flow through a diverging channel with heated circular obstacle
Alam, Md. S.; Shaha, J.; Khan, M. A. H.; Nasrin, R.
2016-07-01
A numerical study of steady MHD mixed convection heat transfer and fluid flow through a diverging channel with heated circular obstacle is carried out in this paper. The circular obstacle placed at the centre of the channel is hot with temperature Th. The top and bottom walls are non-adiabatic. The basic nonlinear governing partial differential equations are transformed into dimensionless ordinary differential equations using similarity transformations. These equations have been solved numerically for different values of the governing parameters, namely Reynolds number (Re), Hartmann number (Ha), Richardson number (Ri) and Prandtl number (Pr) using finite element method. The streamlines, isotherms, average Nusselt number and average temperature of the fluid for various relevant dimensionless parameters are displayed graphically. The study revealed that the flow and thermal fields in the diverging channel depend significantly on the heated body. In addition, it is observed that the magnetic field acts to increase the rate of heat transfer within the channel.
Design of a vertical annulus with MHD flow using entropy generation analysis
Mahian Omid
2013-01-01
Full Text Available Optimal design of a heat exchanger is one of the concerns of energy conversion engineers. In the present work, the mixed convection flow between two vertical concentric pipes with constant heat flux at the boundaries and MHD flow effects is considered. To determine the optimal design for such a heat exchanger, at first, the momentum and energy equations are simplified and solved analytically. Next, using entropy generation analysis and cost analysis, the operational costs due to entropy generation are estimated. It is concluded that with an increase in the Hartmann number, the energy costs increase. In addition, for two small deviations from the base radius ratio 2(=P including 9.1=P and 1.2=P , the changes in the energy cost are calculated. It is found that for 9.1=P the energy cost increases by 17.5% while for P = 2.1 the energy cost is reduced by 13.6 %.
Approximate analytical solution of MHD flow of an Oldroyd 8-constant fluid in a porous medium
Faisal Salah
2014-12-01
Full Text Available The steady flow in an incompressible, magnetohydrodynamic (MHD Oldroyd 8-constant fluid in a porous medium with the motion of an infinite plate is investigated. Using modified Darcy’s law of an Oldroyd 8-constant fluid, the equations governing the flow are modelled. The resulting nonlinear boundary value problem is solved using the homotopy analysis method (HAM. The obtained approximate analytical solutions clearly satisfy the governing nonlinear equations and all the imposed initial and boundary conditions. The convergence of the HAM solutions for different orders of approximation is demonstrated. For the Newtonian case, the approximate analytical solution via HAM is shown to be in close agreement with the exact solution. Finally, the variations of velocity field with respect to the magnetic field, porosity and non-Newtonian fluid parameters are graphically shown and discussed.
The Transient MHD Flow Generated by a PeriodicWall Motion in a Porous Space
Mohammed Abdulhameed
2016-01-01
Full Text Available The problem of transient flow of incompressible third grade fluid on the two-dimensional magnetohydrodynamic (MHD flow in a porous space is analyzed. The flow is generated due to the motion of the plate in its plane with a periodic velocity. Under the flow assumptions, the governing nonlinear partial differential equation is transformed into steady-state and transient nonlinear equations. The reduced equation for the transient flow is solved analytically using symmetry approach while the nonlinear steady-state equation is solved using a modified version of He’s homotopy perturbation method. The effect of several operating parameters on the flow hydromagnetic is discussed. The results indicated that for the considered case, t = 1:5 is the moment after which the time-dependent transient motion of the fluid can be approximated with the steady-state motion, described by the steady-state solution. It is clear that, after this value of time t the time-dependent transient solution can be neglected.
Coronal Heating and Acceleration of the High/Low-Speed Solar Wind by Fast/Slow MHD Shock Trains
Suzuki, T K
2004-01-01
We investigate coronal heating and acceleration of the high- and low-speed solar wind in the open field region by dissipation of fast and slow magnetohydrodynamical (MHD) waves through MHD shocks. Linearly polarized \\Alfven (fast MHD) waves and acoustic (slow MHD) waves travelling upwardly along with a magnetic field line eventually form fast switch-on shock trains and hydrodynamical shock trains (N-waves) respectively to heat and accelerate the plasma. We determine one dimensional structure of the corona from the bottom of the transition region (TR) to 1AU under the steady-state condition by solving evolutionary equations for the shock amplitudes simultaneously with the momentum and proton/electron energy equations. Our model reproduces the overall trend of the high-speed wind from the polar holes and the low-speed wind from the mid- to low-latitude streamer except the observed hot corona in the streamer. The heating from the slow waves is effective in the low corona to increase the density there, and plays ...
Chang, S.L.; Lottes, S.A.; Bouillard, J.X.; Petrick, M.
1997-11-01
This report covers application of Argonne National Laboratory`s (ANL`s) computer codes to simulation and analysis of components of the magnetohydrodynamic (MHD) power train system at the Component Development and Integration Facility (CDIF). Major components of the system include a 50-MWt coal-fired, two-stage combustor and an MHD channel. The combustor, designed and built by TRW, includes a deswirl section between the first and the second-stage combustor and a converging nozzle following the second-stage combustor, which connects to the MHD channel. ANL used computer codes to simulate and analyze flow characteristics in various components of the MHD system. The first-stage swirl combustor was deemed a mature technology and, therefore, was not included in the computer simulation. Several versions of the ICOMFLO computer code were used for the deswirl section and second-stage combustor. The MGMHD code, upgraded with a slag current leakage submodel, was used for the MHD channel. Whenever possible data from the test facilities were used to aid in calibrating parameters in the computer code, to validate the computer code, or to set base-case operating conditions for computations with the computer code. Extensive sensitivity and parametric studies were done on cold-flow mixing in the second-stage combustor, reacting flow in the second-stage combustor and converging nozzle, and particle-laden flow in the deswirl zone of the first-stage combustor, the second-stage combustor, and the converging nozzle. These simulations with subsequent analysis were able to show clearly in flow patterns and various computable measures of performance a number of sensitive and problematical areas in the design of the power train. The simulations of upstream components also provided inlet parameter profiles for simulation of the MHD power generating channel. 86 figs., 18 tabs.
The Influence of Uniform Suction/Injection on Heat Transfer of MHD Hiemenz Flow in Porous Media
Ghsemi, E; Soleimani, S; Barari, Amin
2012-01-01
The steady two-dimensional laminar forced magneto-hydrodynamic (MHD) Hiemenz flow against a flat plate with variable wall temperature in a porous medium is analyzed. The transformed nonlinear boundary-layer equations are solved analytically by homotopy analysis method (HAM). Results for the veloc...
Heat Transfer in MHD Mixed Convection Flow of a Ferrofluid along a Vertical Channel.
Gul, Aaiza; Khan, Ilyas; Shafie, Sharidan; Khalid, Asma; Khan, Arshad
2015-01-01
This study investigated heat transfer in magnetohydrodynamic (MHD) mixed convection flow of ferrofluid along a vertical channel. The channel with non-uniform wall temperatures was taken in a vertical direction with transverse magnetic field. Water with nanoparticles of magnetite (Fe3O4) was selected as a conventional base fluid. In addition, non-magnetic (Al2O3) aluminium oxide nanoparticles were also used. Comparison between magnetic and magnetite nanoparticles were also conducted. Fluid motion was originated due to buoyancy force together with applied pressure gradient. The problem was modelled in terms of partial differential equations with physical boundary conditions. Analytical solutions were obtained for velocity and temperature. Graphical results were plotted and discussed. It was found that temperature and velocity of ferrofluids depend strongly on viscosity and thermal conductivity together with magnetic field. The results of the present study when compared concurred with published work.
Tasawar Hayat
Full Text Available This paper investigates the unsteady MHD flow of viscous fluid between two parallel rotating disks. Fluid fills the porous space. Energy equation has been constructed by taking Joule heating, thermal stratification and radiation effects into consideration. We convert system of partial differential equations into system of highly nonlinear ordinary differential equations after employing the suitable transformations. Convergent series solutions are obtained. Behavior of different involved parameters on velocity and temperature profiles is examined graphically. Numerical values of skin friction coefficient and Nusselt number are computed and inspected. It is found that tangential velocity profile is increasing function of rotational parameter. Fluid temperature reduces for increasing values of thermal stratification parameter. At upper disk heat transfer rate enhances for larger values of Eckert and Prandtl numbers.
Influence of aligned MHD on convective boundary layer flow of viscoelastic fluid
Aziz, Laila Amera; Kasim, Abdul Rahman Mohd; Al-Sharifi, H. A. M.; Salleh, Mohd Zuki; Mohammad, Nurul Farahain; Shafie, Sharidan; Ali, Anati
2017-05-01
Effects of aligned Magnetohydrodynamics (MHD) on the mixed convection boundary layer flow of viscoelastic fluid past a circular cylinder with Newtonian heating is investigated. Appropriate transformation is applied to the governing partial differential equations to transform them into dimensionless forms which are then solved using finite difference method known as Keller box. For verification purpose, the preliminary numerical solutions of the model are compared with previous study with a particular condition that the magnetic and viscosity effect are both absent. With strong agreement between the previous and current results, the authors believe that the extended outcome produced from the present model is accurate. Findings from the study will be presented in tabular and graphical form.
Slip effects on MHD flow and heat transfer of ferrofluids over a moving flat plate
Ramli, Norshafira; Ahmad, Syakila; Pop, Ioan
2017-08-01
In this study, the problem of MHD flow and heat transfer of ferrofluids over a moving flat plate with slip effect and uniform heat flux is considered. The governing ordinary differential equations are solved via shooting method. The effect of slip parameter on the dimensionless velocity, temperature, skin friction and Nusselt numbers are numerically studied for the three selected ferroparticles; magnetite (Fe3O4), cobalt ferrite (CoFe2O4) and Mn-Zn ferrite (Mn-ZnFe2O4) with water-based fluid. The results indicate that dual solutions exist for a plate moving towards the origin. It is found that the slip process delays the boundary layer separation. Moreover, the velocity and thermal boundary-layer thicknesses decrease in the first solution while increase with the increase of the value of slip parameters in second solution.
Hayat, Tasawar; Qayyum, Sumaira; Imtiaz, Maria; Alsaedi, Ahmed
2016-01-01
This paper investigates the unsteady MHD flow of viscous fluid between two parallel rotating disks. Fluid fills the porous space. Energy equation has been constructed by taking Joule heating, thermal stratification and radiation effects into consideration. We convert system of partial differential equations into system of highly nonlinear ordinary differential equations after employing the suitable transformations. Convergent series solutions are obtained. Behavior of different involved parameters on velocity and temperature profiles is examined graphically. Numerical values of skin friction coefficient and Nusselt number are computed and inspected. It is found that tangential velocity profile is increasing function of rotational parameter. Fluid temperature reduces for increasing values of thermal stratification parameter. At upper disk heat transfer rate enhances for larger values of Eckert and Prandtl numbers.
Dissipation on Steady MHD Marangoni Convection Flow over a Flat Surface with Suction and Injection
S. Mohammed Ibrahim
2013-01-01
Full Text Available The combined effects of radiation and mass transfer on a steady MHD two-dimensional Marangoni convection flow over a flat surface in presence of Joule heating and viscous dissipation under influence of suction and injection is studied numerically. The general governing partial differential equations are transformed into a set of nonlinear ordinary differential equations by using unique similarity transformation. Numerical solutions of the similarity equations are obtained using the Runge-Kutta method along with shooting technique. The effects of governing parameters on velocity, temperature, and concentration as well as interface velocity, the surface temperature gradient, and the surface concentration gradient were presented in graphical and tabular forms. Comparisons with previously published work are performed and the results are found to be in excellent agreement.
Hall Effects on Mhd Flow Past an Accelerated Plate with Heat Transfer
Sundarnath J.K.
2015-02-01
Full Text Available Hall current and rotation on an MHD flow past an accelerated horizontal plate relative to a rotating fluid, in the presence of heat transfer has been analyzed. The effects of the Hall parameter, Hartmann number, rotation parameter (non-dimensional angular velocity, Grashof’s number and Prandtl number on axial and transverse velocity profiles are presented graphically. It is found that with the increase in the Hartmann number, the axial and transverse velocity components increase in a direction opposite to that of obtained by increasing the Hall parameter and rotation parameter. Also, when Ω=M2m /(1 + m2 , it is observed that the transverse velocity component vanishes and axial velocity attains a maximum value.
Unsteady MHD free convective Couette flow between vertical porous plates with thermal radiation
Basant K. Jha
2015-10-01
Full Text Available This study investigates the unsteady MHD free convective Couette flow of viscous incompressible electrically conducting fluid between two infinite vertical porous plates in the presence of transverse magnetic field and thermal radiation. Solutions for time dependent energy and momentum equations are obtained by the implicit finite difference method. To check the accuracy of the numerical solutions, steady state solutions for energy and momentum equations are obtained by using the perturbation method. The effect of various parameters controlling the physical situation is discussed with the aid of line graphs. Significant results from this study are that both velocity and temperature increase with the increase in thermal radiation parameter and time. A series of numerical experiments show that steady state velocity and temperature occur when the dimensionless time approaches the values of Prandtl number of the fluid. During the course of numerical computation, an excellent agreement was found between unsteady and steady state solutions at large value of time.
Impact of Chemical Reaction on MHD Mixed Convection Heat and Mass Transfer Flow with Thermophoresis
Prabir Kumar KUNDU
2014-02-01
Full Text Available A mathematical model is analyzed in order to study the effects of chemical reaction and thermophoresis on MHD mixed convection boundary layer flow of an incompressible, electrically conducting fluid past a heated vertical permeable flat plate embedded in a uniform porous medium, by taking into account the radiative heat flux and variable suction. The governing partial differential equations are transformed into a set of coupled ordinary differential equations which are solved analytically using the regular perturbation technique. Numerical results for dimensionless velocity, temperature, concentration as well as the skin friction coefficient, Nusselt number and Sherwood number are presented through graphs and a table for pertinent parameters to show interesting aspects of the solution.doi:10.14456/WJST.2014.35
UNSTEADY PLANE MHD BOUNDARY LAYER FLOW OF A FLUID OF VARIABLE ELECTRICAL CONDUCTIVITY
Zoran B Boričić
2010-01-01
Full Text Available This paper is devoted to the analysis of unsteady plane laminar magnetohydrodynamic (MHD boundary layer flow of incompressible and variable electrical conductivity fluid. The present magnetic field is homogenous and perpendicular to the body surface. Outer electric filed is neglected and magnetic Reynolds number is significantly lower then one i.e. considered problem is in induction-less approximation. Free stream velocity is an arbitrary differentiable function. Fluid electrical conductivity is decreasing function of velocity ratio. In order to solve the described problem multiparametric (generalized similarity method is used and so-called universal equations are obtained. Obtained universal equations are solved numerically in appropriate approximation and a part of obtained results is given in the form of figures and corresponding conclusions.
Entropy Generation on MHD Casson Nanofluid Flow over a Porous Stretching/Shrinking Surface
Jia Qing
2016-04-01
Full Text Available In this article, entropy generation on MHD Casson nanofluid over a porous Stretching/Shrinking surface has been investigated. The influences of nonlinear thermal radiation and chemical reaction have also taken into account. The governing Casson nanofluid flow problem consists of momentum equation, energy equation and nanoparticle concentration. Similarity transformation variables have been used to transform the governing coupled partial differential equations into ordinary differential equations. The resulting highly nonlinear coupled ordinary differential equations have been solved numerically with the help of Successive linearization method (SLM and Chebyshev spectral collocation method. The impacts of various pertinent parameters of interest are discussed for velocity profile, temperature profile, concentration profile and entropy profile. The expression for local Nusselt number and local Sherwood number are also analyzed and discussed with the help of tables. Furthermore, comparison with the existing is also made as a special case of our study.
Heat Transfer Analysis of MHD Water Functionalized Carbon Nanotube Flow over a Static/Moving Wedge
Waqar A. Khan
2015-01-01
Full Text Available The MHD flow and heat transfer from water functionalized CNTs over a static/moving wedge are studied numerically. Thermal conductivity and viscosity of both single and multiple wall carbon nanotubes (CNTs within a base fluid (water of similar volume are investigated to determine the impact of these properties on thermofluid performance. The governing partial differential equations are converted into nonlinear, ordinary, and coupled differential equations and are solved using an implicit finite difference method with quasi-linearization techniques. The effects of volume fraction of CNTs and magnetic and wedge parameters are investigated and presented graphically. The numerical results are compared with the published data and are found to be in good agreement. It is shown that the magnetic field reduces boundary layer thickness and increases skin friction and Nusselt numbers. Due to higher density and thermal conductivity, SWCNTs offer higher skin friction and Nusselt numbers.
Heat Transfer in MHD Mixed Convection Flow of a Ferrofluid along a Vertical Channel.
Aaiza Gul
Full Text Available This study investigated heat transfer in magnetohydrodynamic (MHD mixed convection flow of ferrofluid along a vertical channel. The channel with non-uniform wall temperatures was taken in a vertical direction with transverse magnetic field. Water with nanoparticles of magnetite (Fe3O4 was selected as a conventional base fluid. In addition, non-magnetic (Al2O3 aluminium oxide nanoparticles were also used. Comparison between magnetic and magnetite nanoparticles were also conducted. Fluid motion was originated due to buoyancy force together with applied pressure gradient. The problem was modelled in terms of partial differential equations with physical boundary conditions. Analytical solutions were obtained for velocity and temperature. Graphical results were plotted and discussed. It was found that temperature and velocity of ferrofluids depend strongly on viscosity and thermal conductivity together with magnetic field. The results of the present study when compared concurred with published work.
Effects of Joule Heating and Viscous Dissipation on MHD Marangoni Convection Boundary Layer Flow
Rohana Abdul Hamid
2011-09-01
Full Text Available An analysis is performed to study the effects of the Joule heating and viscous dissipation on the magnetohydrodynamics (MHD Marangoni convection boundary layer flow. The governing partial differential equations are reduced to a system of ordinary differential equations via the similarity transformations. Numerical results of the similarity equations are obtained using the Runge-Kutta-Fehlberg method. Effects of the magnetic field parameter, and the combined effects of the Joule heating and the viscous dissipation are investigated and the numerical results are tabulated in tables and figures. It is found that the magnetic field reduces the fluid velocity but increases the fluid temperature. On the other hand, the combined effects of the Joule heating and viscous dissipation have significantly influenced the surface temperature gradient.
MHD Falkner-Skan flow of Maxwell fluid by rational Chebyshev collocation method
S. ABBASBANDY; T. HAYAT; H. R. GHEHSAREH; A. ALSAEDI
2013-01-01
The magnetohydrodynamics (MHD) Falkner-Skan flow of the Maxwell fluid is studied. Suitable transform reduces the partial differential equation into a nonlinear three order boundary value problem over a semi-infinite interval. An eﬃcient approach based on the rational Chebyshev collocation method is performed to find the solution to the proposed boundary value problem. The rational Chebyshev collocation method is equipped with the orthogonal rational Chebyshev function which solves the problem on the semi-infinite domain without truncating it to a finite domain. The obtained results are presented through the illustrative graphs and tables which demonstrate the affectivity, stability, and convergence of the rational Chebyshev collocation method. To check the accuracy of the obtained results, a numerical method is applied for solving the problem. The variations of various embedded parameters into the problem are examined.
MHD stagnation point flow by a permeable stretching cylinder with Soret-Dufour effects
M Ramzan; M Farooq; T Hayat; A Alsaedi; J Cao
2015-01-01
Combined effects of Soret (thermal-diffusion) and Dufour (diffusion-thermo) in MHD stagnation point flow by a permeable stretching cylinder were studied. Analysis was examined in the presence of heat generation/absorption and chemical reaction. The laws of conservation of mass, momentum, energy and concentration are found to lead to the mathematical development of the problem. Suitable transformations were used to convert the nonlinear partial differential equations into the ordinary differential equations. The series solutions of boundary layer equations through momentum, energy and concentration equations were obtained. Convergence of the developed series solutions was discussed via plots and numerical values. The behaviors of different physical parameters on the velocity components, temperature and concentration were obtained. Numerical values of Nusselt number, skin friction and Sherwood number with different parameters were computed and analyzed. It is found that Dufour and Soret numbers result in the enhancement of temperature and concentration distributions, respectively.
MHD two-layered unsteady fluid flow and heat transfer through a horizontal channel between
Raju T. Linga
2014-02-01
Full Text Available An unsteady magnetohydrodynamic (MHD two-layered fluids flow and heat transfer in a horizontal channel between two parallel plates in the presence of an applied magnetic and electric field is investigated, when the whole system is rotated about an axis perpendicular to the flow. The flow is driven by a constant uniform pressure gradient in the channel bounded by two parallel insulating plates, when both fluids are considered as electrically conducting, incompressible with variable properties, viz. different viscosities, thermal and electrical conductivities. The transport properties of the two fluids are taken to be constant and the bounding plates are maintained at constant and equal temperatures. The governing partial differential equations are then reduced to the ordinary linear differential equations using two-term series. Closed form solutions for primary and secondary velocity, also temperature distributions are obtained in both the fluid regions of the channel. Profiles of these solutions are plotted to discuss the effects of the flow and heat transfer characteristics, and their dependence on the governing parameters involved, such as the Hartmann number, rotation parameter, ratios of the viscosities, heights, electrical and thermal conductivities
Radiation Effect on MHD Stagnation-Point Flow of a Nanofluid over an Exponentially Stretching Sheet
Imran ANWAR
2014-07-01
Full Text Available This paper theoretically investigates the radiation effect on magnetohydrodynamics (MHD stagnation-point flow of a nanofluid over an exponentially stretching sheet under the assumptions of a small magnetic Reynolds number. The sheet is stretched with an exponential velocity in the presence of a non-uniform magnetic field B applied in a transverse direction normal to the flow. By using the modified Bernoulli's equation, a highly nonlinear nanofluid problem is modeled for an electrically conducting nanofluid. The momentum, thermal and concentration boundary layer thicknesses are intensified for the incorporated flow parameters such as Brownian motion parameter Nb, thermophoresis parameter Nt, Prandtl number Pr, Lewis number Le, Hartmann number Mexp and velocity ratio parameter ε. Also by an appropriate similarity transformation, the system of nonlinear partial differential equations is reduced to ordinary differential equations. These equations subjected to the boundary conditions are solved numerically using the Keller-box method. Numerical results are plotted and discussed for pertinent flow parameters. A comparison with existing results in the literature is also provided.doi:10.14456/WJST.2014.11
Aoyagi, Mitsuhiro, E-mail: mao@karma.qse.tohoku.ac.jp; Ito, Satoshi; Hashizume, Hidetoshi
2014-10-15
A 3D MHD flow simulation was conducted to clarify the effects of the inlet flow conditions on the results of the validation experiment carried out previously and on the design window of the first wall using a three-surface-multi-layered channel. MHD pressure drop was largely influenced by the inlet condition. The numerical model with turbulent velocity profile showed qualitatively good agreement with the experimental result. The first wall temperature and pressure distributions obtained by the 3D simulation corresponded well to those obtained by the 2D simulation assuming fully developed flow. This suggested that complicated three-dimensional inlet flow condition generated in the L-shape elbow would not affects the existing design window.
MHD Thin Film Flows of a Third Grade Fluid on a Vertical Belt with Slip Boundary Conditions
Taza Gul; Rehan Ali Shah; Saeed Islam; Muhammad Arif
2013-01-01
The problem of heat transfer analysis is considered in electrically conducting thin film flows with slip boundary conditions. The flow is assumed to be obeying the nonlinear rheological constitutive equation of a third grade fluid. We have solved the governing nonlinear equations of present problems using the traditional Adomian decomposition method (ADM). Particular attention is given to the combined effect of heat and MHD on the velocity field. The results include the profile of velocity, v...
Initial Characterization of V-4Cr-4Ti and MHD Coatings Exposed to Flowing Li
Pint, Bruce A [ORNL; Pawel, Steven J [ORNL; Howell, Michael [ORNL; Moser, Jeremy L [ORNL; Garner, George Walter [ORNL; Santella, Michael L [ORNL; Tortorelli, Peter F [ORNL; Wiffen, Frederick W [ORNL; Distefano, James R [ORNL
2009-01-01
Conduct an experiment with flowing Li in a thermal gradient to determine the compatibility of V-4Cr-4Ti and a multi-layer electrically-insulating coating needed to reduce the magneto hydrodynamic (MHD) force in the first wall of a lithium cooled blanket. A mono-metallic V-4Cr-4Ti thermal convection loop was operated in vacuum ({approx}10{sup -5}Pa) at a maximum Li temperature of 700 C for 2,355h and Li flow rate of 2-3 cm/s. Two-layer, physical vapor deposited Y{sub 2}O{sub 3}-vanadium, electrically-insulating coatings on V-4Cr-4Ti substrates as well as uncoated tensile and sheet specimens were located in the flow path in the hot and cold legs. After exposure, specimens at the top of the hot leg showed a maximum mass loss equivalent to {approx}1.3 {micro}m of uniform metal loss. Elsewhere, small mass gains were observed on the majority of specimens that also showed an increase in hardness and room temperature yield stress and a decrease in ductility consistent with interstitial uptake. Specimens that lost mass showed a decrease in yield stress and hardness. Profilometry showed no significant thickness loss from the coatings.
Why, how and when electrically driven flows and MHD turbulence become three-dimensional
Pothérat, A
2013-01-01
The dimensionality of electrically driven flows and magnetohydrodynamic (MHD) turbulence at low Magnetic Reynolds number is analysed by driving a square array of vortices of alternate spin in a cubic vessel filled with liquid metal, placed in a high homogeneous, static magnetic field $\\mathbf B$. A wide range of steady and unsteady flows is generated by varying the intensity $I$ of the DC current injected to drive them, and their dimensionality is influenced by increasing or decreasing the magnetic field intensity. It is shown theoretically, and then experimentally that three-dimensionality is characterised by scaling laws linking the core velocity $U_b$ near the wall where current is injected to the current intensity $I$, of either forms $U_b\\sim I$ or $U_b\\sim I^{2/3}$, depending on whether three-dimensionality originates from viscous or inertial effects. In turbulent flows. The opposite wall is found to be either active or passive depending whether the ratio of its distance to the bottom wall $h$ to the le...
MHD effects on heat transfer and entropy generation of nanofluid flow in an open cavity
Mehrez, Zouhaier, E-mail: zouhaier.mehrez@yahoo.fr [Laboratoire d’Energétique et des Transferts Thermique et Massique (LETTM), Département de Physique, Faculté des Sciences de Tunis, Université d’el Manar, El Manar 2092 (Tunisia); ISSAT Gabes, Rue Omar Ibn Khattab, Université de Gabes, 6072 Zrig, Gabes (Tunisia); El Cafsi, Afif; Belghith, Ali [Laboratoire d’Energétique et des Transferts Thermique et Massique (LETTM), Département de Physique, Faculté des Sciences de Tunis, Université d’el Manar, El Manar 2092 (Tunisia); Le Quéré, Patrick [LIMSI-CNRS Bat. 508, B.P. 133, 91403 Orsay Cedex (France)
2015-01-15
The present numerical work investigates the effect of an external oriented magnetic field on heat transfer and entropy generation of Cu–water nanofluid flow in an open cavity heated from below. The governing equations are solved numerically by the finite-volume method. The study has been carried out for a wide range of solid volume fraction 0≤φ≤0.06, Hartmann number 0≤Ha≤100, Reynolds number 100≤Re≤500 and Richardson number 0.001≤Ri≤1 at three inclination angles of magnetic field γ: 0°, 45° and 90°. The numerical results are given by streamlines, isotherms, average Nusselt number, average entropy generation and Bejan number. The results show that flow behavior, temperature distribution, heat transfer and entropy generation are strongly affected by the presence of a magnetic field. The average Nusselt number and entropy generation, which increase by increasing volume fraction of nanoparticles, depend mainly on the Hartmann number and inclination angle of the magnetic field. The variation rates of heat transfer and entropy generation while adding nanoparticles or applying a magnetic field depend on the Richardson and Reynolds numbers. - Highlights: • MHD effects on Cu–water nanofluid flow into an open cavity are studied. • Entropy generation and heat transfer are strongly influenced by the magnetic field. • The effect of nanoparticles volume fraction depends on Hartmann number. • The influence of the magnetic field varies by varying Reynolds and Richardson numbers.
MHD Boundary Layer Flow of Dilatant Fluid in a Divergent Channel with Suction or Blowing
Krishnendu Bhattacharyya; G.C.Layek
2011-01-01
@@ An analysis is carried out to study a steady magnetohydrodynamic(MHD) boundary layer How of an electrically conducting incompressible power-law non-Newtonian fluid through a divergent channel.The channel walls are porous and subjected to either suction or blowing of equal magnitude of the same kind of fluid on both walls.The fluid is permeated by a magnetic field produced by electric current along the line of intersection of the channel walls.The governing partial differential equation is transformed into a self-similar nonlinear ordinary differential equation using similarity transformations.The possibility of boundary layer flow in a divergent channel is analyzed with the power-law fluid model.The analysis reveals that the boundary layer flow (without separation) is possible for the case of the dilatant fluid model subjected to suitable suction velocity applied through its porous walls,even in the absence of a magnetic field.Further, it is found that the boundary layer flow is possible even in the presence of blowing for a suitable value of the magnetic parameter.It is found that the velocity increases with increasing values of the power-law index for the case of dilatant fluid.The effects of suction/blowing and magnetic field on the velocity are shown graphically and discussed physical尔
Mikel' son, Yu.Ya.; Yakovich, A.T.; Pavlov, S.I.
1978-01-01
Turbulent stresses are considered in an incompressible fluid due to MHD flow induced within an axisymmetric region by electromagnetic forces on the basis of the linearized equation of motion as well as on the basis of the stress tensor in terms of average velocities and turbulent viscosity. The turbulent viscosity is treated according to the Boussinesq hypothesis (constant turbulent viscosity), according to the generalized Karman hypothesis (turbulent viscosity a function of the derivatives of the velocity components with respect to the respective coordinates), or as the product of its coordinate functions. The results of numerical calculations indicate a close agreement between all these formulas for an average MHD flow and experimental data. Calculations including this additional turbulent force, appropriately related to the flow parameters, are applicable to the design of liquid-metal devices. 7 references, 3 figures.
Ahmad, Rida [School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad 44000 (Pakistan); Mustafa, M., E-mail: meraj_mm@hotmail.com [School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad 44000 (Pakistan); Hayat, T. [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589 (Saudi Arabia); Alsaedi, A. [Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80257, Jeddah 21589 (Saudi Arabia)
2016-06-01
Recent advancements in nanotechnology have led to the discovery of new generation coolants known as nanofluids. Nanofluids possess novel and unique characteristics which are fruitful in numerous cooling applications. Current work is undertaken to address the heat transfer in MHD three-dimensional flow of magnetic nanofluid (ferrofluid) over a bidirectional exponentially stretching sheet. The base fluid is considered as water which consists of magnetite–Fe{sub 3}O{sub 4} nanoparticles. Exponentially varying surface temperature distribution is accounted. Problem formulation is presented through the Maxwell models for effective electrical conductivity and effective thermal conductivity of nanofluid. Similarity transformations give rise to a coupled non-linear differential system which is solved numerically. Appreciable growth in the convective heat transfer coefficient is observed when nanoparticle volume fraction is augmented. Temperature exponent parameter serves to enhance the heat transfer from the surface. Moreover the skin friction coefficient is directly proportional to both magnetic field strength and nanoparticle volume fraction. - Highlights: • Nanofluid flow due to exponentially stretching sheet. • Exponentially varying surface temperature distribution is accounted. • Sparrow–Gregg type Hills (SGH) for temperature distribution exist. • Numerical values of local Nusselt number are presented. • Cooling performance of ferrofluid is superior to pure water.
Unsteady MHD Mixed Convection Flow of a Micropolar Fluid Over a Vertical Wedge
Roy, N. C.; Gorla, R. S. R.
2017-05-01
An analysis is presented to investigate the unsteady magnetohydrodynamic (MHD) mixed convection boundary-layer flow of a micropolar fluid over a vertical wedge in the presence of thermal radiation and heat generation or absorption. The free-stream velocity and surface temperature are assumed to be oscillating in magnitude but not in the direction of the oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the finite difference method for the entire frequency range, and the series solution for low frequency range and the asymptotic series expansion method for the high frequency range. Numerical solutions provide a good agreement with the series solutions. The amplitudes of skin friction and couple stress coefficients are found to be strongly dependent on the Richardson number and the vortex viscosity parameter. The Prandtl number, the conduction-radiation parameter, the surface temperature parameter and the pressure gradient parameter significantly affect the amplitudes of skin friction, couple stress and surface heat transfer rates. However, the amplitudes of skin friction coefficient are considerably affected by the magnetic field parameter, whereas the amplitudes of heat transfer rate are appreciably changed with the heat generation or absorption parameter. In addition, results are presented for the transient skin friction, couple stress and heat transfer rate with the variations of the Richardson number, the vortex viscosity parameter, the pressure gradient parameter and the magnetic field parameter.
Unsteady MHD two-phase Couette flow of fluid-particle suspension in an annulus
Basant K. Jha
2011-12-01
Full Text Available The problem of two-phase unsteady MHD flow between two concentric cylinders of infinite length has been analysed when the outer cylinder is impulsively started. The system of partial differential equations describing the flow problem is formulated taking the viscosity of the particle phase into consideration. Unified closed form expressions are obtained for the velocities and the skin frictions for both cases of the applied magnetic field being fixed to either the fluid or the moving outer cylinder. The problem is solved using a combination of the Laplace transform technique, D’Alemberts and the Riemann-sum approximation methods. The solution obtained is validated by comparisons with the closed form solutions obtained for the steady states which has been derived separately. The governing equations are also solved using the implicit finite difference method to verify the present proposed method. The variation of the velocity and the skin friction with the dimensionless parameters occuring in the problem are illustrated graphically and discussed for both phases.
Radiation effects on an unsteady MHD natural convective flow of a nanofluid past a vertical plate
Parasuraman Loganathan
2015-01-01
Full Text Available Numerical analysis is carried out on an unsteady MHD natural convective boundary layer flow of a nanofluid past an isothermal vertical plate in the presence of thermal radiation. The governing partial differential equations are solved numerically by an efficient, iterative, tri-diagonal, semi-implicit finite-difference method. In particular, we investigate the effects of radiation, magnetic field and nanoparticle volume fraction on the flow and heat transfer characteristics. The nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. The numerical results indicate that in the presence of radiation and magnetic field, an increase in the nanoparticle volume fraction will decrease the velocity boundary layer thickness while increasing the thickness of the thermal boundary layer. Meanwhile, an increase in the magnetic field or nanoparticle volume fraction decreases the average skin-friction at the plate. Excellent validation of the present results has been achieved with the published results in the literature in the absence of the nanoparticle volume fraction.
MHD modeling of coronal loops: injection of high-speed chromospheric flows
Petralia, A; Orlando, S; Klimchuk, J A
2014-01-01
Observations reveal a correspondence between chromospheric type II spicules and bright upwardly moving fronts in the corona observed in the EUV band. However, theoretical considerations suggest that these flows are unlikely to be the main source of heating in coronal magnetic loops. We investigate the propagation of high-speed chromospheric flows into coronal magnetic flux tubes, and the possible production of emission in the EUV band. We simulate the propagation of a dense $10^4$ K chromospheric jet upwards along a coronal loop, by means of a 2-D cylindrical MHD model, including gravity, radiative losses, thermal conduction and magnetic induction. The jet propagates in a complete atmosphere including the chromosphere and a tenuous cool ($\\sim 0.8$ MK) corona, linked through a steep transition region. In our reference model, the jet's initial speed is 70 km/s, its initial density is $10^{11}$ cm$^{-3}$, and the ambient uniform magnetic field is 10 G. We explore also other values of jet speed and density in 1-...
M. RAHIMI EOSBOEE,
2010-12-01
Full Text Available In this study magnetohydrodynamics (MHD boundary layer flow of an upper-convected Maxwell fluid has been investigated. Similarity transformation has been used to reduce the governing differential equations into an ordinary non-linear differential equation. homotopy perturbation Method (HPM has applied to solve this developed nonlinear equation. In this article firstly, the basic idea of the HPM for solving nonlinear differential equations is briefly ntroduced and then it is employed to derive solution of nonlinear governing equation of MHD boundary layer flow with highly nonlinear term. The obtained results from HPM have been compared with numerical Boundary Value problem Method (BVP to verify the accuracy of the proposed method. The effects of the Hartman number (M and Deborah number (β for various conditions have been shown through graphs.
Azeem SHAHZAD
2013-02-01
Full Text Available In this article, we study the power law model of steady state, viscous, incompressible MHD flow over a vertically stretching sheet. Furthermore, heat transfer is also addressed by using the convective boundary conditions. The coupled partial differential equations are transformed into ordinary differential equations (ODEs using similarity transformations. The transformed highly non-linear ODEs are solved by using the Homotopy Analysis Method (HAM. The influence of different parameters on the velocity and temperature fields are analyzed and discussed.
Hayat, Tasawar; Rafiq, Maimona; Ahmad, Bashir
2016-01-01
The objective of present paper is to examine the peristaltic flow of magnetohydrodynamic (MHD) Jeffrey fluid saturating porous space in a channel through rotating frame. Unlike the previous attempts, the flow formulation is based upon modified Darcy's law porous medium effect in Jeffrey fluid situation. In addition the impacts due to Soret and Dufour effects in the radiative peristaltic flow are accounted. Rosseland’s approximation has been utilized for the thermal radiative heat flux. Lubrication approach is implemented for the simplification. Resulting problems are solved for the stream function, temperature and concentration. Graphical results are prepared and analyzed for different parameters of interest entering into the problems. PMID:26808387
Tasawar Hayat
Full Text Available The objective of present paper is to examine the peristaltic flow of magnetohydrodynamic (MHD Jeffrey fluid saturating porous space in a channel through rotating frame. Unlike the previous attempts, the flow formulation is based upon modified Darcy's law porous medium effect in Jeffrey fluid situation. In addition the impacts due to Soret and Dufour effects in the radiative peristaltic flow are accounted. Rosseland's approximation has been utilized for the thermal radiative heat flux. Lubrication approach is implemented for the simplification. Resulting problems are solved for the stream function, temperature and concentration. Graphical results are prepared and analyzed for different parameters of interest entering into the problems.
J.C. Misra
2016-03-01
Full Text Available In the present paper, the problem of oscillatory MHD flow of blood in a porous arteriole in presence of chemical reaction and an external magnetic field has been investigated. Heat and mass transfer during arterial blood flow are also studied. A mathematical model is developed and analyzed by using appropriate mathematical techniques. Expressions for the velocity profile, volumetric flow rate, wall shear stress and rates of heat and mass transfer have been obtained. Variations of the said quantities with different parameters are computed by using MATHEMATICA software. The quantitative estimates are presented through graphs and table.
MHD Modelling of Coronal Loops: Injection of High-Speed Chromospheric Flows
Petralia, A.; Reale, F.; Orlando, S.; Klimchuk, J. A.
2014-01-01
Context. Observations reveal a correspondence between chromospheric type II spicules and bright upward-moving fronts in the corona observed in the extreme-ultraviolet (EUV) band. However, theoretical considerations suggest that these flows are probably not the main source of heating in coronal magnetic loops. Aims. We investigate the propagation of high-speed chromospheric flows into coronal magnetic flux tubes and the possible production of emission in the EUV band. Methods. We simulated the propagation of a dense 104 K chromospheric jet upward along a coronal loop by means of a 2D cylindrical MHD model that includes gravity, radiative losses, thermal conduction, and magnetic induction. The jet propagates in a complete atmosphere including the chromosphere and a tenuous cool (approximately 0.8 MK) corona, linked through a steep transition region. In our reference model, the jet initial speed is 70 km per second, its initial density is 10(exp 11) per cubic centimeter, and the ambient uniform magnetic field is 10 G. We also explored other values of jet speed and density in 1D and different magnetic field values in 2D, as well as the jet propagation in a hotter (approximately 1.5 MK) background loop. Results. While the initial speed of the jet does not allow it to reach the loop apex, a hot shock-front develops ahead of it and travels to the other extreme of the loop. The shock front compresses the coronal plasma and heats it to about 10(exp 6) K. As a result, a bright moving front becomes visible in the 171 Angstrom channel of the SDO/AIA mission. This result generally applies to all the other explored cases, except for the propagation in the hotter loop. Conclusions. For a cool, low-density initial coronal loop, the post-shock plasma ahead of upward chromospheric flows might explain at least part of the observed correspondence between type II spicules and EUV emission excess.
Turbulent magnetic Prandtl numbers obtained with MHD Taylor-Couette flow experiments
Gellert, M
2008-01-01
The stability problem of MHD Taylor-Couette flows with toroidal magnetic fields is considered in dependence on the magnetic Prandtl number. Only the most uniform (but not current-free) field with B\\_in = B\\_out has been considered. For high enough Hartmann numbers the toroidal field is always unstable. Rigid rotation, however, stabilizes the magnetic (kink-)instability. The axial current which drives the instability is reduced by the electromotive force induced by the instability itself. Numerical simulations are presented to probe this effect as a possibility to measure the turbulent conductivity in a laboratory. It is shown numerically that in a sodium experiment (without rotation) an eddy diffusivity 4 times the molecular diffusivity appears resulting in a potential difference of ~34 mV/m. If the cylinders are rotating then also the eddy viscosity can be measured. Nonlinear simulations of the instability lead to a turbulent magnetic Prandtl number of 2.1 for a molecular magnetic Prandtl number of 0.01. The...
Shiraishi, Junya; Miyato, Naoaki; Matsunaga, Go
2016-01-01
It is found that new channels of energy exchange between macro- and microscopic dynamics exist in plasmas. They are induced by macroscopic plasma flow. This finding is based on the kinetic-magnetohydrodynamic (MHD) theory, which analyses interaction between macroscopic (MHD-scale) motion and microscopic (particle-scale) dynamics. The kinetic-MHD theory is extended to include effects of macroscopic plasma flow self-consistently. The extension is realised by generalising an energy exchange term due to wave-particle resonance, denoted by δ WK. The first extension is generalisation of the particle’s Lagrangian, and the second one stems from modification to the particle distribution function due to flow. These extensions lead to a generalised expression of δ WK, which affects the MHD stability of plasmas. PMID:27160346
Blanket-relevant liquid metal MHD channel flows: Data base and optimization simulation development
Evtushenko, I.A.; Kirillov, I.R.; Sidorenkov, S.I. [D.V. Efremov Inst. of Electrophysical Apparatus, St Petersburg (Russian Federation)
1995-12-31
The problems of generalization and integration of test, theoretical and design data relevant to liquid metal (LM) blanket are discussed in present work. First results on MHD data base and LM blanket optimization codes are presented.
Lie group analysis of viscoelastic MHD aligned flow and heat transfer
Asif Ali; Ahmer Mehmood; Muhammad R. Mohyuddin; Keren Wang; Yunming Chen
2005-01-01
Exact solutions for an incompressible, viscoelastic, electrically conducting MHD aligned fluid are obtained for velocity components and temperature profiles. Lie Group method is applied to obtain the solution and the symmetries used are of translational type.
Smolentsev, S., E-mail: sergey@fusion.ucla.edu [University of California, Los Angeles (United States); Courtessole, C.; Abdou, M.; Sharafat, S. [University of California, Los Angeles (United States); Sahu, S. [Institute of Plasma Research (India); Sketchley, T. [University of California, Los Angeles (United States)
2016-10-15
Highlights: • Numerical studies were performed as a pre-experimental analysis to the experiment on MHD PbLi flows in a rectangular duct with a flow channel insert (FCI). • Dynamic testing of foam-based SiC foam-based CVD coated FCI has been performed using MaPLE facility at UCLA. • Two physical models were proposed to explain the experimental results and 3D and 2D computations performed using COMSOL, HIMAG and UCLA codes. • The obtained results suggest that more work on FCI development, fabrication and testing has to be done to assure good hermetic properties before the implementation in a fusion device. - Abstract: A flow channel insert (FCI) is the key element of the DCLL blanket concept. The FCI serves as electrical and thermal insulator to reduce the MHD pressure drop and to decouple the temperature-limited ferritic structure from the flowing hot lead-lithium (PbLi) alloy. The main focus of the paper is on numerical computations to simulate MHD flows in the first experiments on PbLi flows in a stainless steel rectangular duct with a foam-based silicon carbide (SiC) FCI. A single uninterrupted long-term (∼6500 h) test has recently been performed on a CVD coated FCI sample in the flowing PbLi in a magnetic field up to 1.5 T at the PbLi temperature of 300 °C using the MaPLE loop at UCLA. An unexpectedly high MHD pressure drop measured in this experiment suggests that a PbLi ingress into the FCI occurred in the course of the experiment, resulting in degradation of electroinsulating FCI properties. The ingress through the protective CVD layer was further confirmed by the post-experimental microscopic analysis of the FCI. The numerical modeling included 2D and 3D computations using HIMAG, COMSOL and a UCLA research code to address important flow features associated with the FCI finite length, fringing magnetic field, rounded FCI corners and also to predict changes in the MHD pressure drop in the unwanted event of a PbLi ingress. Two physical
Spin-Up Instability of a Levitated Molten Drop in MHD-Flow Transition to Turbulence
Abedian, B.; Hyers, R. W.; Curreri, Peter A. (Technical Monitor)
2002-01-01
When an alternating magnetic field interacts with induced eddy currents in a conducting body, there will be a repulsive force between the body and the driving coil system generating the field. This repulsive force is the basis of electromagnetic levitation, which allows containerless processing of different materials. The eddy currents in the conducting body also generate Joule heating. Axial rotation of electromagnetically levitated objects is a common observation in levitation systems and often an undesirable side effect of such experiments on 1-g and -g. There have been recent efforts to use magnetic damping and suppress this tendency of body rotation. The first report of rotation in EML drops was attributed to a slight asymmetry of the shape and location of the levitation coils could change the axis and speed of rotation. Other theories of sample rotation include a frequency difference in the traveling electromagnetic waves and a phase difference in two different applied fields of the same frequency. All of these different mechanisms share the following characteristics: the torque is small, constant for constant field strength, and very weakly dependent on the sample's temperature and phase (solid or liquid). During experiments on the MSL-1 (First Microgravity Science Laboratory) mission of the Space Shuttle (STS-83 and STS-94, April and July 1997), a droplet of palladium-silicon alloy was electromagnetically levitated for viscosity measurements. For the non-deforming droplet, the resultant MHD flow inside the drop is inferred from motion of impurities on the surface. These observations indicate formation of a pair of co-rotating toroidal flow structures inside the spheroidal levitated drop that undergo secondary flow instabilities. As rise in the fluid temperature rises, the viscosity falls and the internal flow accelerates and becomes oscillatory; and beyond a point in the experiments, the surface impurities exhibit non-coherent chaotic motion signifying
MHD coal-fired flow facility baseline water-quality study. Woods Reservoir, May 1979-April 1980
Cooper, J.
1980-12-01
The Department of Energy (DOE) Magnetohydrodynamics (MHD) Coal-Fired Flow Facility (CFFF) is located on Woods Reservoir at The University of Tennessee Space Institute (UTSI). Part of the role of UTSI, as participants in the DOE program, is to document environmental aspects of coal-fired MHD. In early 1979, prior to operation of the CFFF, a water quality program was initiated to establish baseline conditions for the reservoir. The study was designed to provide an accurate assessment of water quality which could be used as a basis for comparison to evaluate the impact, if any, of the plant operation on the aquatic environment. Results of a one year baseline study of water quality on Woods Reservoir are presented in this report. The key findings are that this reservoir is a eutrophic lake. Its predominant ions are calcium and bicarbonate and its pH is circumneutral.
Melting heat transfer in the MHD flow of a third-grade fluid over a variable-thickness surface
Hayat, Tasawar; Kiran, Asmara; Imtiaz, Maria; Alsaedi, Ahmed; Ayub, M.
2017-06-01
The present study addresses the magnetohydrodynamic (MHD) flow of a third-grade fluid over a nonlinear stretched surface with variable thickness. The heat transfer phenomenon is discussed through melting. The system of nonlinear ordinary differential equations is attained by considering proper transformations. Convergent series solutions of velocity and temperature are developed. Fluid flow, temperature, skin friction coefficient and Nusselt number are examined through graphs for different parameters. It is noted that velocity and temperature decrease with decreasing the wall thickness parameter. It is also revealed that the temperature distribution enhances for increasing values of the Prandtl number. Here the velocity field reduces for increasing values of the melting parameter.
Shen, Bingyu; Zheng, Liancun, E-mail: liancunzheng@ustb.edu.cn; Chen, Shengting [School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083 (China)
2015-10-15
This paper presents an investigation for magnetohydrodynamic (MHD) viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail.
MHD flow and heat transfer due to the axisymmetric stretching of a sheet with induced magnetic field
El-Mistikawy, Tarek M A
2016-01-01
The full MHD equations, governing the flow due to the axisymmetric stretching of a sheet in the presence of a transverse magnetic field, can be cast in a self similar form. This allows evaluation of the induced magnetic field and its effect on the flow and heat transfer. The problem involves three parameters- the magnetic Prandtl number, the magnetic interaction number, and the Prandtl number. Numerical solutions are obtained for the velocity field, the magnetic field, and the temperature, at different values of the magnetic Prandtl number and the magnetic interaction number. The contributions of the viscous dissipation, Joule heating, and streamwise diffusion to the heat flux toward the sheet are assessed.
Veera Krishna, M.; Swarnalathamma, B. V.
2016-05-01
In this paper, we discussed the peristaltic MHD flow of an incompressible and electrically conducting Williamson fluid in a symmetric planar channel with heat and mass transfer under the effect of inclined magnetic field. Viscous dissipation and Joule heating are also taken into consideration. Mathematical model is presented by using the long wavelength and low Reynolds number approximations. The differential equations governing the flow are highly nonlinear and thus perturbation solution for small Weissenberg number (We Effects of the heat and mass transfer on the longitudinal velocity, temperature and concentration are studied in detail. Main observations are presented in the concluding section. The streamlines pattern is also given due attention.
Bingyu Shen
2015-10-01
Full Text Available This paper presents an investigation for magnetohydrodynamic (MHD viscoelastic fluid boundary layer flow and radiation heat transfer over an unsteady stretching sheet in presence of heat source. Time dependent fractional derivative is first introduced in formulating the boundary layer equations. Numerical solutions are obtained by using the finite difference scheme and L1-algorithm approximation. Results indicate that the proposed model describes a basic delaying times framework for viscoelastic flow and radiation heat transfer. The effects of involved parameters on velocity and temperature fields are shown graphically and analyzed in detail.
Tirivanhu Chinyoka
2015-01-01
Full Text Available This article examines the combined effects of buoyancy force and asymmetrical convective cooling on unsteady MHD channel flow and heat transfer characteristics of an incompressible, reactive, variable viscosity and electrically conducting third grade fluid. The chemical kinetics in the flow system is exothermic and the asymmetric convective heat transfers at the channel walls follow the Newton’s law of cooling. The coupled nonlinear partial differential equations governing the problem are derived and solved numerically using a semi-implicit finite difference scheme. Graphical results are presented and physical aspects of the problem are discussed with respect to various parameters embedded in the system.
Shoaib Anwar, Muhammad; Rasheed, Amer
2017-07-01
Heat transfer through a Forchheimer medium in an unsteady magnetohydrodynamic (MHD) developed differential-type fluid flow is analyzed numerically in this study. The boundary layer flow is modeled with the help of the fractional calculus approach. The fluid is confined between infinite parallel plates and flows by motion of the plates in their own plane. Both the plates have variable surface temperature. Governing partial differential equations with appropriate initial and boundary conditions are solved by employing a finite-difference scheme to discretize the fractional time derivative and finite-element discretization for spatial variables. Coefficients of skin friction and local Nusselt numbers are computed for the fractional model. The flow behavior is presented for various values of the involved parameters. The influence of different dimensionless numbers on skin friction and Nusselt number is discussed by tabular results. Forchheimer medium flows that involve catalytic converters and gas turbines can be modeled in a similar manner.
Jyotsna Rani Pattnaik
2017-03-01
Full Text Available An analysis of unsteady MHD free convection flow, heat and mass transfer past an exponentially accelerated inclined plate embedded in a saturated porous medium with uniform permeability, variable temperature and concentration has been carried out. The novelty of the present study was to analyze the effect of angle of inclination on the flow phenomena in the presence of heat source/sink and destructive reaction. The Laplace transformation method has been used to solve the governing equations. The effects of the material parameters, magnetic field and the permeability of the porous medium are discussed. From the present analysis it is reported that the presence of magnetic field and porous medium prevents the flow reversal. Angle of inclination and heat source sustains a retarding effect on velocity. The present study has an immediate application in understanding the drag experienced at the heated/cooled and inclined surfaces in a seepage flow.
M.M. Bhatti
2016-06-01
Full Text Available In this article, the simultaneous effects of slip and Magnetohydrodynamics (MHD on peristaltic blood flow of Jeffrey fluid model have been investigated in a non-uniform porous channel. The governing equation of blood flow for Jeffrey fluid model is solved with the help of long wavelength and creeping flow regime. The solution of the resulting differential equation is solved analytically and a closed form solution is presented. The impact of all the physical parameters is plotted for velocity profile and pressure rise. Nowadays, Magnetohydrodynamics is applicable in various magnetic drug targeting for cancer diseases and also very helpful to control the flow. The present analysis is also described for Newtonian fluid (λ1→0 as a special case of our study. It is observed that magnitude of the velocity is opposite near the walls due to slip effects whereas similar behavior has been observed for magnetic field.
Muhammad Zubair Akbar
2016-04-01
Full Text Available The paper presents the numerical study of heat and mass transfer analysis in a viscous unsteady MHD nanofluid flow through a channel with porous walls and medium in the presence of metallic nanoparticles. The two cases for effective thermal conductivity are discussed in the analysis through H-C model. The impacts of the governing parameters on the flow, heat and mass transfer aspects of the issue are talked about. Under the patronage of small values of permeable Reynolds number and relaxation/contraction parameter, we locate that, when wall contraction is together with suction, flow turning is encouraged close to the wall where the boundary layer is shaped. On the other hand, when the wall relaxation is coupled with injection, the flow adjacent to the porous walls decreased. The outcome of the exploration may be beneficial for applications of biotechnology. Numerical solutions for the velocity, heat and mass transfer rate at the boundary are obtained and analyzed.
Process Flow Diagrams for Training and Operations
Venter, Jacobus
This paper focuses on the use of process flow diagrams for training first responders who execute search and seizure warrants at electronic crime scenes. A generic process flow framework is presented, and the design goals and layout characteristics of process flow diagrams are discussed. An evaluation of the process flow diagrams used in training courses indicates that they are beneficial to first responders performing searches and seizures, and they speed up investigations, including those conducted by experienced personnel.
Hemant Poonia
2015-06-01
Full Text Available In this paper the effects of Hall current on MHD free convection flow in a vertical rotating channel filled with porous medium have been studied. A uniform magnetic field is applied in the direction normal to the plates. The entire system rotates about an axis normal to the planes of the plates with uniform angular velocity ' . The temperature of one of the plates varies periodically and the temperature difference of the plates is high enough to induce radiative heat transfer. The effects of various parameters on the velocity and temperature field are shown graphically. Also the results on Skin Frication and Nusselt Number are shown in tables.
Noreen Sher Akbar; S. Nadeem; Rizwan Ul Haq; Z.H. Khan
2013-01-01
The aim of the present paper is to study the numerical solutions of the steady MHD two dimensional stagnation point flow of an incompressible nano fluid towards a stretching cylinder. The effects of radiation and convective boundary condition are also taken into account. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The result-ing nonlinear momentum, energy and nano particle equations are simplified using similarity trans-formations. Numerical solutions have been obtained for the velocity, temperature and nanoparticle fraction profiles. The influence of physical parameters on the velocity, temperature, nanoparticle fraction, rates of heat transfer and nanoparticle fraction are shown graphically.
Dr. G. Prabhakara Rao,
2015-04-01
Full Text Available We consider a two-dimensional MHD natural convection flow of an incompressible viscous and electrically conducting fluid through porous medium past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations of velocity and temperature fields with appropriate boundary conditions are solved by the ordinary differential equations by introducing appropriate coordinate transformations. We solve that ordinary differential equations and find the velocity profiles, temperature profile, the skin friction and nusselt number. The effects of Grashof number (Gr, Hartmann number (M and Prandtl number (Pr, Darcy parameter (D-1 on velocity profiles and temperature profiles are shown graphically.
A.S. Idowu
2015-03-01
Full Text Available Radiation on magnetohydrodynamic (MHD boundary layer flow of a viscous fluid over an exponentially stretching sheet was considered together with it’s effects. The new technique of homotopy analysis method (nHAM was used to obtain the convergent series expressions for velocity and temperature, where the governig system of partial differential equations has been transformed into ordinary differential equations. The interpretation to these expressions is shown physically through graphs. We observed that the effects of Prandtl and Magnetic number acts in opposite to each other on the temperature.
S.P. Anjali Devi
2010-01-01
Full Text Available Viscous and Joule dissipation effects are considered on MHD nonlinear flow and heat transfer past a stretching porous surface embedded in a porous medium under a transverse magnetic field. Analytical solutions of highly nonlinear momentum equation and confluent hypergeometric similarity solution of heat transfer equations in the case when the plate stretches with velocity varying linearly with distance are obtained. The effect of various parameters like suction parameter, Prandtl number, Magnetic parameter, and Eckert number entering into the velocity field, temperature distribution and skin friction co-efficient at the wall are discussed with the aid of graphs.
Sushila
2013-09-01
Full Text Available In this paper, we present an efficient analytical approach based on new homotopy perturbation sumudu transform method (HPSTM to investigate the magnetohydrodynamics (MHD viscous flow due to a stretching sheet. The viscous fluid is electrically conducting in the presence of magnetic field and the induced magnetic field is neglected for small magnetic Reynolds number. Finally, some numerical comparisons among the new HPSTM, the homotopy perturbation method and the exact solution have been made. The numerical solutions obtained by the proposed method show that the approach is easy to implement and computationally very attractive.
S. Mohammed Ibrahim
2014-01-01
Full Text Available The steady two-dimensional radiative MHD boundary layer flow of an incompressible, viscous, electrically conducting fluid caused by a nonisothermal linearly stretching sheet placed at the bottom of fluid saturated porous medium in the presence of viscous dissipation and chemical reaction is studied. The governing system of partial differential equations is converted to ordinary differential equations by using the similarity transformations, which are then solved by shooting method. The dimensionless velocity, temperature, and concentration are computed for different thermophysical parameters, namely, the magnetic parameter, permeability parameter, radiation parameter, wall temperature parameter, Prandtl number, Eckert number, Schmidt number, and chemical reaction.
Krishna, M. Veera; Swarnalathamma, B. V.
2017-07-01
We considered the transient MHD flow of a reactive second grade fluid through porous medium between two infinitely long horizontal parallel plates when one of the plate is set into uniform accelerated motion in the presence of a uniform transverse magnetic field under Arrhenius reaction rate. The governing equations are solved by Laplace transform technique. The effects of the pertinent parameters on the velocity, temperature are discussed in detail. The shear stress and Nusselt number at the plates are also obtained analytically and computationally discussed with reference to governing parameters.
Kazi Humayun Kabir
2015-01-01
Full Text Available An analysis is presented to investigate the influences of viscous and pressure stress work on MHD natural convection flow along a uniformly heated vertical wavy surface. The governing equations are first modified and then transformed into dimensionless non-similar equations by using set of suitable transformations. The transformed boundary layer equations are solved numerically using the implicit finite difference method, known as Keller-box scheme. Numerical results for the velocity profiles, temperature profiles, skin friction coefficient, the rate of heat transfers, streamlines and isotherms are shown graphically. Some results of skin friction, rate of heat transfer are presented in tabular form for selected values of physical parameters.
Mabood, F., E-mail: mabood1971@yahoo.com [School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 (Malaysia); Khan, W.A., E-mail: wkhan_2000@yahoo.com [Department of Mechanical Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1 (Canada); Ismail, A.I.M., E-mail: izani@cs.usm.my [School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800 (Malaysia)
2015-01-15
The MHD laminar boundary layer flow with heat and mass transfer of an electrically conducting water-based nanofluid over a nonlinear stretching sheet with viscous dissipation effect is investigated numerically. This is the extension of the previous study on flow and heat transfer of a nanofluid over nonlinear stretching sheet (Rana and Bhargava, Commun. Nonlinear Sci. Numer. Simul. 17 (2012) 212–226). The governing equations are reduced to nonlinear ordinary differential equations using suitable similarity transformation. The effects of the governing parameters on dimensionless quantities like velocity, temperature, nanoparticle concentration, friction factor, local Nusselt, and Sherwood numbers are explored. It is found that the dimensionless velocity decreases and temperature increases with magnetic parameter, and the thermal boundary layer thickness increases with Brownian motion and thermophoresis parameters. - Highlights: • MHD flow of nanofluid and heat transfer over a nonlinear stretching sheet has not been studied yet. • Numerical solutions are computed with Runge–Kutta Fehlberg fourth–fifth order method. • Previous published results can be obtained from present study. • Reduced Nusselt and Sherwood numbers decrease with magnetic parameter.
Khan, Najeeb Alam
2016-01-01
This study deals with the investigation of MHD flow of Williamson fluid over an infinite rotating disk with the effects of Soret, Dufour, and anisotropic slip. The anisotropic slip and the Soret and Dufour effects are the primary features of this study, which greatly influence the flow, heat and mass transport properties. In simultaneous appearance of heat and mass transfer in a moving fluid, the mass flux generated by temperature gradients is known as the thermal-diffusion or Soret effect and the energy flux created by a composition gradient is called the diffusion-thermo or Dufour effect, however, difference in slip lengths in streamwise and spanwise directions is named as anisotropic slip. The system of nonlinear partial differential equations (PDEs), which governs the flow, heat and mass transfer characteristics, is transformed into ordinary differential equations (ODEs) with the help of von K\\'arm\\'an similarity transformation. A numerical solution of the complicated ODEs is carried out by a MATLAB routi...
Arshad Khan
Full Text Available This study investigates the effects of an arbitrary wall shear stress on unsteady magnetohydrodynamic (MHD flow of a Newtonian fluid with conjugate effects of heat and mass transfer. The fluid is considered in a porous medium over a vertical plate with ramped temperature. The influence of thermal radiation in the energy equations is also considered. The coupled partial differential equations governing the flow are solved by using the Laplace transform technique. Exact solutions for velocity and temperature in case of both ramped and constant wall temperature as well as for concentration are obtained. It is found that velocity solutions are more general and can produce a huge number of exact solutions correlative to various fluid motions. Graphical results are provided for various embedded flow parameters and discussed in details.
Farhad Ali
2013-01-01
on free convection unsteady magnetohydrodynamic (MHD flow of viscous fluid embedded in a porous medium is presented. The flow in the fluid is induced due to uniform motion of the plate. The dimensionless coupled linear partial differential equations are solved by using Laplace transform method. The solutions that have been obtained are expressed in simple forms in terms of elementary function exp(· and complementary error function erfc(·. They satisfy the governing equations; all imposed initial and boundary conditions and can immediately be reduced to their limiting solutions. The influence of various embedded flow parameters such as the Hartmann number, permeability parameter, Grashof number, dimensionless time, Prandtl number, chemical reaction parameter, Schmidt number, and Soret number is analyzed graphically. Numerical solutions for skin friction, Nusselt number, and Sherwood number are also obtained in tabular forms.
A. K. Acharya
2014-01-01
Full Text Available Free convective magnetohydrodynamics (MHD flow of a viscous incompressible and electrically conducting fluid past a hot vertical porous plate embedded in a porous medium in the presence of heat source has been studied in this paper. The temperature of the plate varies both in space and time. The main objective of this paper is to study the effect of porosity of the medium coupled with the variation of plate temperature with regard to space and in time. The effect of pertinent parameters characterizing the flow has been presented through the graphs. It is important to record that the presence of porous media has no significant contribution to the flow characteristics and viscous dissipation compensates for the heating and cooling of the plate due to convective current.
Multiple Solutions of Mixed Convective MHD Casson Fluid Flow in a Channel
Jawad Raza
2016-01-01
Full Text Available A numerical investigation is made to determine the occurrence of the multiple solutions of MHD Casson fluid in a porous channel. Governing partial differential equation of the proposed problem converted into nonlinear ordinary differential equations by using similarity transformation. Numerical technique known as shooting method is used to investigate the existence of the multiple solutions for the variations of different parameters. Effects of physical parameters on velocity profile, temperature, concentration, and skin friction are presented in pictorial and tabulation representation.
Loganathan Parasuraman
2015-01-01
Full Text Available An analysis has been carried out to investigate the influence of combined effects of MHD, suction and radiation on forced convection boundary layer flow of a nanofluid over an exponentially stretching sheet, embedded in a thermally stratified medium. The governing boundary layer equations of the problem are formulated and transformed into ordinary differential equations, using a similarity transformation. The resulting ordinary differential equations are solved numerically, by the shooting method. The effects of the governing parameters on the flow and heat transfer characteristics are studied and discussed in detail. Different types of nanoparticles, namely, Cu, Ag, Al2O3 and TiO2, with water as the base fluid, are studied. It is found that the effects of the radiation parameter, volume fraction and suction are same on the temperature profiles, in contrast to the effects of the thermal stratification. Comparisons with previously published works are performed in some special cases, and found to be in good agreement.
MHD Thin Film Flows of a Third Grade Fluid on a Vertical Belt with Slip Boundary Conditions
Taza Gul
2013-01-01
Full Text Available The problem of heat transfer analysis is considered in electrically conducting thin film flows with slip boundary conditions. The flow is assumed to be obeying the nonlinear rheological constitutive equation of a third grade fluid. We have solved the governing nonlinear equations of present problems using the traditional Adomian decomposition method (ADM. Particular attention is given to the combined effect of heat and MHD on the velocity field. The results include the profile of velocity, volume flux, skin friction, average velocity, and the temperature distribution across the film. The effects of model parameters on velocity, skin friction and temperature variation have been studied. Optimal homotopy asymptotic method (OHAM is also used for comparison. The numerical results and absolute errors are derived in tables.
Sharma, Kalpna; Gupta, Sumit
2017-06-01
This paper investigates steady two dimensional flow of an incompressible magnetohydrodynamic (MHD) boundary layer flow and heat transfer of nanofluid over an impermeable surface in presence of thermal radiation and viscous dissipation. By using similarity transformation, the arising governing equations of momentum, energy and nanoparticle concentration are transformed into coupled nonlinear ordinary differential equations, which are than solved by homotopy analysis method (HAM). The effect of different physical parameters, namely, Prandtl number Pr, Eckert number Ec, Magnetic parameter M, Brownian motion parameter Nb, Thermophoresis parameter Nt, Lewis parameter Le and Radiation parameter Rd on the velocity, temperature and concentration profiles along with the Nusselt number and skin friction coefficient are discussed graphically and in tabular form in details. The present results are also compared with existing limiting solutions.
Ferdows, M.
2012-01-01
Magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed. 2012 M. Ferdows et al.
A.M. Rashad
2017-04-01
Full Text Available The present study explores the impact of anistropic slip on transient three dimensional MHD flow of Cobalt-kerosene ferrofluid over an inclined radiate stretching surface. The governing partial differential equations for this study are solved by the Thomas algorithm with finite-difference type. The impacts of several significant parameters on flow and heat transfer characteristics are exhibited graphically. The conclusion is revealed that the local Nusselt number is significantly promoted due to influence of thermal radiation whereas diminished with elevating the solid volume fraction, magnet parameter and slip factors. Further, the skin friction coefficients visualizes a considerable enhancement with boosting the magnet and radiation parameters, but a prominent reduction is recorded by elevating the solid volume fraction and slip factors.
Alireza AZIMI
2014-07-01
Full Text Available In this paper the velocity fields associated with the two-dimensional unsteady magnetohydrodynamic (MHD flow of a viscous fluid between moving parallel plates have been investigated. The governing Navier-Stokes equations for the flow are reduced to a fourth order nonlinear ordinary differential equation. The Homotopy Perturbation Method (HPM and Reconstruction of Variational Iteration Method (RVIM have been used to achieve analytical solutions. The obtained approximate results have been compared with numerical ones and results from pervious works in some cases. It has been shown that the current study is accurate and validated and can be used for other nonlinear cases.doi:10.14456/WJST.2014.70
M. Ferdows
2012-01-01
Full Text Available Magnetohydrodynamic (MHD boundary layer flow of a nanofluid over an exponentially stretching sheet was studied. The governing boundary layer equations are reduced into ordinary differential equations by a similarity transformation. The transformed equations are solved numerically using the Nactsheim-Swigert shooting technique together with Runge-Kutta six-order iteration schemes. The effects of the governing parameters on the flow field and heat transfer characteristics were obtained and discussed. The numerical solutions for the wall skin friction coefficient, the heat and mass transfer coefficient, and the velocity, temperature, and concentration profiles are computed, analyzed, and discussed graphically. Comparison with previously published work is performed and excellent agreement is observed.
Rubab, Khansa; Mustafa, M
2016-01-01
This letter investigates the MHD three-dimensional flow of upper-convected Maxwell (UCM) fluid over a bi-directional stretching surface by considering the Cattaneo-Christov heat flux model. This model has tendency to capture the characteristics of thermal relaxation time. The governing partial differential equations even after employing the boundary layer approximations are non linear. Accurate analytic solutions for velocity and temperature distributions are computed through well-known homotopy analysis method (HAM). It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted. Penetration depth of temperature is a decreasing function of thermal relaxation time. The analysis for classical Fourier heat conduction law can be obtained as a special case of the present work. To our knowledge, the Cattaneo-Christov heat flux model law for three-dimensional viscoelastic flow problem is just introduced here.
Khansa Rubab
Full Text Available This letter investigates the MHD three-dimensional flow of upper-convected Maxwell (UCM fluid over a bi-directional stretching surface by considering the Cattaneo-Christov heat flux model. This model has tendency to capture the characteristics of thermal relaxation time. The governing partial differential equations even after employing the boundary layer approximations are non linear. Accurate analytic solutions for velocity and temperature distributions are computed through well-known homotopy analysis method (HAM. It is noticed that velocity decreases and temperature rises when stronger magnetic field strength is accounted. Penetration depth of temperature is a decreasing function of thermal relaxation time. The analysis for classical Fourier heat conduction law can be obtained as a special case of the present work. To our knowledge, the Cattaneo-Christov heat flux model law for three-dimensional viscoelastic flow problem is just introduced here.
Kalidas Das
2015-12-01
Full Text Available The present paper investigates numerically the influence of melting heat transfer and thermal radiation on MHD stagnation point flow of an electrically conducting non-Newtonian fluid (Jeffrey fluid over a stretching sheet with partial surface slip. The governing equations are reduced to non-linear ordinary differential equations by using a similarity transformation and then solved numerically by using Runge–Kutta–Fehlberg method. The effects of pertinent parameters on the flow and heat transfer fields are presented through tables and graphs, and are discussed from the physical point of view. Our analysis revealed that the fluid temperature is higher in case of Jeffrey fluid than that in the case of Newtonian fluid. It is also observed that the wall stress increases with increasing the values of slip parameter but the effect is opposite for the rate of heat transfer at the wall.
Muhim Chutia
2015-01-01
Full Text Available A numerical study on steady laminar magnetohydrodynamics (MHD mixed convection flow of an electrically conducting fluid in a vertical square duct under the action of transverse magnetic field has been investigated. The walls are assumed as perfectly electrically insulated. In this study both force and free convection flows are considered. The viscous dissipation and Joule heat are also considered in the energy equation and walls of the duct are kept at constant temperature. The enclosure is heated by uniform volumetric heat density. The governing equations of momentum, induction and energy are first transformed into dimensionless equations by using dimensionless quantities, then these are solved employing finite difference method for velocity, induced magnetic field and temperature distribution. The computed results for velocity, induced magnetic field and temperature distribution are presented graphically for different dimensionless parameters Hartmaan number M, Prandtl number Pr, Grashof number Gr and magnetic Reynolds number Rm.
LEE; ChunHian
2010-01-01
Direct numerical simulation (DNS) of incompressible magnetohydrodynamic (MHD) turbulent channel flow has been performed under the low magnetic Reynolds number assumption.The velocity-electric field and electric-electric field correlations were studied in the present work for different magnetic field orientations.The Kenjeres-Hanjalic (K-H) model was validated with the DNS data in a term by term manner.The numerical results showed that the K-H model makes good predictions for most components of the velocity-electric field correlations.The mechanisms of turbulence suppression were also analyzed for different magnetic field orientations utilizing the DNS data and the K-H model.The results revealed that the dissipative MHD source term is responsible for the turbulence suppression for the case of streamwise and spanwise magnetic orientation,while the Lorentz force which speeds up the near-wall fluid and decreases the production term is responsible for the turbulence suppression for the case of the wall normal magnetic orientation.
Magnetic collimation of meridional-self-similar general relativistic MHD flows
Globus, Noemie; Cayatte, Véronique; Celnikier, Ludwik M
2014-01-01
We present a model for the spine of relativistic MHD outflows in the Kerr geometry. Meridional self-similarity is invoked to derive semi-analytical solutions close to the polar axis. The study of the energy conservation along a particular field line gives a simple criterion for the collimation of jets. Such parameter have already been derived in the classical case by Sauty et al. 1999 and also extended to the Schwarzschild metric by Meliani et al. 2006. We generalize the same study to the Kerr metric. We show that the rotation of the black hole increases the magnetic self-confinement.
Valdmane, R.A.; Krishberg, R.R.; Lielpeter, Ya.Ya.; Mikryukov, Ch.K.; Ulmanis, L.Ya.
1977-07-01
A study is made of the velocity distribution along the duct width of an induction MHD machine with a traveling magnetic field under pump, generator and damping conditions. The computed velocity profiles were compared to those obtained on a sodium circuit under pump and damping conditions. The parameter values for electromagnetic interaction E in the experiments and in the computations changed from 2 to 4.5. Agreement was obtained between the measured velocity distribution and the compared ones at values E > 1. 6 references, 7 figures.
Numerical investigation of the LM MHD flows in a curved duct with an FCI with varying slot locations
Yang, Jong Hoon; Yan, Yue [Department of Mechanical Engineering, Graduate School, Kyung Hee University, Yong-in si, Kyunggi-do 446-701 (Korea, Republic of); Kim, Chang Nyung, E-mail: cnkim@khu.ac.kr [Department of Mechanical Engineering, College of Engineering, Kyung Hee University, Yong-in si, Kyunggi-do 446-701 (Korea, Republic of)
2016-04-15
Highlights: • This study numerically investigates the liquid-metal magnetohydrodynamic flows in a curved duct with an FCI. • The effects of the location of FCI slot and of the curvature radius on the flow behavior are reviewed. • The influence of the FCI slot position on the equalization of the pressure in the inner fluid region (inside the FCI) and the gap fluid region (outer the FCI) is examined. - Abstract: This study numerically investigates the liquid-metal (LM) magnetohydrodynamic (MHD) flows in a curved duct with an FCI having three different slot locations and having no slot under a uniform magnetic field perpendicular to the duct. The flow velocity, current density, electric potential, Lorentz force, and pressure in different flow situations are presented in detail. The effects of the location of FCI slot and of the curvature radius on the flow behavior are reviewed. The flow field is examined with an introduction of the electric-field component and electro-motive component of the current, allowing us to analyze the interdependency of the flow variables. The effect of the FCI slot position on the equalization of the pressure in the inner fluid region (inside the FCI) and the gap fluid region (outer the FCI) is examined. The result shows that and the case with an FCI slot located in the neutral position yields the smallest pressure gradient in the main flow direction among the cases with an FCI slot, resulting in the smallest pressure drop. Also, in a flow situation with smaller radius of curvature with the FCI slot in the neutral position, the axial velocity near the inner (in terms of the curvature) part of a cross-section is higher than that near the outer part.
K. Sumathi
2016-07-01
Full Text Available This paper deals with the influence of Hall and ion slip effects on three dimensional unsteady MHD flow of a viscous ncompressible fluid between the vertical flat porous plates separated by a finite distance in a slip flow regime. The moving plate is subjected to a constant injection V0 and the stationary plate to a transverse sinusoidal suction velocity distribution, so that the flow becomes three dimensional. Approximate solutions for cross flow, main flow velocities, skin friction and rate of heat transfer were found using perturbation techniques. The effects of various parameters involved in the problem on flow characteristics were studied numerically.
R. N. Barik
2013-09-01
Full Text Available An analysis is made to study the effects of diffusion-thermo and chemical reaction on fully developed laminar MHD flow of electrically conducting viscous incompressible fluid in a vertical channel formed by two vertical parallel plates was taken into consideration with uniform temperature and concentration. The analytical solution by Laplace transform technique of partial differential equations is used to obtain the expressions for the velocity, temperature and concentration. It is interesting to note that during the course of computation, the transient solution at large time coincides with steady state solution derived separately and the diffusion-thermo effect creates an anomalous situation in temperature and velocity profiles for small Prandtl numbers. The study is restricted to only destructive reaction and non-conducting case cannot be derived as a particular case still it is quite interesting and more realistic than the earlier one.
Impact of thermal radiation on MHD slip flow of a ferrofluid over a non-isothermal wedge
Rashad, A. M.
2017-01-01
This article is concerned with the problem of magnetohydrodynamic (MHD) mixed convection flow of Cobalt-kerosene ferrofluid adjacent a non-isothermal wedge under the influence of thermal radiation and partial slip. Such type of problems are posed by electric generators and biomedical enforcement. The governing equations are solved using the Thomas algorithm with finite-difference type and solutions for a wide range of magnet parameter are presented. It is found that local Nusselt number manifests a considerable diminishing for magnetic parameter and magnifies intensively in case of slip factor, thermal radiation and surface temperature parameters. Further, the skin friction coefficient visualizes a sufficient enhancement for the parameters thermal radiation, surface temperature and magnetic field, but a huge reduction is recorded by promoting the slip factor.
Tripathi, Bhavya
2016-01-01
In this paper, effects of heat transfer on the blood flow through a stenosed, inclined non-tapered porous artery subject to the action of external magnetic field is investigated. Viscosity is assumed as variable viscosity with variable Hematocrit throughout the region of the artery. Governing equations have been modeled by taking blood as incompressible magnetohydrodynamic (MHD) Newtonian fluid. The energy equation is formulated by taking an extra factor of the heat source in its equation. The nonlinear momentum equations are simplified under the assumption of mild stenosis. Homotopy perturbation method (HPM) is used to solve nonlinear equations of velocity and temperature profiles. Effects of porosity parameter (Z), applied magnetic field parameter (M), variable hematocrit parameter(Hr), Brinkman number (Br), heat source parameter (Q) and the Grashof number (Gr) on velocity and temperature profiles are discussed graphically.
Rajnish Kumar
2016-06-01
Full Text Available An analysis is made to study radiation effect on MHD (magnetohydrodynamic flow of nanofluid in the presence of chemical reactions and mixed convection due to non-uniform heat source through a porous medium. The model for the nanofluid incorporates and analyses radiation parameter, Brownian motion, thermopheresis and magnetic field consequences. The nonlinear differential equations are solved for different values of governing parameters by using the function ‘bvp4c’ of MATLAB. A comparative study of our result with previously reported results is given. It is worth citing that the thermal boundary layer thickness reduces with rise in unsteadiness of parameter . The decrease in value of thermal radiation means an enhancement in Rosseland absorptivity.
Rana, B. M. Jewel; Ahmed, Rubel; Ahmmed, S. F.
2017-06-01
Unsteady MHD free convection flow past a vertical porous plate in porous medium with radiation, diffusion thermo, thermal diffusion and heat source are analyzed. The governing non-linear, partial differential equations are transformed into dimensionless by using non-dimensional quantities. Then the resultant dimensionless equations are solved numerically by applying an efficient, accurate and conditionally stable finite difference scheme of explicit type with the help of a computer programming language Compaq Visual Fortran. The stability and convergence analysis has been carried out to establish the effect of velocity, temperature, concentration, skin friction, Nusselt number, Sherwood number, stream lines and isotherms line. Finally, the effects of various parameters are presented graphically and discussed qualitatively.
S.K. Parida
2015-12-01
Full Text Available This work considers the two-dimensional steady MHD boundary layer flow of heat and mass transfer over a flat plate with partial slip at the surface subjected to the convective heat flux. The particular attraction lies in searching the effects of variable viscosity and variable thermal diffusivity on the behavior of the flow. In addition, non-linear thermal radiation effects and thermophoresis are taken into account. The governing nonlinear partial differential equations for the flow, heat and mass transfer are transformed into a set of coupled nonlinear ordinary differential equations by using similarity variable, which are solved numerically by applying Runge–Kutta fourth–fifth order integration scheme in association with quasilinear shooting technique. The novel results for the dimensionless velocity, temperature, concentration and ambient Prandtl number within the boundary layer are displayed graphically for various parameters that characterize the flow. The local skin friction, Nusselt number and Sherwood number are shown graphically. The numerical results obtained for the particular case are fairly in good agreement with the result of Rahman [6].
Rabbi, Khan Md.; Rakib, Tawfiqur; Das, Sourav; Mojumder, Satyajit; Saha, Sourav
2016-07-01
This paper demonstrates magneto-hydrodynamic (MHD) mixed convection flow through a channel with a rectangular obstacle at the entrance region using non-Newtonian power law fluid. The obstacle is kept at uniformly high temperature whereas the inlet and top wall of the channel are maintained at a temperature lower than obstacle temperature. Poiseuille flow is implemented as the inlet velocity boundary condition. Grid independency test and code validation are performed to justify the computational accuracy before solving the present problem. Galerkin weighted residual method has been appointed to solve the continuity, momentum and energy equations. The problem has been solved for wide range of pertinent parameters like Richardson number (Ri = 0.1 - 10) at a constant Reynolds number (Re = 100), Hartmann number (Ha = 0 - 100), power index (n = 0.6 - 1.6). The flow and thermal field have been thoroughly discussed through streamline and isothermal lines respectively. The heat transfer performance of the given study has been illustrated by average Nusselt number plots. It is observed that increment of Hartmann number (Ha) tends to decrease the heat transfer rate up to a critical value (Ha = 20) and then let increase the heat transfer performance. Thus maximum heat transfer rate has been recorded for higher Hartmann number and Rayleigh number in case of pseudo-plastic (n = 0.6) non-Newtonian fluid flow.
Sharanya Subramanian; P K Swain; A V Deshpande; P Satyamurthy
2015-05-01
Conventionally, obtaining a converged solution for a MagnetoHydro-Dynamic problem entails a highly resolved Hartmann boundary layer, leading to excessive time and computational requirements. For high Hartmann number flows through electrically conducting channels, majority of the current loops close through the walls and the Hartmann layer contributes only a small fraction of the global current path. Hence, the effect on flow parameters due to coarsening the mesh of the Hartmann Layer was investigated using the ANSYS FLUENT code. Numerical simulations have been carried out in square and rectangular ducts with wall conductance ratio of 0.156 and 0.078 respectively. Magnetic field was varied from 1T to 4T to obtain solution for Hartmann numbers $(Ha = Ba \\sqrt{\\sigma/\\mu})$ in the range of 260–1040 for the square duct, and 520–2080 for the rectangular duct. B, $\\alpha$, $\\mu$, and $\\sigma$ are the strength of applied magnetic field, characteristic length of the channel, dynamic viscosity and electrical conductivity of the fluid respectively. The errors in estimating core and side layer peak velocity and fully developed pressure gradient were found to be low even for a grid system having 46% coarser grid than a well-resolved system. The analysis indicated that for high Hartmann number flows through thick, conducting ducts, coarsening the mesh in the Hartmann boundary layer reduced computational time, not compromising on the solution accuracy and appears to be a promising option for complex geometry MHD simulation.
Alok Kumar Pandey
2016-12-01
Full Text Available The purpose of present study is to identify the effects of viscous dissipation and suction/injection on MHD flow of a nanofluid past a wedge with convective surface in the appearance of slip flow and porous medium. The basic non-linear PDEs of flow and energy are altered into a set of non-linear ODEs using auxiliary similarity transformations. The system of equations together with coupled boundary conditions have been solved numerically by applying Runge-Kutta-Fehlberg procedure via shooting scheme. The influence of relevant parameters on non-dimensional velocity and temperature profiles are depicted graphically and investigated in detail. The results elucidate that as enhance in the Eckert number, the skin friction coefficient increases, while heat transfer rate decreases. The outcomes also specify that thermal boundary layer thickness declines with an increase in suction parameter. Moreover, it is accelerated with augment in injection parameter. The results are analogized with the study published earlier and it creates a fine concord.
A A AFIFY; M J UDDIN; M FERDOWS
2014-01-01
Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic (MHD) flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transfor-mation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The ob-tained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta-Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.
M.V.D.N.S.Madhavi
2017-03-01
Full Text Available We analysed in this paper the problem of MHD mixed convection flow from a vertical plate embedded in a saturated porous medium in the presence of melting, thermal dispersion, radiation and heat absorption or generation effects for aiding and opposing external flows. Similarity solution for the governing equations is obtained for the flow equations in steady state. The equations are numerically solved by Runge-Kutta fourth order method coupled with shooting technique. The effect of melting and heat absorption or generation under different parametric conditions on velocity, temperature and heat transfer was analyzed for both aiding and opposing flows
G. Domairry
2009-01-01
Full Text Available An analysis has been performed to study magneto-hydrodynamic (MHD squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid. We investigate the combined effect of inertia, electromagnetic forces, and suction or injection. With the introduction of a similarity transformation, the continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation. An approximate solution of the equation subject to the appropriate boundary conditions is derived using the homotopy perturbation method (HPM and compared with the direct numerical solution (NS. Results showing the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the axial and radial velocity distributions are presented and discussed. The approximate solution is found to be highly accurate for the ranges of parameters investigated. Because of its simplicity, versatility and high accuracy, the method can be applied to study linear and nonlinear boundary value problems arising in other engineering applications.
Mohammed J Uddin
Full Text Available Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
Krishnendu Bhattacharyya
2013-01-01
Full Text Available The two-dimensional magnetohydrodynamic (MHD stagnation-point flow of electrically conducting non-Newtonian Casson fluid and heat transfer towards a stretching sheet have been considered. The effect of thermal radiation is also investigated. Implementing similarity transformations, the governing momentum, and energy equations are transformed to self-similar nonlinear ODEs and numerical computations are performed to solve those. The investigation reveals many important aspects of flow and heat transfer. If velocity ratio parameter (B and magnetic parameter (M increase, then the velocity boundary layer thickness becomes thinner. On the other hand, for Casson fluid it is found that the velocity boundary layer thickness is larger compared to that of Newtonian fluid. The magnitude of wall skin-friction coefficient reduces with Casson parameter (β. The velocity ratio parameter, Casson parameter, and magnetic parameter also have major effects on temperature distribution. The heat transfer rate is enhanced with increasing values of velocity ratio parameter. The rate of heat transfer is enhanced with increasing magnetic parameter M for B > 1 and it decreases with M for B < 1. Moreover, the presence of thermal radiation reduces temperature and thermal boundary layer thickness.
Ul Haq, Rizwan [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Mechanical and Materials Engineering, Spencer Engineering Building, Room 3055, University of Western Ontario, London, Ontario (Canada); Nadeem, Sohail [Department of Mathematics, Quaid-I-Azam University, Islamabad 44000 (Pakistan); Khan, Z.H. [School of Mathematical Sciences, Peking University, Beijing 100871 (China); Department of Mathematics, University of Malakand, Dir (Lower), Khyber Pakhtunkhwa (Pakistan); Noor, N.F.M., E-mail: drfadiya@um.edu.my [Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2015-01-15
In the present study, thermal conductivity and viscosity of both single-wall and multiple-wall Carbon Nanotubes (CNT) within the base fluids (water, engine oil and ethylene glycol) of similar volume have been investigated when the fluid is flowing over a stretching surface. The magnetohydrodynamic (MHD) and viscous dissipation effects are also incorporated in the present phenomena. Experimental data consists of thermo-physical properties of each base fluid and CNT have been considered. The mathematical model has been constructed and by employing similarity transformation, system of partial differential equations is rehabilitated into the system of non-linear ordinary differential equations. The results of local skin friction and local Nusselt number are plotted for each base fluid by considering both Single Wall Carbon Nanotube (SWCNT) and Multiple-Wall Carbon Nanotubes (MWCNT). The behavior of fluid flow for water based-SWCNT and MWCNT are analyzed through streamlines. Concluding remarks have been developed on behalf of the whole analysis and it is found that engine oil-based CNT have higher skin friction and heat transfer rate as compared to water and ethylene glycol-based CNT. - Graphical abstract: Comparison among three different base fluids in the presence of SWCNTs and MWCNTs for skin friction and local Nusselt number.
A Mahdy
2016-01-01
Full Text Available In this contribution a numerical study is carried out to analyze the effect of slip at the boundary of unsteady two-dimensional MHD flow of a non-Newtonian fluid over a stretching surface having a prescribed surface temperature in the presence of suction or blowing at the surface. Casson fluid model is used to characterize the non-Newtonian fluid behavior. With the help of similarity transformations, the governing partial differential equations corresponding to the momentum and heat transfer are reduced to a set of non-linear ordinary differential equations, which are then solved for local similar solutions using the very robust computer algebra software MATLAB. The flow features and heat transfer characteristics for different values of the governing parameters are graphically presented and discussed in detail. Comparison with available results for certain cases is excellent. The effect of increasing values of the Casson parameter is seen to suppress the velocity field. But the temperature is enhanced with increasing Casson parameter. For increasing slip parameter, velocity increases and thermal boundary layer becomes thinner in the case of suction or blowing.
Uddin, Mohammed J; Khan, Waqar A; Ismail, Ahmed I
2012-01-01
Steady two dimensional MHD laminar free convective boundary layer flows of an electrically conducting Newtonian nanofluid over a solid stationary vertical plate in a quiescent fluid taking into account the Newtonian heating boundary condition is investigated numerically. A magnetic field can be used to control the motion of an electrically conducting fluid in micro/nano scale systems used for transportation of fluid. The transport equations along with the boundary conditions are first converted into dimensionless form and then using linear group of transformations, the similarity governing equations are developed. The transformed equations are solved numerically using the Runge-Kutta-Fehlberg fourth-fifth order method with shooting technique. The effects of different controlling parameters, namely, Lewis number, Prandtl number, buoyancy ratio, thermophoresis, Brownian motion, magnetic field and Newtonian heating on the flow and heat transfer are investigated. The numerical results for the dimensionless axial velocity, temperature and nanoparticle volume fraction as well as the reduced Nusselt and Sherwood number have been presented graphically and discussed. It is found that the rate of heat and mass transfer increase as Newtonian heating parameter increases. The dimensionless velocity and temperature distributions increase with the increase of Newtonian heating parameter. The results of the reduced heat transfer rate is compared for convective heating boundary condition and found an excellent agreement.
Raju CSK
2016-01-01
Full Text Available In this study we analyzed the momentum and heat transfer characteristics of MHD boundary layer flow over an exponentially stretching surface in porous medium in the presence of radiation, non-uniform heat source/sink, external pressure and suction/injection. Dual solutions are presented for both suction and injection cases. The heat transfer analysis is carried out for both prescribed surface temperature (PST and prescribed heat flux (PHF cases. The governing equations of the flow are transformed into system of nonlinear ordinary differential equations by using similarity transformation and solved numerically using bvp4c Matlab package. The impact of various non-dimensional governing parameters on velocity, temperature profiles for both PST and PHF cases, friction factor and rate of heat transfer is discussed and presented with the help of graphs and tables. Results indicate that dual solutions exist only for certain range of suction or injection parameters. It is also observed that the exponential parameter have tendency to increase the heat transfer rate for both PST and PHF cases.
A.M. Rashad
2014-04-01
Full Text Available This work is focused on the study of unsteady magnetohydrodynamics boundary-layer flow and heat transfer for a viscous laminar incompressible electrically conducting and rotating fluid due to a stretching surface embedded in a saturated porous medium with a temperature-dependent viscosity in the presence of a magnetic field and thermal radiation effects. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The Rosseland diffusion approximation is used to describe the radiative heat flux in the energy equation. With appropriate transformations, the unsteady MHD boundary layer equations are reduced to local nonsimilarity equations. Numerical solutions of these equations are obtained by using the Runge–Kutta integration scheme as well as the local nonsimilarity method with second order truncation. Comparisons with previously published work have been conducted and the results are found to be in excellent agreement. A parametric study of the physical parameters is conducted and a representative set of numerical results for the velocity in primary and secondary flows as well as the local skin-friction coefficients and the local Nusselt number are illustrated graphically to show interesting features of Darcy number, viscosity-variation, magnetic field, rotation of the fluid, and conduction radiation parameters.
MHD FLOW OF A NEWTONIAN FLUID OVER A STRETCHING SHEET: AN APPROXIMATE SOLUTION
Chakraborty, B.K; Mazumdar, H.P.
2000-01-01
An approximate solution to the problem of steady laminar flow of a viscous incompressible electrically con ducting fluid over a stretching sheet is presented. The approach is based on the idea of stretching the variables of the flow problem and then using least squares method to minimize the residual of a differential equation. The effects of the magnetic field on the flow characteristics are demonstrated through numerical computations with di f ferent values of the Hartman monber.
JHANKAL ANUJ
2015-01-01
Full Text Available MHD boundary layer flow near stagnation point of linear stretching sheet with variable thermal conductivity are solved using He’s Homotopy Perturbation Method (HPM, which is one of the semi-exact method. Similarity transformation has been used to reduce the governing differential equations into an ordinary non-linear differential equation. The main advantage of HPM is that it does not require the small parameter in the equations and hence the limitations of traditional perturbations can be eliminated. In this paper firstly, the basic idea of the HPM for solving nonlinear differential equations is briefly introduced and then it is employed to derive solution of nonlinear governing equations of MHD boundary layer flow with nonlinear term. The influence of various relevant physical characteristics are presented and discussed.
Mohammed Almakki
2017-07-01
Full Text Available The entropy generation in unsteady three-dimensional axisymmetric magnetohydrodynamics (MHD nanofluid flow over a non-linearly stretching sheet is investigated. The flow is subject to thermal radiation and a chemical reaction. The conservation equations are solved using the spectral quasi-linearization method. The novelty of the work is in the study of entropy generation in three-dimensional axisymmetric MHD nanofluid and the choice of the spectral quasi-linearization method as the solution method. The effects of Brownian motion and thermophoresis are also taken into account. The nanofluid particle volume fraction on the boundary is passively controlled. The results show that as the Hartmann number increases, both the Nusselt number and the Sherwood number decrease, whereas the skin friction increases. It is further shown that an increase in the thermal radiation parameter corresponds to a decrease in the Nusselt number. Moreover, entropy generation increases with respect to some physical parameters.
Muthucumaraswamy R.
2016-02-01
Full Text Available The problem of MHD free convection flow with a parabolic starting motion of an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction has been examined in detail in this paper. The fluid considered here is a gray, absorbing emitting radiation but a non-scattering medium. The dimensionless governing coupled linear partial differential equations are solved using the Laplace transform technique. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time on the velocity, temperature, concentration. The results are discussed graphically and qualitatively. The numerical results reveal that the radiation induces a rise in both the velocity and temperature, and a decrease in the concentration. The model finds applications in solar energy collection systems, geophysics and astrophysics, aerospace and also in the design of high temperature chemical process systems.
Muthucumaraswamy, R.; Sivakumar, P.
2016-02-01
The problem of MHD free convection flow with a parabolic starting motion of an infinite isothermal vertical plate in the presence of thermal radiation and chemical reaction has been examined in detail in this paper. The fluid considered here is a gray, absorbing emitting radiation but a non-scattering medium. The dimensionless governing coupled linear partial differential equations are solved using the Laplace transform technique. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, chemical reaction parameter, thermal Grashof number, mass Grashof number, Schmidt number and time on the velocity, temperature, concentration. The results are discussed graphically and qualitatively. The numerical results reveal that the radiation induces a rise in both the velocity and temperature, and a decrease in the concentration. The model finds applications in solar energy collection systems, geophysics and astrophysics, aerospace and also in the design of high temperature chemical process systems.
Combined effect of free and forced convection on MHD flow in a rotating porous channel
D. R. V. Prasada Rao
1982-01-01
Full Text Available This paper gives a steady linear theory of the combined effect of the free and forced convection in rotating hydromagnetic viscous fluid flows in a porous channel under the action of a uniform magnetic field. The flow is governed by the Grashof number G, the Hartmann number H, the Ekman number E, and the suction Reynolds number S. The solutions for the velocity field, temperature distribution, magnetic field, mass rate of flow and the shear stresses on the channel boundaries are obtained using a perturbation method with the small parameter S. The nature of the associated boundary layers is investigated for various values of the governing flow parameters. The velocity, the temperature, and the shear stresses are discussed numerically by drawing profiles with reference to the variations in the flow parameters.
Shateyi, Stanford
2017-07-01
The spectral relaxation method is employed to examine natural convective heat and mass transfer, MHD flow over a permeable moving vertical plate with convective boundary condition in the presence of viscous dissipation, thermal radiation and chemical reaction. The governing partial differential equations were transformed into a system of nonlinear ordinary differential equations by using a similarity approach. The pertinent results are then displayed in tabular form and graphically.
S. Srinivas
2016-01-01
Full Text Available The present work investigates the effects of thermal-diffusion and diffusion-thermo on MHD flow of viscous fluid between expanding or contracting rotating porous disks with viscous dissipation. The partial differential equations governing the flow problem under consideration have been transformed by a similarity transformation into a system of coupled nonlinear ordinary differential equations. An analytical approach, namely the homotopy analysis method is employed in order to obtain the solutions of the ordinary differential equations. The effects of various emerging parameters on flow variables have been discussed numerically and explained graphically. Comparison of the HAM solutions with the numerical solutions is performed.
Jagdish PRAKASH
2014-01-01
Full Text Available This paper studies flow, heat, and mass transfer characteristics of unsteady mixed convective magnetohydrodynamic (MHD flow of a heat absorbing fluid in an accelerated vertical wavy plate, subject to varying temperature and mass diffusion, with the influence of buoyancy, thermal radiation and Dufour effect. The momentum, energy and mass diffusion equations are coupled non-linear partial differential equations, which are solved by perturbation technique. The features of the fluid flow, heat and mass transfer characteristics are analyzed by plotting graphs, and the physical aspects are discussed in detail to interpret the effects of significant parameters of the problem.doi:10.14456/WJST.2014.69
Alexakis, A.
2009-04-01
Most astrophysical and planetary systems e.g., solar convection and stellar winds, are in a turbulent state and coupled to magnetic fields. Understanding and quantifying the statistical properties of magneto-hydro-dynamic (MHD) turbulence is crucial to explain the involved physical processes. Although the phenomenological theory of hydro-dynamic (HD) turbulence has been verified up to small corrections, a similar statement cannot be made for MHD turbulence. Since the phenomenological description of Hydrodynamic turbulence by Kolmogorov in 1941 there have been many attempts to derive a similar description for turbulence in conducting fluids (i.e Magneto-Hydrodynamic turbulence). However such a description is going to be based inevitably on strong assumptions (typically borrowed from hydrodynamics) that do not however necessarily apply to the MHD case. In this talk I will discuss some of the properties and differences of the energy and helicity cascades in turbulent MHD and HD flows. The investigation is going to be based on the analysis of direct numerical simulations. The cascades in MHD turbulence appear to be a more non-local process (in scale space) than in Hydrodynamics. Some implications of these results to turbulent modeling will be discussed
Effects of mass transfer on MHD flow of casson fluid with chemical reaction and suction
S. A. Shehzad
2013-03-01
Full Text Available Effect of mass transfer in the magnetohydrodynamic flow of a Casson fluid over a porous stretching sheet is addressed in the presence of a chemical reaction. A series solution for the resulting nonlinear flow is computed. The skin friction coefficient and local Sherwood number are analyzed through numerical values for various parameters of interest. The velocity and concentration fields are illustrated for several pertinent flow parameters. We observed that the Casson parameter and Hartman number have similar effects on the velocity in a qualitative sense. We further analyzed that the concentration profile decreases rapidly in comparison to the fluid velocity when we increased the values of the suction parameter.
Hodographic study of non-Newtonian MHD aligned steady plane fluid flows
P. V. Nguyen
1990-01-01
Full Text Available A study is made of non-Newtonian HHD aligned steady plane fluid flows to find exact solutions for various flow configurations. The equations of motion have been transformed to the hodograph plane. A Legendre-transform function is used to recast the equations in the hodograph plane in terms of this transform function. Solutions for various flow configurations are obtained. Applications are investigated for the fluids of finite and infinite electrical conductivity bringing out the similarities and contrasts in the solutions of these types of fluids.
Fogerty, Erica; Carroll-Nellenback, Jonathan; Frank, Adam; Heitsch, Fabian; Pon, Andy
2017-09-01
We present numerical simulations of reorienting oblique shocks that form in the collision layer between magnetized colliding flows. Reorientation aligns post-shock filaments normal to the background magnetic field. We find that reorientation begins with pressure gradients between the collision region and the ambient medium. This drives a lateral expansion of post-shock gas, which reorients the growing filament from the outside-in (i.e. from the flow/ambient boundary, towards the colliding flows axis). The final structures of our simulations resemble polarization observations of filaments in Taurus and Serpens South, as well as the integral-shaped filament in Orion A. Given the ubiquity of colliding flows in the interstellar medium, shock reorientation may be relevant to the formation of filaments normal to magnetic fields.
MHD Stagnation Flow of a Newtonian Fluid towards a Uniformly Heated and Moving Vertical Plate
Mehmet Şirin Demir
2016-01-01
Full Text Available Stagnation flow of an electrically conducting incompressible viscous fluid towards a moving vertical plate in the presence of a constant magnetic field is investigated. By using the appropriate transformations for the velocity components and temperature, the partial differential equations governing flow and heat transfer are reduced to a set of nonlinear ordinary differential equations. These equations are solved approximately using a numerical technique for the following two problems: (i two-dimensional stagnation-point flow on a moving vertical plate, (ii axisymmetric stagnation-point flow on a moving vertical plate. The effects of non-dimensional parameters on the velocity components, wall shear stresses, temperature and heat transfer are examined carefully.
Fogerty, Erica L; Frank, Adam; Heitsch, Fabian; Pon, Andy
2016-01-01
We present numerical simulations of reorienting oblique shocks that form in the collision layer between magnetized colliding flows. Reorientation aligns parsec-scale post-shock filaments normal to the background magnetic field. We find that reorientation begins with pressure gradients between the collision region and the ambient medium. This drives a lateral expansion of post-shock gas, which reorients the growing filament from the outside-in (i.e. from the flow-ambient boundary, toward the colliding flows axis). The final structures of our simulations resemble polarization observations of filaments in Taurus and Serpens South, as well as the integral-shaped filament in Orion A. Given the ubiquity of colliding flows in the interstellar medium, shock reorientation may be relevant to the formation of filaments normal to magnetic fields.
Fully developed MHD natural convection flow in a vertical annular microchannel: An exact solution
Basant K. Jha
2015-07-01
Full Text Available An exact solution of steady fully developed natural convection flow of viscous, incompressible, electrically conducting fluid in a vertical annular micro-channel with the effect of transverse magnetic field in the presence of velocity slip and temperature jump at the annular micro-channel surfaces is obtained. Exact solution is expressed in terms of modified Bessel function of the first and second kind. The solution obtained is graphically represented and the effects of radius ratio (η, Hartmann number (M, rarefaction parameter (βvKn, and fluid–wall interaction parameter (F on the flow are investigated. During the course of numerical computations, it is found that an increase in Hartmann number leads to a decrease in the fluid velocity, volume flow rate and skin friction. Furthermore, it is found that an increase in curvature radius ratio leads to an increase in the volume flow rate.
Convective MHD Oscillatory Flow past a Uniformly Moving Infinite Vertical Plate
N. Ahmed
1992-01-01
Full Text Available The convective magnetohydrodynamic flow past a uniformly moving infinite vertical plate, with the magnetic field and the suction velocity applied normal to the plate has been analysed. Presence of heat source or sink has also been considered. The findings are expected to throw light on some problems of defence applications in the areas of aeronautical designs and also flow and heat transfer problems of a chemically reacting fluid.
Qasim, Muhammad; Khan, Zafar Hayat; Khan, Waqar Ahmad; Ali Shah, Inayat
2014-01-01
This study investigates the magnetohydrodynamic (MHD) flow of ferrofluid along a stretching cylinder. The velocity slip and prescribed surface heat flux boundary conditions are employed on the cylinder surface. Water as conventional base fluid containing nanoparticles of magnetite (Fe3O4) is used. Comparison between magnetic (Fe3O4) and non-magnetic (Al2O3) nanoparticles is also made. The governing non-linear partial differential equations are reduced to non-linear ordinary differential equations and then solved numerically using shooting method. Present results are compared with the available data in the limiting cases. The present results are found to be in an excellent agreement. It is observed that with an increase in the magnetic field strength, the percent difference in the heat transfer rate of magnetic nanoparticles with Al2O3 decreases. Surface shear stress and the heat transfer rate at the surface increase as the curvature parameter increases, i.e curvature helps to enhance the heat transfer.
C. Sulochana
2016-02-01
Full Text Available We analyzed the momentum and heat transfer characteristics of unsteady MHD flow of a dusty nanofluid over a vertical stretching surface in presence of volume fraction of dust and nano particles with non uniform heat source/sink. We considered two types of nanofluids namely Ag-water and Cu-water embedded with conducting dust particles. The governing equations are transformed in to nonlinear ordinary differential equations by using similarity transformation and solved numerically using Shooting technique. The effects of non-dimensional governing parameters on velocity and temperature profiles for fluid and dust phases are discussed and presented through graphs. Also, the skin friction coefficient and Nusselt number are discussed and presented for two dusty nanofluids separately in tabular form. Results indicate that an increase in the volume fraction of dust particles enhances the heat transfer in Cu-water nanofluid compared with Ag-water nanofluid and a raise in the volume fraction of nano particles shows uniform heat transfer in both Cu-water and Ag-water nanofluids.
Yahaya Shagaiya Daniel
2015-09-01
Full Text Available This paper investigates the theoretical influence of buoyancy and thermal radiation on MHD flow over a stretching porous sheet. The model which constituted highly nonlinear governing equations is transformed using similarity solution and then solved using homotopy analysis method (HAM. The analysis is carried out up to the 5th order of approximation and the influences of different physical parameters such as Prandtl number, Grashof number, suction/injection parameter, thermal radiation parameter and heat generation/absorption coefficient and also Hartman number on dimensionless velocity, temperature and the rate of heat transfer are investigated and discussed quantitatively with the aid of graphs. Numerical results obtained are compared with the previous results published in the literature and are found to be in good agreement. It was found that when the buoyancy parameter and the fluid velocity increase, the thermal boundary layer decreases. In case of the thermal radiation, increasing the thermal radiation parameter produces significant increases in the thermal conditions of the fluid temperature which cause more fluid in the boundary layer due to buoyancy effect, causing the velocity in the fluid to increase. The hydrodynamic boundary layer and thermal boundary layer thickness increase as a result of increase in radiation.
Sandeep Naramgari
2015-11-01
Full Text Available Present study deals with the buoyancy-driven MHD mixed convection stagnation-point flow, heat and mass transfer of a nanofluid over a non-isothermal stretching sheet in presence of induced magneticfield, radiation, chemical reaction, suction/injection and heat source/sink. The basic governing partial differential equations are reduced to a set of ordinary differential equations by using appropriate similarity transformation. The resulting system is solved numerically by bvp5c Matlab package. Numerical results are validated by comparing with the published results. The influence of non-dimensional governing parameters on velocity, induced magneticfield, temperature and concentration profiles along with coefficient of skin friction, local Nusselt and Sherwood numbers are discussed and presented with the help of graphs and tables. Comparisons are made with the existed studies. Results indicate that dual solutions exists only for certain range of suction/ injection parameter and injection parameter have tendency to enhance the momentum, thermal and concentration boundary layer thickness.
Zhilkin, A G; Mason, P A; 10.1134/S1063772912040087
2012-01-01
We performed 3D MHD calculations of stream accretion in cataclysmic variable stars for which the white dwarf primary star possesses a strong and complex magnetic field. These calculations are motivated by observations of polars; cataclysmic variables containing white dwarfs with magnetic fields sufficiently strong to prevent the formation of an accretion disk. So an accretion stream flows from the L1 point and impacts directly onto one or more spots on the surface of the white dwarf. Observations indicate that the white dwarf, in some binaries, possesses a complex (non-dipolar) magnetic field. We perform simulations of 10 polars or equivalently one asynchronous polar at 10 different beat phases. Our models have an aligned dipole plus quadrupole magnetic field centered on the white dwarf primary. We find that for a sufficiently strong quadrupole component an accretion spot occurs near the magnetic equator for slightly less than half of our simulations while a polar accretion zone is active for most of the rest...
Buoyancy effects on the 3D MHD stagnation-point flow of a Newtonian fluid
Borrelli, A.; Giantesio, G.; Patria, M. C.; Roşca, N. C.; Roşca, A. V.; Pop, I.
2017-02-01
This work examines the steady three-dimensional stagnation-point flow of an electrically conducting Newtonian fluid in the presence of a uniform external magnetic field H0 under the Oberbeck-Boussinesq approximation. We neglect the induced magnetic field and examine the three possible directions of H0 which coincide with the directions of the axes. In all cases it is shown that the governing nonlinear partial differential equations admit similarity solutions. We find that the flow has to satisfy an ordinary differential problem whose solution depends on the Hartmann number M, the buoyancy parameter λ and the Prandtl number Pr. The skin-friction components along the axes are computed and the stagnation-point is classified. The numerical integration shows the existence of dual solutions and the occurrence of the reverse flow for some values of the parameters.
Numerical simulation of MHD pulsatile flow of a biofluid in a channel
Kashif Ali
2015-08-01
Full Text Available The purpose of this paper is to numerically study the interaction of an external magnetic field with the flow of a biofluid through a Darcy-Forchhmeir porous channel, due to an oscillatory pressure gradient, in the presence of wall transpiration as well as chemical reaction considerations. We have noticed that if the Reynolds number of the wall transpiration flow is increased, the average (or maximum velocity of the main flow direction is raised. Similar effect has also been observed for the rheological parameter and the Darcy parameter, whereas an opposite trend has been noted for both the Forchheimer quadratic drag parameter and the magnetic parameter. Further, an increase in the Reynolds number results in straightening the concentration profile, thus making it an almost linear function of the dimensionless spatial variable.
Magnetite micropolar nanofluid non-aligned MHD flow with mixed convection
Tabassum, Rabil; Mehmood, R.; Akbar, N. S.
2017-06-01
The magnetite micropolar nanofluid ( Fe3O4 /water) oblique flow in the presence of mixed convection and magnetic field is considered in the present investigation. Magnetite nanoparticles are added to water in order to examine the temperature and velocity characteristics of the flow. Appropriate transformations are employed to obtain the governing equations. Numerical solutions are attained by the Range-Kutta-Fehlberg integration scheme with the shooting method. Characteristics of flow velocity profiles, temperature distribution, micro-rotation, shear stress and heat flux are remarkably influenced by magnetic parameter, magnetite nanoparticles volume fraction and mixed convection parameter. The obtained results indicate that the shear stress at the wall decreases but the local heat flux increases with increase in the nanoparticles volume fraction. Moreover, an increase in the magnetic field strength consequently enhances the shear stress at the surface but decreases the local heat transfer rate at the surface.
Stability of MHD jet flows between nonconducting plates in a transverse field
Levin, V.B.; Shtern, V.N.
1985-06-01
The linear stability of jet flows of a conducting fluid between parallel nonconducting plates in a transverse field is examined. It is assumed that the flow is caused by the current between linear electrodes situated on one of the plates, and that the velocity profile for the initial flow and for perturbations is a Hartmann profile across the plates. Hartmann boundary layers are modeled with respect to the friction force. Neutral curves and dependences of the critical Reynolds number on the Hartmann number are obtained; the dependence is found to be linear for finite-width electrodes, and proportional to the square root of Ha for infinitely thin electrodes. A comparison with experimental data is carried out. 13 references.
Heat transfer in MHD unsteady stagnation point flow with variable wall temperature
Soundalgekar, V.M.; Murty, T.V.R.; Takhar, H.S.
of free-stream oscillations cn the flow of an incompressible viscous fluid past a semi-infinite boay. The small amplituae pheno menon was studied. The unsteady motion of a semi-infinite plate in a viscous fluid was also studied by Cheng and ElJiott 2.... In section2~the mathematical analysis is considered and in section 3 the conclusions are set onto REAT TRANSFER 385 2. MATHBMATICAL ANALYSIS MHO flow of an incompressible viscous fluid near a forward stagnation point of a blunt-nosed two dimensional body...
A. S. Eegunjobi
2013-01-01
Full Text Available This paper examines the effects of the thermodynamic second law on steady flow of an incompressible variable viscosity electrically conducting fluid in a channel with permeable walls and convective surface boundary conditions. The nonlinear model governing equations are solved numerically using shooting quadrature. Numerical results of the velocity and temperature profiles are utilised to compute the entropy generation number and the Bejan number. The results revealed that entropy generation minimization can be achieved by appropriate combination of the regulated values of thermophysical parameters controlling the flow systems.
Heat Transfer to MHD Oscillatory Viscoelastic Flow in a Channel Filled with Porous Medium
Rita Choudhury
2012-01-01
Full Text Available The combined effect of a transverse magnetic field and radiative heat transfer on unsteady flow of a conducting optically thin viscoelastic fluid through a channel filled with saturated porous medium and nonuniform walls temperature has been discussed. It is assumed that the fluid has small electrical conductivity and the electromagnetic force produced is very small. Closed-form analytical solutions are constructed for the problem. The effects of the radiation and the magnetic field parameters on velocity profile and shear stress for different values of the viscoelastic parameter with the combination of the other flow parameters are illustrated graphically, and physical aspects of the problem are discussed.
ZHANG Guo-yan; PENG Yan; ZHAO Ling-zhi; LI Ran; SHA Ci-wen
2007-01-01
A new method of recovering maritime oil-spill based on electromagnetic force, the so-called MHD oil-spill recovery method was proposed in the IEECAS. The operating process of MHD channel was described in this article. Numerical study was carried out using a two-dimensional water-air two-phase model and the VOF method. The agreement between the numerical and the experimental results was reached.
Dev Krishan Singh
2015-01-01
Full Text Available An analysis of an unsteady MHD convective flow of an electrically conducting viscous incompressible fluid through porous medium filled in a vertical porous channel is carried out. The two porous plates are subjected to a constant injection and suction velocity as shown in Fig. 1a, b. The temperature of the plate at y*= + 9 2 is assumed to be varying in space and time as T*(y*, z*, t* = T1 (y* + (T2 - T1COS (πz*d -ω*t*. A magnetic field of uniform strength is applied perpendicular to the plates of the channel. The temperature difference between the plates is high enough to induce the heat due to radiation. It is also assumed that the conducting fluid is opticallythin gray gas, absorbing/ emitting radiation and non-scattering. The Hall current effects have also been taken into account. Exact solution of the partial differential equations governing the flow under the prescribed boundary conditions has been obtained for the velocity and the temperature fields. The primary and secondary velocities, temperature and the skin-friction and Nusselt number for the rate of heat transfer in terms of their amplitudes and phase angles have been shown graphically to observe the effects of suction parameter λ, Grashof number Gr, Hartmann number M, Hall parameter H, the permeability of the porous medium K, Prandtl number Pr, radiation parameter N, pressure gradient A and the frequency of oscillation ω. The final results are then discussed in detail in the last section of the paper with the help of figures.
Govindarajan Arunachalam
2014-01-01
Full Text Available An investigation of unsteady MHD free convective flow and mass transfer during the motion of a viscous incompressible fluid through a porous medium, bounded by an infinite vertical porous surface, in a rotating system is presented. The porous plane surface and the porous medium are assumed to rotate in a solid body rotation. The vertical surface is subjected to uniform constant suction perpendicular to it and the temperature at this surface fluctuates in time about a non-zero constant mean. Analytical expressions for the velocity, temperature and concentration fields are obtained using the perturbation technique. The effects of R (rotation parameter, k0 (permeability parameter, M (Hartmann number and w (frequency parameter on the flow characteristics are discussed. It is observed that the primary velocity component decreases with the increase in either of the rotation parameter R, the permeability parameter k0, or the Hartmann number M. It is also noted that the primary skin friction increases whenever there is an increase in the Grashof number Gr or the modified Grashof number Gm. It is clear that the heat transfer coefficient in terms of the Nusselt number decreases in the case of both air and water when there is an increase in the Hartmann number M. It is observed that the magnitude of the secondary velocity profiles increases whenever there is an increase in either of the Grashof number or the modified Grashof number for mass transfer or the permeability of the porous media. Concentration profiles decreases with an increase in the Schmidt number.
Chemical reaction in MHD flow past a vertical plate with mass ...
(2010) have studied effects of chemical reaction on two different models. ...... magneto hydrodynamic flow past a flat plate will Hall effects, Journal of the Physical ... nonisothermal stretching sheet, Hindawi Publishing Corporation Journal of ... the heat transfer performance of a sinusoidal corrugated enclosure by employing.
MHD flow in a cylindrical vessel of finite size with turbulent boundary layers
Gorbachev, L.P.; Nikitin, N.V.
1979-01-01
The hydrodynamic characteristics of flows generated by electromagnetic forces in a cylindrical vessel of finite size, for the case of large values of the hydrodynamic and small values of the magnetic Reynolds numbers have been inadequately analyzed in previous literature, since neither the nonlinear nor the linear theory adequately accounts for secondary flows due to the strong action of boundary layers formed at the end faces of the cylinders at large Reynolds numbers and the results do not agree with experimental data. This paper generalizes the previously more accurate nonlinear scheme of the same authors, the basis for which was the fact that viscosity at large Reynolds numbers is manifest only close to solid surfaces. Two cases are treated: crossed fields and a rotating magnetic field in the cylindrical vessel, where the entire flow region is broken down into an inviscid core and end face boundary layers. It is assumed that the velocity distribution near the end surfaces obeys an empirical one-seventh power law, which is applicable to turbulent liquid flow in a tube in a range of Re = 3 x 10/sup 3/ to 10/sup 5/ simple engineering formulas are derived for the angular velocity, which exhibit good agreement with the experimental data for Hartmann numbers less than 10. The procedure can be generalized to the case of a rotating magnetic field having several pairs of poles. 6 references, 2 figures.
MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation
Hayat, Tasawar; Imtiaz, Maria; Alsaedi, Ahmed; Kutbi, Marwan A.
2015-12-01
An analysis has been carried out for the three dimensional flow of viscous nanofluid in the presence of partial slip and thermal radiation effects. The flow is induced by a permeable stretching surface. Water is treated as a base fluid and alumina as a nanoparticle. Fluid is electrically conducting in the presence of applied magnetic field. Entire different concept of nonlinear thermal radiation is utilized in the heat transfer process. Different from the previous literature, the nonlinear system for temperature distribution is solved and analyzed. Appropriate transformations reduce the nonlinear partial differential system to ordinary differential system. Convergent series solutions are computed for the velocity and temperature. Effects of different parameters on the velocity, temperature, skin friction coefficient and Nusselt number are computed and examined. It is concluded that heat transfer rate increases when temperature and radiation parameters are increased.
Computational analysis of MHD flow, heat and mass transfer in trapezoidal porous cavity
Younsi Ramdane
2009-01-01
Full Text Available Numerical simulations are conducted for two-dimensional steady-state double diffusive flow in a trapezoidal porous cavity, submitted to axial magnetic field. The Darcy equation, including Brinkmamn and Forchheimer terms account for viscous and inertia effects, respectively is used for the momentum equation, and a SIMPLER algorithm, based on finite volume approach is used to solve the pressure-velocity coupling. An extensive series of numerical simulations is conducted in the range: 103 ≤ Ra ≤ 106,1 ≤ Ha ≤ 102, Da =10-5, N = 1, and Le = 10. It is shown that the application of a transverse magnetic field normal to the flow direction decreases the Nusselt number and Sherwood number. Illustrative graphs are presented.
MHD stagnation point flow of Carreau fluid toward a permeable shrinking sheet: Dual solutions
N.S. Akbar
2014-12-01
Full Text Available Present analysis is carried out to study the two-dimensional stagnation-point flow of an in-compressible Carreau fluid toward a shrinking surface. The formulation of the Carreau fluid model has been developed first time for boundary layer problem of shrinking sheet and the governing partial differential equations are rehabilitated into ordinary differential equations using similarity transformations. The simplified nonlinear boundary value problem is solved by Runge-Kutta method after converting into the system of initial value problem using shooting method. Dual solutions are obtained graphically and results are shown for various parameters involved in the flow equations. Numerical values of skin friction coefficients are also computed.
MHD copper-water nanofluid flow and heat transfer through convergent-divergent channel
Azimi, Mohammadreza; Riazi, Rouzbeh [Faculty of New Sciences and TechnologiesUniversity of Tehran, Tehran (Iran, Islamic Republic of)
2016-10-15
This work is focused on the analytical solution of a nanofluid consisting of pure water with copper nanoparticle steady flow through convergent-divergent channel. The velocity and temperature distributions are determined by a novel method called Reconstruction of variational iteration method (RVIM). The effects of angle of the channel, Reynolds and Hartmann numbers on the nanofluid flow are then investigated. The influences of solid volume fraction and Eckert number upon the temperature distribution are discussed. Based on the achieved results, Nusselt number enhances with increment of solid volume fraction of nanoparticles, Reynolds and Eckert numbers. Also the fourth order Runge-Kutta method, which is one of the most relevant numerical techniques, is used to investigate the validity and accuracy of RVIM and good agreement is observed between the solutions obtained from RVIM and some known numerical results.
Scrutiny of underdeveloped nanofluid MHD flow and heat conduction in a channel with porous walls
M. Fakour
2014-11-01
Full Text Available In this paper, laminar fluid flow and heat transfer in channel with permeable walls in the presence of a transverse magnetic field is investigated. Least square method (LSM for computing approximate solutions of nonlinear differential equations governing the problem. We have tried to show reliability and performance of the present method compared with the numerical method (Runge–Kutta fourth-rate to solve this problem. The influence of the four dimensionless numbers: the Hartmann number, Reynolds number, Prandtl number and Eckert number on non-dimensional velocity and temperature profiles are considered. The results show analytical present method is very close to numerically method. In general, increasing the Reynolds and Hartman number is reduces the nanofluid flow velocity in the channel and the maximum amount of temperature increase and increasing the Prandtl and Eckert number will increase the maximum amount of theta.
Md. Sarwar Alam
2016-01-01
Full Text Available The present work inspects the entropy generation on radiative heat transfer in the flow of variable thermal conductivity optically thin viscous Cu–water nanofluid with an external magnetic field through a parallel isothermal plate channel. Our approach uses the power series from the governing non-linear differential equations for small values of thermal conductivity variation parameter which are then analysed by various generalizations of Hermite- Padé approximation method. The influences of the pertinent flow parameters on velocity, temperature, thermal conductivity criticality conditions and entropy generation are discussed quantitatively both numerically and graphically. A stability analysis has been performed for the rate of heat transfer which signifies that the lower solution branch is stable and physically acceptable, whereas the upper solution branch is unstable.
Radiation and chemical reaction effects on MHD flow along a moving vertical porous plate
Ramana Reddy G.V.
2016-02-01
Full Text Available This paper presents an analysis of the effects of magnetohydrodynamic force and buoyancy on convective heat and mass transfer flow past a moving vertical porous plate in the presence of thermal radiation and chemical reaction. The governing partial differential equations are reduced to a system of self-similar equations using the similarity transformations. The resultant equations are then solved numerically using the fourth order Runge-Kutta method along with the shooting technique. The results are obtained for the velocity, temperature, concentration, skin-friction, Nusselt number and Sherwood number. The effects of various parameters on flow variables are illustrated graphically, and the physical aspects of the problem are discussed.
MHD Flow with Hall Current and Ion-Slip Effects due to a Stretching Porous Disk
Faiza M. N. El-Fayez
2013-01-01
Full Text Available A partially ionized fluid is driven by a stretching disk, in the presence of a magnetic field that is strong enough to produce significant hall current and ion-slip effects. The limiting behavior of the flow is studied, as the magnetic field strength grows indefinitely. The flow variables are properly scaled, and uniformly valid asymptotic expansions of the velocity components are obtained. The leading order approximations show sinusoidal behavior that is decaying exponentially, as we move away from the disk surface. The two-term expansions of the radial and azimuthal surface shear stress components, as well as the far field inflow speed, compare well with the corresponding finite difference solutions, even at moderate magnetic fields. The effect of mass transfer (suction or injection through the disk is also considered.
Some unsteady turbulent MHD flows in flat channels and circular pipes
Nemirovskiy, Yu.V.; Kheynloo, Ya.L.
1979-04-01
An analysis is made of the kinematic characteristics of turbulent pulsating flow of an electrically conductive fluid in a flat channnel and in a circular pipe in longitudinal and azimuthal magnetic fields. It is assumed that walls are impermeable, and that all averaged flow characteristics depend only on the transverse coordinate in accordance with the equation of continuity (the medium is taken as incompressible) and equations of motion of electrically conductive media. Disregarding the Hall effect, a system of equations is derived for the averaged velocity components and the motion of the medium. The calculations are based on a semiempirical method developed by the authors. The theoretical results agree satisfactorily with experimental data. 4 references, 2 figures.
Chinyoka, T.; Makinde, O. D.
2013-01-01
The thermodynamic second law analysis is utilized to investigate the inherent irreversibility in an unsteady hydromagnetic generalized Couette flow with variable electrical conductivity in the presence of induced electric field. Based on some simplified assumption, the model nonlinear governing equations are obtained and solved numerically using semidiscretization finite difference techniques. Effects of various thermophysical parameters on the fluid velocity, temperature, current density, skin friction, the Nusselt number, entropy generation number, and the Bejan number are presented graphically and discussed quantitatively. PMID:23956691
Heat Transfer on Steady MHD rotating flow through porous medium in a parallel plate channel
Dr. G. Prabhakara Rao,
2015-04-01
Full Text Available We discussed the combined effects of radiative heat transfer and a transverse magnetic field on steady rotating flow of an electrically conducting optically thin fluid through a porous medium in a parallel plate channel and non-uniform temperatures at the walls. The analytical solutions are obtained from coupled nonlinear partial differential equations for the problem. The computational results are discussed quantitatively with the aid of the dimensionless parameters entering in the solution.
Numerical investigation of MHD flow of blood and heat transfer in a stenosed arterial segment
Majee, Sreeparna; Shit, G. C.
2017-02-01
A numerical investigation of unsteady flow of blood and heat transfer has been performed with an aim to provide better understanding of blood flow through arteries under stenotic condition. The blood is treated as Newtonian fluid and the arterial wall is considered to be rigid having deposition of plaque in its lumen. The heat transfer characteristic has been analyzed by taking into consideration of the dissipation of energy due to applied magnetic field and the viscosity of blood. The vorticity-stream function formulation has been adopted to solve the problem using implicit finite difference method by developing well known Peaceman-Rachford Alternating Direction Implicit (ADI) scheme. The quantitative profile analysis of velocity, temperature and wall shear stress as well as Nusselt number is carried out over the entire arterial segment. The streamline and temperature contours have been plotted to understand the flow pattern in the diseased artery, which alters significantly in the downstream of the stenosis in the presence of magnetic field. Both the wall shear stress and Nusselt number increases with increasing magnetic field strength. However, wall shear stress decreases and Nusselt number enhances with Reynolds number. The results show that with an increase in the magnetic field strength upto 8 T, does not causes any damage to the arterial wall, but the study is significant for assessing temperature rise during hyperthermic treatment.
Ali, M. M.; Alim, M. A.; Maleque, M. A.; Ahmed, Syed Sabbir
2017-06-01
A numerical study has been carried out to analyze the flow and heat transfer characteristics due to the effects of magnetohydrodynamic free convection flow in a differentially heated enclosure having a hot tilted square block. The vertical and horizontal walls of the cavity are non-uniformly heated while the walls of the tilted block are uniformly heated. The basic partial differential equations of the physical problem are solved numerically using finite element technique along with Galerkin's weighted residual simulation. Calculations have been performed for different values of buoyancy parameter (102 ≤ Ra ≤ 105) and magnetic field parameter (0 ≤ Ha ≤ 60) and obtained results are illustrated in terms of streamlines, isotherms, average Nusselt number and average temperature. The results show that the flow pattern and temperature distributions affected noticeably for the effect of aforementioned parameters. In addition, an increase in average Nusselt number is found for the whole range of Rayleigh number and average temperature decreased for increasing Rayleigh number. Comparison between the obtained results and the previously published results on the basis of special case is a good agreement.
MHD three-dimensional flow of nanofluid with velocity slip and nonlinear thermal radiation
Hayat, Tasawar [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia); Imtiaz, Maria, E-mail: mi_qau@yahoo.com [Department of Mathematics, Quaid-I-Azam University 45320, Islamabad 44000 (Pakistan); Alsaedi, Ahmed; Kutbi, Marwan A. [Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589 (Saudi Arabia)
2015-12-15
An analysis has been carried out for the three dimensional flow of viscous nanofluid in the presence of partial slip and thermal radiation effects. The flow is induced by a permeable stretching surface. Water is treated as a base fluid and alumina as a nanoparticle. Fluid is electrically conducting in the presence of applied magnetic field. Entire different concept of nonlinear thermal radiation is utilized in the heat transfer process. Different from the previous literature, the nonlinear system for temperature distribution is solved and analyzed. Appropriate transformations reduce the nonlinear partial differential system to ordinary differential system. Convergent series solutions are computed for the velocity and temperature. Effects of different parameters on the velocity, temperature, skin friction coefficient and Nusselt number are computed and examined. It is concluded that heat transfer rate increases when temperature and radiation parameters are increased. - Highlights: • Three-dimensional nanofluid flow with partial slip and nonlinear thermal radiation is studied. • Increasing values of velocity slip parameter decrease the velocity profiles. • The temperature increases via larger nanoparticle volume fraction. • Surface temperature gradient increases for higher temperature and radiation parameters.
S. S. Das, L. K. Mishra, P. K. Mishra
2011-09-01
Full Text Available This paper investigates the effect of heat source on free convective flow of a viscous incompressible electrically conducting fluid through a porous medium bounded by an oscillating porous plate in the slip flow regime in presence of a transverse magnetic field. The governing equations of the flow field are solved analytically and the expressions for velocity, temperature, skin friction t and the heat flux in terms of Nusselts number Nu are obtained. The effects of the important flow parameters such as magnetic parameter M, permeability parameter Kp, Grashof number for heat transfer Gr, heat source parameter S and rarefaction parameter R on the velocity of the flow field are analyzed quantitatively with the help of figures.
Chandaneswar Midya
2012-01-01
An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible Buid over a linearly shrinking surface is presented. The Row is permeated by an externally applied magnetic Geld normal to the plane of the flow. The equations governing the Row and concentration Reid are reduced into a set of nonlinear ordinary differential equations using similarity variables. Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall mass flux (PMF) as boundary conditions. The study reveals that the concentration over a shrinking sheet is signiRcantly different from that of a stretching surface. It s found that te solute boundary layer thickness is enhanced with the increasing values of the Schmidt number and the power-law index parameter, but decreases with enhanced vaJues of magnetic and reaction rate parameters for the PSC case. For the PMF case, the solute boundary layer thickness decreases with the increase of the Schmidt number, magnetic and reaction rate parameter for power-law index parameter n = 0. Negative solute boundary layer thickness is observed for the PMF case when n = 1 and 2, and these facts may not be realized in real-world applications.%An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible fluid over a linearly shrinking surface is presented.The flow is permeated by an externally applied magnetic field normal to the plane of the flow.The equations governing the flow and concentration field are reduced into a set of nonlinear ordinary differential equations using similarity variables.Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall
Heat transfer to MHD oscillatory dusty fluid flow in a channel filled with a porous medium
Om Prakash; O D Makinde; Devendra Kumar; Y K Dwivedi
2015-06-01
In this paper, we examine the combined effects of thermal radiation, buoyancy force and magnetic field on oscillatory flow of a conducting optically thin dusty fluid through a vertical channel filled with a saturated porous medium. The governing partial differential equations are obtained and solved analytically by variable separable method. Numerical results depicting the effects of various embedded parameters like radiation number, Hartmann number and Grashof number on dusty fluid velocity profiles, temperature profiles, Nusselt number and skin friction coefficient are presented graphically and discussed qualitatively.
MHD Flow with Hall current and Joule Heating Effects over an Exponentially Stretching Sheet
Srinivasacharya, D.; Jagadeeshwar, P.
2017-06-01
The aim of the present paper is to study the influence of Hall current and Joule heating on flow, heat and mass transfer over an exponentially stretching sheet in a viscous fluid. Using similarity transformations the governing nonlinear coupled equations are converted into ordinary differential equations. These equations are linearized using the successive linearization method and then solved using the Chebyshev pseudo spectral method. The influence of magnetic parameter, Hall parameter, suction/injection parameter and slip parameter on the physical quantities are presented graphically. The obtained results are compared with the previously published results for special cases.
Chandrakala P.
2014-02-01
Full Text Available The effects of thermal radiation on a flow past an impulsively started infinite vertical plate in the presence of a magnetic field have been studied. The fluid considered is a gray, absorbing-emitting radiation but non-scattering medium. The dimensionless governing equations are solved by an efficient, more accurate, unconditionally stable and fast converging implicit scheme. The effects of velocity and temperature for different parameters such as the thermal radiation, magnetic field, Schmidt number, thermal Grashof number and mass Grashof number are studied. It is observed that the velocity decreases in the presence of thermal radiation or a magnetic field
A New Code for Numerical Simulation of MHD Astrophysical Flows With Chemistry
Kulikov, Igor; Protasov, Viktor
2016-01-01
The new code for numerical simulation of magnetic hydrodynamical astrophysical flows with consideration of chemical reactions is given in the paper. At the heart of the code - the new original low-dissipation numerical method based on a combination of operator splitting approach and piecewise-parabolic method on the local stencil. The details of the numerical method are described; the main tests and the scheme of parallel implementation are shown. The chemodynamics of the hydrogen while the turbulent formation of molecular clouds is modeled.
Garg B.P.
2015-02-01
Full Text Available An analysis of an oscillatory magnetohydrodynamic (MHD convective flow of a second order (viscoelastic, incompressible, and electrically conducting fluid through a porous medium bounded by two infinite vertical parallel porous plates is presented. The two porous plates with slip-flow condition and the no-slip condition are subjected respectively to a constant injection and suction velocity. The pressure gradient in the channel varies periodically with time. A magnetic field of uniform strength is applied in the direction perpendicular to the planes of the plates. The induced magnetic field is neglected due to the assumption of a small magnetic Reynolds number. The temperature of the plate with no-slip condition is non-uniform and oscillates periodically with time and the temperature difference of the two plates is assumed high enough to induce heat radiation. The entire system rotates in unison about the axis perpendicular to the planes of the plates. Adopting complex variable notations, a closed form solution of the problem is obtained. The analytical results are evaluated numerically and then presented graphically to discuss in detail the effects of different parameters of the problem. The velocity, temperature and the skin-friction in terms of its amplitude and phase angle have been shown graphically to observe the effects of the viscoelastic parameter γ, rotation parameter Ω, suction parameter λ , Grashof number Gr, Hartmann number M, the pressure A, Prandtl number Pr, radiation parameter N and the frequency of oscillation ω .
Initial characterization of V-4Cr-4Ti and MHD coatings exposed to flowing Li
Pint, B.A. [Materials Science and Technology Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6156 (United States)], E-mail: pintba@ornl.gov; Pawel, S.J.; Howell, M.; Moser, J.L.; Garner, G.W.; Santella, M.L.; Tortorelli, P.F.; Wiffen, F.W.; DiStefano, J.R. [Materials Science and Technology Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, TN 37831-6156 (United States)
2009-04-30
A mono-metallic V-4Cr-4Ti thermal convection loop was operated in vacuum ({approx}10{sup -5} Pa) at a maximum Li temperature of 700 deg. C for 2355 h and Li flow rate of 2-3 cm/s. Two-layer, physical vapor deposited Y{sub 2}O{sub 3}-vanadium, electrically insulating coatings on V-4Cr-4Ti substrates as well as tensile and sheet specimens were located in the flow path in the hot and cold legs. After exposure, specimens at the top of the hot leg showed a maximum mass loss equivalent to {approx}1.3 {mu}m of metal loss. Elsewhere, small mass gains were observed on the majority of specimens resulting in an increase in hardness and room temperature yield stress and a decrease in ductility consistent with the observed uptake of N and C from the Li. Specimens that lost mass showed a decrease in yield stress and hardness. Profilometry showed no significant thickness loss from the coatings.
MHD flow over a permeable stretching/shrinking sheet of a nanofluid with suction/injection
Sandeep Naramgari
2016-06-01
Full Text Available In this study we analyzed the influence of thermal radiation and chemical reaction on two dimensional steady magnetohydrodynamic flow of a nanofluid past a permeable stretching/shrinking sheet in the presence of suction/injection. We considered nanofluid volume fraction on the boundary is submissive controlled, which makes the present study entirely different from earlier studies and physically more realistic. The equations governing the flow are solved numerically. Effects of non-dimensional governing parameters on velocity, temperature and concentration profiles are discussed and presented through graphs. Also, coefficient of skin friction and local Nusselt number is investigated for stretching/shrinking and suction/injection cases separately and presented through tables. Comparisons with existed results are presented. Present results have an excellent agreement with the existed studies under some special assumptions. Results indicate that the enhancement in Brownian motion and thermophoresis parameters depreciates the nanoparticle concentration and increases the mass transfer rate. Dual solutions exist only for certain range of stretching/shrinking and suction/injection parameters.
Simulation of MHD CuO–water nanofluid flow and convective heat transfer considering Lorentz forces
Sheikholeslami, Mohsen; Bandpy, Mofid Gorji [Department of Mechanical Engineering, Babol University of Technology, Babol (Iran, Islamic Republic of); Ellahi, R., E-mail: rellahi@engr.ucr.edu [Department of Mechanical Engineering, University of California Riverside (United States); Department of Mathematics and Statistics, FBAS, IIUI, H-10 Sector, Islamabad (Pakistan); Zeeshan, A. [Department of Mathematics and Statistics, FBAS, IIUI, H-10 Sector, Islamabad (Pakistan)
2014-11-15
Magnetic field effect on CuO–water nanofluid flow and heat transfer in an enclosure which is heated from below is investigated. Lattice Boltzmann method is applied to solve the governing equations. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL (Koo–Kleinstreuer–Li) correlation. In this model effect of Brownian motion on the effective thermal conductivity is considered. Effect of active parameter such as: Hartmann number, heat source length, nanoparticle volume fraction and Rayleigh numbers on the flow and heat transfer characteristics have been examined. The results reveal that the enhancement in heat transfer increases as Hartmann number and heat source length increase but it decreases with increase of Rayleigh number. Also it can be found that effect of Hartmann number and heat source length is more pronounced at high Rayleigh number. - Highlights: • This paper analyses the magnetic effect on CuO–water nanofluid. • Koo–Kleinstreuer–Li correlation and Lattice Boltzmann method are used. • Effects of pertinent parameters are presented through tables and graphs.
Numerical investigation of the turbulent MHD flow in a circular pipe with transverse magnetic field
Dechamps, Xavier; Rasquin, Michel; Degrez, Gérard
2012-11-01
In modern industrial metallurgical processes, external magnetic fields are often applied to control the motion of liquid metals by a non-intrusive means. The desired results are for example the damping of unwanted motions or the homogenization of a liquid zone in a partially solidified ingot. Because of the commonly appearing parameters in these processes, one can assume the quasi-static assumption for the magnetohydrodynamic equations. Here we are interested in the numerical study of the turbulent flow of a liquid metal inside an electrically insulated pipe with a transverse uniform magnetic field. For this purpose, we will use a hybrid spectral/finite element solver, which allows to study complex flows in Cartesian and axisymmetric geometries. For the case of interest, we consider a bulk Reynolds number of 8200 and a Hartmann number ranging between 5 and 30. Here, the main points of interest are the evolution of the skin friction coefficient as a function of the ratio of the Hartmann number Ha over the Reynolds number Re (with 0 FNRS) is aknowledged.
Om Prakash; Devendra Kumar; Y K Dwivedi
2012-12-01
The paper investigates the effects of heat transfer in MHD flow of viscoelastic stratified fluid in porous medium on a parallel plate channel inclined at an angle . A laminar convection flow for incompressible conducting fluid is considered. It is assumed that the plates are kept at different temperatures which decay with time. The partial differential equations governing the flow are solved by perturbation technique. Expressions for the velocity of fluid and particle phases, temperature field, Nusselt number, skin friction and flow flux are obtained within the channel. The effects of various parameters like stratification factor, magnetic field parameter, Prandtl number on temperature field, heat transfer, skin friction, flow flux, velocity for both the fluid and particle phases are displayed through graphs and discussed numerically.
Radiation effects on the MHD flow near the stagnation point of a stretching sheet: revisited
Pop, Ioan; Ishak, Anuar; Aman, Fazlina
2011-10-01
This paper considers the effects of radiation on the flow near the two-dimensional stagnation point of a stretching sheet immersed in a viscous and incompressible electrically conducting fluid in the presence of an applied constant magnetic field. The external velocity and the stretching velocity of the sheet are assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a system of ordinary differential equations using a similarity transformation, before being solved numerically by the Keller-box method. The features of the heat transfer characteristics for different values of the governing parameters are analyzed and discussed. The results indicate that the heat transfer rate at the surface decreases in the presence of radiation.
Prasad K.V.
2016-02-01
Full Text Available The present analysis is focused on the study of the magnetic effect on coupled heat and mass transfer by mixed convection boundary layer flow over a slender cylinder in the presence of a chemical reaction. The buoyancy effect due to thermal diffusion and species diffusion is investigated. Employing suitable similarity transformations, the governing equations are transformed into a system of coupled non-linear ordinary differential equations and are solved numerically via the implicit, iterative, second order finite difference method. The numerical results obtained are compared with the available results in the literature for some special cases and the results are found to be in excellent agreement. The velocity, temperature, and the concentration profiles are presented graphically and analyzed for several sets of the pertinent parameters. The pooled effect of the thermal and mass Grashof number is to enhance the velocity and is quite the opposite for temperature and the concentration fields.
Akbarzadeh, Pooria
2016-05-12
In this paper, magneto-hydrodynamic blood flows through porous arteries are numerically simulated using a locally modified homogenous nanofluids model. Blood is taken into account as the third-grade non-Newtonian fluid containing nanoparticles. In the modified nanofluids model, the viscosity, density, and thermal conductivity of the solid-liquid mixture (nanofluids) which are commonly utilized as an effective value, are locally combined with the prevalent single-phase model. The modified governing equations are solved numerically using Newton's method and a block tridiagonal matrix solver. The results are compared to the prevalent nanofluids single-phase model. In addition, the efficacies of important physical parameters such as pressure gradient, Brownian motion parameter, thermophoresis parameter, magnetic-field parameter, porosity parameter, and etc. on temperature, velocity and nanoparticles concentration profiles are examined.
Thermophoretic MHD slip flow over a permeable surface with variable fluid properties
K. Das
2015-03-01
Full Text Available The present paper focuses on the analysis of thermophoretic hydromagnetic slip flow over a permeable flat plate with convective surface heat flux at the boundary and temperature dependent fluid properties in the presence of non-uniform heat source/sink. The transverse magnetic field is assumed to be a function of the distance from the origin. Also it is assumed that the liquid viscosity and the thermal conductivity vary as an inverse function and a linear function of temperature, respectively. The shooting method is employed to yield the numerical solutions for the model. Results show that the thermal boundary layer thickness reduces with increase of surface convection parameter whereas reverse effect occurs for viscosity parameter. It is also observed that the thermophoretic parameter decreases the concentration distribution across the boundary layer.
MHD flow of Burger's fluid over an off-centered rotating disk in a porous medium
Khan, Najeeb Alam; Khan, Sidra; Ullah, Saif
2015-08-01
In this study, off-centered stagnation flow of three dimensional Burger's fluid over an infinite rotating disk in a porous medium with a uniform magnetic field, which is applying normal to the disk, is investigated. A uniform suction/injection is applied through the surface of the porous disk. The structure has been modeled in the form of ordinary differential equations, which are reduced from partial differential equations by using the similarity transformation. Analytical solution is obtained by non-perturbation technique of homotopy analysis method (HAM). The influence of non-dimensional parameters on velocity profile is presented in graphical form and the numerical comparison is made with the viscous fluid as a special case.
MHD Energy Bypass Scramjet Engine
Mehta, Unmeel B.; Bogdanoff, David W.; Park, Chul; Arnold, Jim (Technical Monitor)
2001-01-01
Revolutionary rather than evolutionary changes in propulsion systems are most likely to decrease cost of space transportation and to provide a global range capability. Hypersonic air-breathing propulsion is a revolutionary propulsion system. The performance of scramjet engines can be improved by the AJAX energy management concept. A magneto-hydro-dynamics (MHD) generator controls the flow and extracts flow energy in the engine inlet and a MHD accelerator downstream of the combustor accelerates the nozzle flow. A progress report toward developing the MHD technology is presented herein. Recent theoretical efforts are reviewed and ongoing experimental efforts are discussed. The latter efforts also include an ongoing collaboration between NASA, the US Air Force Research Laboratory, US industry, and Russian scientific organizations. Two of the critical technologies, the ionization of the air and the MHD accelerator, are briefly discussed. Examples of limiting the combustor entrance Mach number to a low supersonic value with a MHD energy bypass scheme are presented, demonstrating an improvement in scramjet performance. The results for a simplified design of an aerospace plane show that the specific impulse of the MHD-bypass system is better than the non-MHD system and typical rocket over a narrow region of flight speeds and design parameters. Equilibrium ionization and non-equilibrium ionization are discussed. The thermodynamic condition of air at the entrance of the engine inlet determines the method of ionization. The required external power for non-equilibrium ionization is computed. There have been many experiments in which electrical power generation has successfully been achieved by magneto-hydrodynamic (MHD) means. However, relatively few experiments have been made to date for the reverse case of achieving gas acceleration by the MHD means. An experiment in a shock tunnel is described in which MHD acceleration is investigated experimentally. MHD has several
Effects of chemical reactions on MHD micropolar fluid flow past a vertical plate in slip-flow regime
R.C.Chaudhary; Abhay Kumar Jha
2008-01-01
Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical reaction of the first order.A uniform magnetic field acts perpendicular to the porous surface absorb micropolar fluid with a suction velocity varying with time.The free stream velocity follows an exponentially increasing or decreasing small perturbation law.Using the approximate method,the expressions for the velocity microrotation,temperature,and concentration are obtained.Futher,the results of the skin friction coefficient,the couple stress coefficient,and the rate of heat and mass transfer at the wall are presented with various values of fluid properties and flow conditions.
N. Sandeep
2016-03-01
Full Text Available We analyzed the unsteady magnetohydrodynamic radiative flow and heat transfer characteristics of a dusty nanofluid over an exponentially permeable stretching surface in presence of volume fraction of dust and nano particles. We considered two types of nanofluids namely Cu-water and CuO-water embedded with conducting dust particles. The governing equations are transformed into nonlinear ordinary differential equations by using similarity transformation and solved numerically using Runge–Kutta based shooting technique. The effects of non-dimensional governing parameters namely magneticfield parameter, mass concentration of dust particles, fluid particle interaction parameter, volume fraction of dust particles, volume fraction of nano particles, unsteadiness parameter, exponential parameter, radiation parameter and suction/injection parameter on velocity profiles for fluid phase, dust phase and temperature profiles are discussed and presented through graphs. Also, friction factor and Nusselt numbers are discussed and presented for two dusty nanofluids separately. Comparisons of the present study were made with existing studies under some special assumptions. The present results have an excellent agreement with existing studies. Results indicated that the enhancement in fluid particle interaction increases the heat transfer rate and depreciates the wall friction. Also, radiation parameter has the tendency to increase the temperature profiles of the dusty nanofluid.
Effects of MHD on Cu–water nanofluid flow and heat transfer by means of CVFEM
Sheikholeslami, M.; Gorji Bandpy, M. [Department of Mechanical Engineering, Mazandaran Institute of Technology, Babol, Islamic Republic of Iran (Iran, Islamic Republic of); Department of Mechanical Engineering, Babol University of Technology, Babol, Islamic Republic of Iran (Iran, Islamic Republic of); Ellahi, R., E-mail: rellahi@engr.ucr.edu [Department of Mechanical Engineering, Bourns Hall A373, University of California Riverside (United States); Department of Mathematics and Statistics, FBAS, IIUI, H-10 Sector, Islamabad (Pakistan); Hassan, Mohsan [Department of Mathematics and Statistics, FBAS, IIUI, H-10 Sector, Islamabad (Pakistan); Soleimani, Soheil [Department of Mechanical and Materials Engineering, Florida International University, Miami, FL 33199 (United States)
2014-01-15
In this study magnetohydrodynamic effect on natural convection heat transfer of Cu–water nanofluid in an enclosure with hot elliptic cylinder is investigated. The governing equations of fluid motion and heat transfer in their vorticity stream function form are used to simulate the nanofluid flow and heat transfer. Control Volume based Finite Element Method (CVFEM) is applied to solve these equations. The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. The calculations are performed for different governing parameters such as the Hartmann number, Rayleigh number, nanoparticle volume fraction and inclined angle of inner cylinder. Also a correlation of average Nusselt number corresponding to active parameters is presented. The results indicate that Nusselt number is an increasing function of nanoparticle volume fraction, Rayleigh numbers and inclination angle while it is a decreasing function of Hartmann number. Also it can be found that increasing Rayleigh number leads to decrease heat transfer enhancement while opposite trend is observed with augment of Hartmann number. - Highlights: • Magnetic effect on natural convection heat transfer of Cu–water nanofluid is presented via Control Volume based Finite Element Method (CVFEM). • The effective thermal conductivity and viscosity of nanofluid are calculated using the Maxwell–Garnetts (MG) and Brinkman models, respectively. • The calculations were performed for Hartmann number, Rayleigh number, nanoparticle volume fraction and inclined angle of elliptic inner cylinder. • A correlation of Nusselt number corresponding is also presented. • Comparison of present work is made with the existing literature.
Nickeler, D H; Fahr, H -J
2012-01-01
A stellar wind passing through the reverse shock is deflected into the astrospheric tail and leaves the stellar system either as a sub-Alfvenic or as a super-Alfvenic tail flow. An example is our own heliosphere and its heliotail. We present an analytical method of calculating stationary, incompressible, and field-aligned plasma flows in the astrotail of a star. We present a recipe for constructing an astrosphere with the help of only a few parameters, like the inner Alfven Mach number and the outer Alfven Mach number, the magnetic field strength within and outside the stellar wind cavity, and the distribution of singular points of the magnetic field within these flows. Within the framework of a one-fluid approximation, it is possible to obtain solutions of the MHD equations for stationary flows from corresponding static MHD equilibria, by using noncanonical mappings of the canonical variables. The canonical variables are the Euler potentials of the magnetic field of magnetohydrostatic equilibria. Thus we sta...
Ali, Farhad; Saqib, Muhammad; Khan, Ilyas; Sheikh, Nadeem Ahmad; Jan, Syed Aftab Alam
2017-02-01
This paper carries out an exact analysis of the MHD free convection flow of a Walters'-B fluid over an oscillating isothermal vertical plate embedded in a porous medium. Exact solutions are produced for velocity, temperature and concentration with the aid of the Laplace transform technique. Similarly, at the wall, the corresponding shear stress is also calculated from the velocity expression. The obtained results confirm an excellent agreement with previously published work. The influence of various pertinent parameters is plotted and illustrated graphically. Finally, the numerical results for the skin friction are exhibited in tabular form.
Hossain, Delowar; Samad, Abdus; Alam, Mahmud
2017-06-01
The ion-slip effects on unsteady MHD free convection flow past an infinite vertical porous plate with the effect of temperature stratified porous medium in a rotating system with viscous dissipation and Joule heating has been studied numerically. Introducing a time dependent suction to the plate, a similarity procedure has been adopted by taking a time dependent similarity parameter. The governing differential equations are transformed by introducing usual similarity variables. The resultant equations are solved numerically using Runge-Kutta method along with shooting technique. Resulting non-dimensional velocity and temperature profiles are then presented graphically for different values of the parameters entering into the problem.
Hamid, Rohana Abdul; Nazar, Roslinda
2017-08-01
In this paper, the problem of magnetohydrodynamic (MHD) boundary layer flow and heat transfer of a nanofluid with the influences of the chemical reaction and thermal radiation over an exponentially shrinking sheet is studied numerically. The model used for the nanofluid is called the Buongiorno model which incorporates the effects of the Brownian motion and thermophoresis. The governing dimensionless ordinary differential equations are solved using the bvp4c method. The effects of the magnetic field parameter, thermal radiation parameter and chemical reaction parameter on the velocity, temperature and concentration profiles of the nanofluid over an exponentially permeable shrinking sheet are discussed and presented through graphs and tables.
Jha A.K.
2014-02-01
Full Text Available The present paper deals with the unsteady motion of an MHD free convection flow of an incompressible non- Newtonian viscoelastic fluid past an infinite vertical plate in the presence of a heat source and Soret effect. A parametric study illustrating the influence of various parameters on the temperature, velocity as well as on the skin-friction and rate of heat transfer is conducted. The results of the effect of the magnetic field, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions are examined and shown graphically
Sheikh, Mariam; Abbas, Zaheer
2015-12-01
The effects of chemical reaction and heat generation/absorption on MHD flow over an oscillatory stretching surface in a viscous fluid have been studied in the presence of thermophoresis. The porous plate is oscillated back and forth in its own plane and suction/injection is also taking into account. The similarity solution of the developed non-linear governing partial differential equations is constructed in the form of series using homotopy analysis method. The convergence of the obtained series solutions is discussed in the whole domain (0 ≤ η ≤ ∞) . A parametric study of the all governing parameters is accomplished and the physical results are shown graphically.
T. Hayat; M. Mustafa; S. Obaidat
2011-01-01
Magnetohydrodynamic (MHD) mixed convection stagnation-point flow and heat transfer of power-law fluids towards a stretching surface is investigated.The homotopy analysis method (HAM) is used in finding the series solution for a nonlinear problem.Closed form solutions for velocity and temperature fields are presented in the limiting cases.Graphical results are shown.It is found that velocity and temperature are decreasing functions of power law index.Numerical computations for shear stress coefficient and local Nusselt number are reported.The present results are also compared with the existing numerical solution in a limiting sense.
J. Anand Rao
2012-01-01
Full Text Available In the present paper , an analysis is carried out the chemical reaction effects on an unsteady magneto hydrodynamics (MHD free convection fluid flow past a semi-infinite vertical plate embedded in a porous medium with heat absorption was formulated. The non dimensional governing equations are formed with the help of suitable dimensionless governing parameter. The resultant coupled non dimensional governing equations are solved by a finite element method. The effect of important physical parameters on the velocity, temperature and concentration are shown graphically and also discussed the skin-friction coefficient, Nusselt number and Sherwood number are shown in tables.
EL-Dabe, N. T.; Attia, H. A.; Essawy, M. A. I.; Ramadan, A. A.; Abdel-Hamid, A. H.
2016-11-01
The steady MHD axisymmetric flow of an incompressible viscous electrically conducting nanofluid impinging on a permeable plate is investigated with heat and mass transfer. An external uniform magnetic field as well as a uniform inflow, in the presence of either suction or injection, are applied normal to the plate. The effects of heat (generation/absorption) and chemical reaction have been accentuated. This study indicates the incorporated influence of both the thermophoresis phenomenon and the Brownian behavior. Numerical solutions for the governing non-linear momentum, energy and nanoparticle equations have been obtained. The rates of heat and mass transfer are presented and discussed.
Z. G. Makukula
2011-01-01
Full Text Available We use recent innovative solution techniques to investigate the problem of MHD viscous flow due to a shrinking sheet with a chemical reaction. A comparison is made of the convergence rates, ease of use, and expensiveness (the number of iterations required to give convergent results of three seminumerical techniques in solving systems of nonlinear boundary value problems. The results were validated using a multistep, multimethod approach comprising the use of the shooting method, the Matlab bvp4c numerical routine, and with results in the literature.
Md. Jashim Uddin
2012-01-01
Full Text Available Steady viscous incompressible MHD laminar boundary layer slip flow of an electrically conducting nanofluid over a convectively heated permeable moving linearly stretching sheet has been investigated numerically. The effects of Brownian motion, thermophoresis, magnetic field, and heat generation/absorption are included in the nanofluid model. The similarity transformations for the governing equations are developed. The effects of the pertinent parameters, Lewis number, magnetic field, Brownian motion, heat generation, thermophoretic, momentum slip and Biot number on the flow field, temperature, skin friction factor, heat transfer rate, and nanoparticle, volume fraction rate are displayed in both graphical and tabular forms. Comparisons of analytical (for special cases and numerical solutions with the existing results in the literature are made and is found a close agreement, that supports the validity of the present analysis and the accuracy of our numerical computations. Results for the reduced Nusselt and Sherwood numbers are provided in tabular and graphical forms for various values of the flow controlling parameters which govern the momentum, energy, and the nanoparticle volume fraction transport in the MHD boundary layer.
Characteristics of laminar MHD fluid hammer in pipe
Huang, Z.Y.; Liu, Y.J., E-mail: yajun@scut.edu.cn
2016-01-01
As gradually wide applications of MHD fluid, transportation as well as control with pumps and valves is unavoidable, which induces MHD fluid hammer. The paper attempts to combine MHD effect and fluid hammer effect and to investigate the characteristics of laminar MHD fluid hammer. A non-dimensional fluid hammer model, based on Navier–Stocks equations, coupling with Lorentz force is numerically solved in a reservoir–pipe–valve system with uniform external magnetic field. The MHD effect is represented by the interaction number which associates with the conductivity of the MHD fluid as well as the external magnetic field and can be interpreted as the ratio of Lorentz force to Joukowsky force. The transient numerical results of pressure head, average velocity, wall shear stress, velocity profiles and shear stress profiles are provided. The additional MHD effect hinders fluid motion, weakens wave front and homogenizes velocity profiles, contributing to obvious attenuation of oscillation, strengthened line packing and weakened Richardson annular effect. Studying the characteristics of MHD laminar fluid hammer theoretically supplements the gap of knowledge of rapid-transient MHD flow and technically provides beneficial information for MHD pipeline system designers to better devise MHD systems. - Highlights: • Characteristics of laminar MHD fluid hammer are discussed by simulation. • MHD effect has significant influence on attenuation of wave. • MHD effect strengthens line packing. • MHD effect inhibits Richardson annular effect.
K.V.S. Raju
2014-06-01
Full Text Available This paper deals with a steady MHD forced convective flow of a viscous fluid of finite depth in a saturated porous medium over a fixed horizontal channel with thermally insulated and impermeable bottom wall in the presence of viscous dissipation and joule heating. The governing equations are solved in the closed form and the exact solutions are obtained for velocity and temperature distributions when the temperatures on the fixed bottom and on the free surface are prescribed. The expressions for flow rate, mean velocity, temperature, mean temperature, mean mixed temperature in the flow region and the Nusselt number on the free surface have been obtained. The cases of large and small values of porosity coefficients have been obtained as limiting cases. Further, the cases of small depth (shallow fluid and large depth (deep fluid are also discussed. The results are presented and discussed with the help of graphs.
Reed, C.B.; Mattas, R.F.; Smith, D.L.; Chung, H.; Tsai, H.-C. [Argonne National Lab., IL (United States); Morgan, G.D.; Wille, G.W. [McDonnell Douglas Aerospace, St. Louis, MO (United States). High Energy Systems; Johnson, W.R. [General Atomics, San Diego, CA (United States); Young, C. [Century Tubes, Inc., San Diego, CA (United States)
1996-12-31
To test the magnetohydrodynamic (MHD) pressure drop reduction performance of candidate insulator coatings for the ITER Vanadium/Lithium Breeding Blanket, a test section comprised of a V- 4Cr-4Ti liner inside a stainless steel pipe was designed and fabricated. Theoretically, the MHD pressure drop reduction benefit resulting, from an electrically insulating coating on a vanadium- lined pipe is identical to the benefit derived from an insulated pipe fabricated of vanadium alone. A duplex test section design consisting of a V alloy liner encased in a SS pressure boundary provided protection for vanadium from atmospheric contamination during operation at high temperature and obviated any potential problems with vanadium welding while also minimizing the amount of V alloy material required. From the MHD and insulator coating- point of view, the test section outer SS wall and inner V alloy liner can be modeled simply as a wall having a sandwich construction. Two 52.3 mm OD x 2.9 m long V-alloy tubes were fabricated by Century Tubes from 64 mm x 200 mm x 1245 mm extrusions produced by Teledyne Wah Chang. The test section`s duplex structure was subsequently fabricated at Century Tubes by drawing down a SS pipe (2 inch schedule 10) over one of the 53.2 mm diameter V tubes.
Global MHD model of the earth's magnetosphere
Wu, C. C.
1983-01-01
A global MHD model of the earth's magnetosphere is defined. An introduction to numerical methods for solving the MHD equations is given with emphasis on the shock-capturing technique. Finally, results concerning the shape of the magnetosphere and the plasma flows inside the magnetosphere are presented.
MHD Integrated Topping Cycle Project
1992-03-01
The Magnetohydrodynamics (MHD) Integrated Topping Cycle (ITC) Project represents the culmination of the proof-of-concept (POC) development stage in the US Department of Energy (DOE) program to advance MHD technology to early commercial development stage utility power applications. The project is a joint effort, combining the skills of three topping cycle component developers: TRW, Avco/TDS, and Westinghouse. TRW, the prime contractor and system integrator, is responsible for the 50 thermal megawatt (50 MW{sub t}) slagging coal combustion subsystem. Avco/TDS is responsible for the MHD channel subsystem (nozzle, channel, diffuser, and power conditioning circuits), and Westinghouse is responsible for the current consolidation subsystem. The ITC Project will advance the state-of-the-art in MHD power systems with the design, construction, and integrated testing of 50 MW{sub t} power train components which are prototypical of the equipment that will be used in an early commercial scale MHD utility retrofit. Long duration testing of the integrated power train at the Component Development and Integration Facility (CDIF) in Butte, Montana will be performed, so that by the early 1990's, an engineering data base on the reliability, availability, maintainability and performance of the system will be available to allow scaleup of the prototypical designs to the next development level. This Sixteenth Quarterly Technical Progress Report covers the period May 1, 1991 to July 31, 1991.
MHD Integrated Topping Cycle Project
1992-03-01
The Magnetohydrodynamics (MHD) Integrated Topping Cycle (ITC) Project represents the culmination of the proof-of-concept (POC) development stage in the US Department of Energy (DOE) program to advance MHD technology to early commercial development stage utility power applications. The project is a joint effort, combining the skills of three topping cycle component developers: TRW, Avco/TDS, and Westinghouse. TRW, the prime contractor and system integrator, is responsible for the 50 thermal megawatt (50 MW{sub t}) slagging coal combustion subsystem. Avco/TDS is responsible for the MHD channel subsystem (nozzle, channel, diffuser, and power conditioning circuits), and Westinghouse is responsible for the current consolidation subsystem. The ITC Project will advance the state-of-the-art in MHD power systems with the design, construction, and integrated testing of 50 MW{sub t} power train components which are prototypical of the equipment that will be used in an early commercial scale MHD utility retrofit. Long duration testing of the integrated power train at the Component Development and Integration Facility (CDIF) in Butte, Montana will be performed, so that by the early 1990's, an engineering data base on the reliability, availability, maintainability and performance of the system will be available to allow scaleup of the prototypical designs to the next development level. This Sixteenth Quarterly Technical Progress Report covers the period May 1, 1991 to July 31, 1991.
Kh. Abdul Maleque
2013-01-01
Full Text Available A local similarity solution of unsteady MHD natural convection heat and mass transfer boundary layer flow past a flat porous plate within the presence of thermal radiation is investigated. The effects of exothermic and endothermic chemical reactions with Arrhenius activation energy on the velocity, temperature, and concentration are also studied in this paper. The governing partial differential equations are reduced to ordinary differential equations by introducing locally similarity transformation (Maleque (2010. Numerical solutions to the reduced nonlinear similarity equations are then obtained by adopting Runge-Kutta and shooting methods using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are obtained for both steady and unsteady cases then presented graphically in the form of velocity, temperature, and concentration profiles. Comparison has been made for steady flow ( and shows excellent agreement with Bestman (1990, hence encouragement for the use of the present computations.
D. Lourdu Immaculate
2015-06-01
Full Text Available The present paper deals with the influence of thermophoretic particle deposition on the MHD mixed convective heat and mass transfer flow in a vertical channel in the presence of radiative heat flux with thermal-diffusion and diffusion-thermo effects. The resulting nonlinear coupled equations are solved under appropriate boundary conditions using the homotopy analysis method. The influence of involved parameters on heat and mass transfer characteristics of the fluid flow is presented graphically. It is noted that fluid velocity is an increasing function of radiation parameter, Dufour number, Buoyancy ratio parameter and mixed convection parameter whereas the magnetic parameter, thermophoresis constant, Soret number and Schimidt number lead to suppress the velocity. The fluid temperature increases with increasing radiation parameter and Dufour number. The convergence of homotopy analysis method (HAM solutions is discussed and a good agreement is found between the analytical and the numerical solution.
Smith, S. P.; Jardin, S. C.; Freidberg, J. P.; Guazzotto, L.
2008-11-01
The ideal MHD linear stability normal modes and frequencies for a circular cylindrical plasma (having an arbitrary equilibrium flow) interacting with a resistive wall are calculated. Projections of the plasma displacement are expanded as finite elements, using a Galerkin approach to form the inner products. A Green's function approach is taken to couple the perturbed wall currents to the plasma surface perturbations. The standard linear form, φAx=B x, is obtained by introducing an auxiliary variable, u=φξ+iV .∇ξ, and an additional degree of freedom representing the perturbed current in the resistive wall. It is shown that having projections aligned with (or perpendicular to) the equilibrium magnetic field is more important for correctly calculating the slow wave part of the spectrum than having a higher order finite element expansion with non-field-aligned projections. Investigations into the effects of axial and azimuthal flows on the resistive wall mode are also presented.
Tempelmeyer, K E; Sokolov, Y N [eds.
1979-04-01
The third joint test with a Soviet U-25B MHD generator and a US superconducting magnet system (SCMS) was conducted in the Soviet U-25B Facility. The primary objectives of the 3rd test were: (1) to operate the facility and MHD channel over a wider range of test parameters, and (2) to study the performance of all components and systems of the flow train at increased mass flow rates of combustion products (up to 4 kg/s), at high magnetic-field induction (up to 5 T), and high values of the electrical field in the MHD generator. The third test has demonstrated that all components and systems of the U-25B facility performed reliably. The electric power generated by the MHD generaor reached a maximum of 575 kW during this test. The MHD generator was operated under electrical loading conditions for 9 hours, and the combustor for a total of approximately 14 hours. Very high Hall fields (2.1 kV/m) were produced in the MHD channel, with a total Hall voltage of 4.24 kV. A detailed description is given of (1) performance of all components and systems of the U-25B facility, (2) analysis of the thermal, gasdynamic, and electrical characteristics of the MHD generator, (3) results of plasma diagnostic studies, (4) studies of vibrational characteristics of the flow train, (5) fluctuation of electrodynamic and gasdynamic parameters, (6) interaction of the MHD generator with the superconducting magnet, and (7) an operational problem, which terminated the test.
Nonlinear helical MHD instability
Zueva, N.M.; Solov' ev, L.S.
1977-07-01
An examination is made of the boundary problem on the development of MHD instability in a toroidal plasma. Two types of local helical instability are noted - Alfven and thermal, and the corresponding criteria of instability are cited. An evaluation is made of the maximum attainable kinetic energy, limited by the degree to which the law of conservation is fulfilled. An examination is made of a precise solution to a kinematic problem on the helical evolution of a cylindrical magnetic configuration at a given velocity distribution in a plasma. A numerical computation of the development of MHD instability in a plasma cylinder by a computerized solution of MHD equations is made where the process's helical symmetry is conserved. The development of instability is of a resonance nature. The instability involves the entire cross section of the plasma and leads to an inside-out reversal of the magnetic surfaces when there is a maximum unstable equilibrium configuration in the nonlinear stage. The examined instability in the tore is apparently stabilized by a magnetic hole when certain limitations are placed on the distribution of flows in the plasma. 29 references, 8 figures.
Yamamoto, Yoshinobu, E-mail: yamamotoy@yamanashi.ac.jp [Division of Mechanical Engineering, University of Yamanashi, 4-3-11 Takeda, Kofu 400-8511 (Japan); Kunugi, Tomoaki, E-mail: kunugi@nucleng.kyoto-u.ac.jp [Department of Nuclear Engineering, Kyoto University, C3-d2S06, Kyoto-Daigaku Katsura, Nishikyo-Ku 615-8540, Kyoto (Japan)
2016-11-01
Highlights: • We show the applicability to predict the heat transfer imposed on a uniform wall-normal magnetic field by means of the zero-equation heat transfer model. • Quasi-theoretical turbulent Prandtl numbers with various molecular Prandtl number fluids were obtained. • Improvements of the prediction accuracy in turbulent kinetic energy and turbulent dissipation rate under the magnetic fields were accomplished. - Abstract: Zero-equation heat transfer models based on the constant turbulent Prandtl number are evaluated using direct numerical simulation (DNS) data for fully developed channel flows imposed on a uniform wall-normal magnetic field. Quasi-theoretical turbulent Prandtl numbers are estimated by DNS data of various molecular Prandtl number fluids. From the viewpoint of highly-accurate magneto-hydrodynamic (MHD) heat transfer prediction, the parameters of the turbulent eddy viscosity of the k–É› model are optimized under the magnetic fields. Consequently, we use the zero-equation model based on a constant turbulent Prandtl number to demonstrate MHD heat transfer, and show the applicability of using this model to predict the heat transfer.
Khan, Zeeshan; Islam, Saeed; Shah, Rehan Ali; Khan, Muhammad Altaf; Bonyah, Ebenezer; Jan, Bilal; Khan, Aurangzeb
Modern optical fibers require a double-layer coating on the glass fiber in order to provide protection from signal attenuation and mechanical damage. The most important plastic resins used in wires and optical fibers are plastic polyvinyl chloride (PVC) and low and high density polyethylene (LDPE/HDPE), nylon and Polysulfone. One of the most important things which affect the final product after processing is the design of the coating die. In the present study, double-layer optical fiber coating is performed using melt polymer satisfying Oldroyd 8-constant fluid model in a pressure type die with the effect of magneto-hydrodynamic (MHD). Wet-on-wet coating process is applied for double-layer optical fiber coating. The coating process in the coating die is modeled as a simple two-layer Couette flow of two immiscible fluids in an annulus with an assigned pressure gradient. Based on the assumptions of fully developed laminar and MHD flow, the Oldroyd 8-constant model of non-Newtonian fluid of two immiscible resin layers is modeled. The governing nonlinear equations are solved analytically by the new technique of Optimal Homotopy Asymptotic Method (OHAM). The convergence of the series solution is established. The results are also verified by the Adomian Decomposition Method (ADM). The effect of important parameters such as magnetic parameter Mi , the dilatant constant α , the Pseodoplastic constant β , the radii ratio δ , the pressure gradient Ω , the speed of fiber optics V , and the viscosity ratio κ on the velocity profiles, thickness of coated fiber optics, volume flow rate, and shear stress on the fiber optics are investigated. At the end the result of the present work is also compared with the experimental results already available in the literature by taking non-Newtonian parameters tends to zero.
Ramamoorthy MUTHURAJ
2013-07-01
Full Text Available This paper investigates the magnetohydrodynamic (MHD mixed convective heat and mass transfer flow in a vertical wavy porous space in the presence of a heat source with the combined effects of chemical reaction and wall slip condition. The dimensionless governing equations are perturbed into: mean (zeroth-order part and a perturbed part, using amplitude as a small parameter. The perturbed quantities are obtained by perturbation series expansion for small wavelength in which terms of exponential order arise. The results obtained show that the velocity, temperature and concentration fields are appreciably influenced by the presence of chemical reaction, magnetic field, porous medium, heat source/sink parameter and wall slip condition. Further, the results of the skin friction and rate of heat and mass transfer at the wall are presented for various values of parameters entering into the problem and discussed with the help of graphs.
Abdel-Wahed, Mohamed; Akl, Mohamed
2016-09-01
Analysis of the MHD Nanofluid boundary layer flow over a rotating disk with a constant velocity in the presence of hall current and non-linear thermal radiation has been covered in this work. The variation of viscosity and thermal conductivity of the fluid due to temperature and nanoparticles concentration and size is considered. The problem described by a system of P.D.E that converted to a system of ordinary differential equations by the similarity transformation technique, the obtained system solved analytically using Optimal Homotopy Asymptotic Method (OHAM) with association of mathematica program. The velocity profiles and temperature profiles of the boundary layer over the disk are plotted and investigated in details. Moreover, the surface shear stress, rate of heat transfer explained in details.
Naganthran, Kohilavani; Nazar, Roslinda
2017-08-01
In this study, the influence of the first order chemical reaction towards the magnetohydrodynamics (MHD) stagnation-point boundary layer flow past a permeable stretching/shrinking surface (sheet) is considered numerically. The governing boundary layer equations are transformed into a system of ordinary differential equations from the system of partial differential equations by using a proper similarity transformation so that it can be solved numerically by the "bvp4c" function in Matlab software. The main numerical solutions are presented graphically and discussed in the relevance of the governing parameters. It is found that dual solutions exist when the sheet is stretched and shrunk. Stability analysis is done to determine which solution is stable and valid physically. The results of the stability analysis show that the first solution (upper branch) is physically stable and realizable while the second solution (lower branch) is impracticable.
A.G Vijaya Kumar,
2011-04-01
Full Text Available The objective of the present study is to investigate Radiation effects on unsteady MHD flow of an electrically conducting radiating, viscous, incompressible fluid past an impulsively started movingexponentially accelerated vertical plate with variable temperature in the presence of heat generation and applied transverse magnetic field. The fluid is considered is gray, absorbing/emitting radiation but a nonscattering medium. At time t > 0, the temperature of the plate raised linearly with time t. The dimensionless governing equations involved in the present analysis are solved using the Laplace transform technique. The velocity, temperature, skin friction and the rate of heat transfer are shown graphically and with some numerical computations in terms of the parameters M(the magnetic fieldparameter, R(the radiation parameter, H(the heat source parameter, Pr(the prendtl number, a(exponential index and t(time.
S. Abdul Gaffar
2016-06-01
Full Text Available A mathematical study is presented to analyze the nonlinear, non-isothermal, magnetohydrodynamic (MHD free convection boundary layer flow, heat and mass transfer of non-Newtonian Eyring–Powell fluid from a vertical surface in a non-Darcy, isotropic, homogenous porous medium, in the presence of Hall currents and ionslip currents. The governing nonlinear coupled partial differential equations for momentum conservation in the x, and z directions, heat and mass conservation, in the flow regime are transformed from an (x, y, z coordinate system to a (ξ, η coordinate system in terms of dimensionless x-direction velocity (f′ and z-direction velocity (G, dimensionless temperature and concentration functions (θ and ϕ under appropriate boundary conditions. Both Darcian and Forchheimer porous impedances are incorporated in both momentum equations. Computations are also provided for the variation of the x and z direction shear stress components and also heat and mass transfer rates. It is observed that with increasing ɛ, primary velocity, secondary velocity, heat and mass transfer rates are decreased whereas, the temperature, concentration and skin friction are increased. An increasing δ is found to increase primary and secondary velocities, skin friction, heat and mass transfer rates. But the temperature and concentration decrease. Increasing βe and βi are seen to increase primary velocity, skin friction, heat and mass transfer rates whereas secondary velocity, temperature and concentration are decreased. Excellent correlation is achieved with a Nakamura tridiagonal finite difference scheme (NTM. The model finds applications in magnetic materials processing, MHD power generators and purification of crude oils.
Muhammad Ramzan
Full Text Available The aim of present paper is to study the series solution of time dependent MHD second grade incompressible nanofluid towards a stretching sheet. The effects of mixed convection and thermal radiation are also taken into account. Because of nanofluid model, effects Brownian motion and thermophoresis are encountered. The resulting nonlinear momentum, heat and concentration equations are simplified using appropriate transformations. Series solutions have been obtained for velocity, temperature and nanoparticle fraction profiles using Homotopy Analysis Method (HAM. Convergence of the acquired solution is discussed critically. Behavior of velocity, temperature and concentration profiles on the prominent parameters is depicted and argued graphically. It is observed that temperature and concentration profiles show similar behavior for thermophoresis parameter Νt but opposite tendency is noted in case of Brownian motion parameter Νb. It is further analyzed that suction parameter S and Hartman number Μ depict decreasing behavior on velocity profile.
Muhammad Ramzan
Full Text Available The present exploration discusses the influence of Newtonian heating on the magnetohydrodynamic (MHD three dimensional couple stress nanofluid past a stretching surface. Viscous dissipation and Joule heating effects are also considered. Moreover, the nanofluid model includes the combined effects of thermophoresis and Brownian motion. Using an appropriate transformation, the governing non linear partial differential equations are converted into nonlinear ordinary differential equations. Series solutions using Homotopy Analysis method (HAM are computed. Plots are presented to portrait the arising parameters in the problem. It is seen that an increase in conjugate heating parameter results in considerable increase in the temperature profile of the stretching wall. Skin friction coefficient, local Nusselt and local Sherwood numbers tabulated and analyzed. Higher values of conjugate parameter, Thermophoresis parameter and Brownian motion parameter result in enhancement of temperature distribution.
M. Umamaheswar
2016-09-01
Full Text Available A numerical investigation is carried out on an unsteady MHD free convection flow of a well-known non-Newtonian visco elastic second order Rivlin-Erickson fluid past an impulsively started semi-infinite vertical plate in the presence of homogeneous chemical reaction, thermal radiation, thermal diffusion, radiation absorption and heat absorption with constant mass flux. The presence of viscous dissipation is also considered at the plate under the influence of uniform transverse magnetic field. The flow is governed by a coupled nonlinear system of partial differential equations which are solved numerically by using finite difference method. The effects of various physical parameters on the flow quantities viz. velocity, temperature, concentration, Skin friction, Nusselt number and Sherwood number are studied numerically. The results are discussed with the help of graphs. We observed that the velocity decreases with an increase in magnetic field parameter, Schmidt number, and Prandtl number while it increases with an increase in Grashof number, modified Grashof number, visco-elastic parameter and Soret number. Temperature increases with an increase in radiation absorption parameter, Eckert number and visco-elastic parameter while it decreases with increasing values of radiation parameter, Prandtl number and heat absorption parameter. Concentration increases with increase in Soret number while it decreases with an increase in Schmidt number and chemical reaction parameter.
Muhaimin, I.; Kandasamy, R., E-mail: future990@gmail.com; Khamis, Azme B.; Roslan, Rozaini
2013-08-15
Highlights: • Thermophoresis particle deposition in the presence of chemical reaction has a substantial effect on unsteady flow. • Thermophoresis is expected to alter the concentration boundary layer significantly. • Similarity transformation is used for unsteady flow field. • Destructive reaction plays a dominant role on concentration field. -- Abstract: An analysis is presented to investigate the effect of thermophoresis particle deposition and temperature dependent viscosity on unsteady MHD mixed convective heat and mass transfer of a viscous, incompressible and electrically conducting fluid past a porous wedge in the presence of chemical reaction. The wall of the wedge is embedded in a uniform non-Darcian porous medium in order to allow for possible fluid wall suction or injection. The results are compared with those known from the literature and excellent agreement between the results is obtained. The governing partial differential equations of the problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary layer analysis. Numerical calculations are carried out for different values of dimensionless parameter in the problem and an analysis of the results obtained show that the flow field is influenced appreciably by the applied magnetic field and thermophoresis particle deposition.
B. R. Rout
2013-01-01
Full Text Available This paper aims to investigate the influence of chemical reaction and the combined effects of internal heat generation and a convective boundary condition on the laminar boundary layer MHD heat and mass transfer flow over a moving vertical flat plate. The lower surface of the plate is in contact with a hot fluid while the stream of cold fluid flows over the upper surface with heat source and chemical reaction. The basic equations governing the flow, heat transfer, and concentration are reduced to a set of ordinary differential equations by using appropriate transformation for variables and solved numerically by Runge-Kutta fourth-order integration scheme in association with shooting method. The effects of physical parameters on the velocity, temperature, and concentration profiles are illustrated graphically. A table recording the values of skin friction, heat transfer, and mass transfer at the plate is also presented. The discussion focuses on the physical interpretation of the results as well as their comparison with previous studies which shows good agreement as a special case of the problem.
Bilal, S.; Khalil-ur-Rehman; Malik, M. Y.; Hussain, Arif; Khan, Mair
Present work is communicated to identify characteristics of magnetohydrodynamic (MHD) three dimensional boundary layer flow of Williamson fluid confined by a bidirectional stretched surface. Conductivity of working fluid is assumed to be temperature dependent. Generative/absorptive heat transfer is also taken into account. Mathematical model is formulated in the form of partial expressions and then transmuted into ordinary differential equations with the help of newfangled set of similarity transformations. The resulting non-linear differential system of equations is solved numerically with the aid of Runge-Kutta algorithm supported by shooting method. Flow features are exemplified quantitatively through graphs. Scintillating results for friction factor and convective heat transfer are computed and scrutinized tabularly. Furthermore, the accuracy of present results is tested with existing literature and we found an excellent agreement. It is inferred that velocity along x-direction mounts whereas along y-direction depreciates for incrementing values of stretching ratio parameter. Moreover, it is also elucidated that non-linearity index tends to decrement the velocity and thermal distributions of fluid flow.
Akbar, Noreen Sher; Tripathi, D.; Bég, O. Anwar; Khan, Z. H.
2016-11-01
A theoretical investigation of magnetohydrodynamic (MHD) flow and heat transfer of electrically-conducting viscoplastic fluids through a channel is conducted. The robust Casson model is implemented to simulate viscoplastic behavior of fluids. The external magnetic field is oblique to the fluid flow direction. Viscous dissipation effects are included. The flow is controlled by the metachronal wave propagation generated by cilia beating on the inner walls of the channel. The mathematical formulation is based on deformation in longitudinal and transverse velocity components induced by the ciliary beating phenomenon with cilia assumed to follow elliptic trajectories. The model also features velocity and thermal slip boundary conditions. Closed-form solutions to the non-dimensional boundary value problem are obtained under physiological limitations of low Reynolds number and large wavelength. The influence of key hydrodynamic and thermo-physical parameters i.e. Hartmann (magnetic) number, Casson (viscoplastic) fluid parameter, thermal slip parameter and velocity slip parameter on flow characteristics are investigated. A comparative study is also made with Newtonian fluids (corresponding to massive values of plastic viscosity). Stream lines are plotted to visualize trapping phenomenon. The computations reveal that velocity increases with increasing the magnitude of Hartmann number near the channel walls whereas in the core flow region (center of the channel) significant deceleration is observed. Temperature is elevated with greater Casson parameter, Hartmann number, velocity slip, eccentricity parameter, thermal slip and also Brinkmann (dissipation) number. Furthermore greater Casson parameter is found to elevate the quantity and size of the trapped bolus. In the pumping region, the pressure rise is reduced with greater Hartmann number, velocity slip, and wave number whereas it is enhanced with greater cilia length.
del Valle, M V; Kowal, G
2016-01-01
Fast magnetic reconnection may occur in different astrophysical sources, producing flare-like emission and particle acceleration. Currently, this process is being studied as an efficient mechanism to accelerate particles via a first-order Fermi process. In this work we analyse the acceleration rate and the energy distribution of test particles injected in three-dimensional magnetohydrodynamical (MHD) domains with large-scale current sheets where reconnection is made fast by the presence of turbulence. We study the dependence of the particle acceleration time with the relevant parameters of the embedded turbulence, i.e., the Alfv\\'en speed $V_{\\rm A}$, the injection power $P_{\\rm inj}$ and scale $k_{\\rm inj}$ ($k_{\\rm inj} = 1/l_{\\rm inj}$). We find that the acceleration time follows a power-law dependence with the particle kinetic energy: $t_{acc} \\propto E^{\\alpha}$, with $0.2 < \\alpha < 0.6$ for a vast range of values of $c / V_{\\rm A} \\sim 20 - 1000$. The acceleration time decreases with the Alfv\\'en...
M. Schüssler
Full Text Available Two aspects of solar MHD are discussed in relation to the work of the MHD simulation group at KIS. Photospheric magneto-convection, the nonlinear interaction of magnetic field and convection in a strongly stratified, radiating fluid, is a key process of general astrophysical relevance. Comprehensive numerical simulations including radiative transfer have significantly improved our understanding of the processes and have become an important tool for the interpretation of observational data. Examples of field intensification in the solar photosphere ('convective collapse' are shown. The second line of research is concerned with the dynamics of flux tubes in the convection zone, which has far-reaching implications for our understanding of the solar dynamo. Simulations indicate that the field strength in the region where the flux is stored before erupting to form sunspot groups is of the order of 10^{5} G, an order of magnitude larger than previous estimates based on equipartition with the kinetic energy of convective flows.
Key words. Solar physics · astrophysics and astronomy (photosphere and chromosphere; stellar interiors and dynamo theory; numerical simulation studies.
Prabhakar Reddy B.
2014-05-01
Full Text Available The thermal diffusion and viscous dissipation effects on an unsteady MHD free convection heat and mass transfer flow of an incompressible, electrically conducting, fluid past an infinite vertical porous plate embedded in a porous medium of time dependent permeability under oscillatory suction velocity in the presence of a heat absorbing sink have been studied. It is considered that the influence of a uniform magnetic field acts normal to the flow and the permeability of the porous medium fluctuates with time. The dimensionless governing equations for this investigation have been solved numerically by using the efficient Galerkin finite element method. The numerical results obtained have been presented through graphs and tables for the thermal Grashof number (Gr > 0 corresponding to the cooling of the porous plate and (Gr < 0 corresponding to heating of the porous plate to observe the effects of various material parameters encountered in the problem under investigation. Numerical data for skin-friction, Nusselt and Sherwood numbers are tabulated and then discussed.
Srinivasa Raju, Rallabandi
2016-10-01
The present investigation is concerned with the effects of thermal diffusion (Soret) and diffusion thermo (Dufour) on an unsteady MHD free convective flow with heat and mass transfer of an electrically conducting fluid in the presence of chemical reaction. A uniform magnetic field acts perpendicular to the porous surface, which absorbs the fluid with a suction velocity varying with time. The problem is governed by coupled non-linear partial differential equations with appropriate boundary conditions. A finite element numerical solution is developed to solve the resulting well-posed two-point boundary value problem. The present numerical results are compared with available data and are found in an excellent agreement. The expressions for velocity, temperature and concentration fields are obtained. With the aid of these, the expressions for the coefficient of skin-friction, the rate of heat transfer in the form of Nusselt number and the rate of mass transfer in the form of Sherwood number are derived. Finally the effects of various physical parameters of the flow quantities are studied with the help of graphs and tables.
E.Hemalatha
2015-09-01
Full Text Available This paper analyzes the radiation and chemical reaction effects on MHD steady two-dimensional laminar viscous incompressible radiating boundary layer flow over a flat plate in the presence of internal heat generation and convective boundary condition. It is assumed that lower surface of the plate is in contact with a hot fluid while a stream of cold fluid flows steadily over the upper surface with a heat source that decays exponentially. The Rosseland approximation is used to describe radiative heat transfer as we consider optically thick fluids. The governing boundary layer equations are transformed into a system of ordinary differential equations using similarity transformations, which are then solved numerically by employing fourth order Runge-Kutta method along with shooting technique. The effects of various material parameters on the velocity, temperature and concentration as well as the skin friction coefficient, the Nusselt number, the Sherwood number and the plate surface temperature are illustrated and interpreted in physical terms. A comparison of present results with previously published results shows an excellent agreement.
Farhad Ali
2013-01-01
Full Text Available The focus of this paper is to analyze the influence of thermal radiation on some unsteady magnetohydrodynamic (MHD free convection flows of an incompressible Brinkman type fluid past a vertical flat plate embedded in a porous medium with the Newtonian heating boundary condition. The fluid is considered as a gray absorbing-emitting but nonscattering medium and the Rosseland approximation in the energy equations is used to describe the radiative heat flux for optically thick fluid. For a detailed analysis of the problem, four important situations of flow due to (i impulsive motion of the plate (ii uniform acceleration of the plate (iii nonuniform acceleration of the plate, and (iv highly nonuniform acceleration of the plate are considered. The governing equations are first transformed into a system of dimensionless equations and then solved analytically using the Laplace transform technique. Numerical results for temperature and velocity are shown graphically, while skin friction and Nusselt number are computed in tables. The results show that temperature and velocity increase on increasing radiation and Newtonian heating parameters. However, the results of magnetic and porosity parameters on velocity are found quite opposite.
Zhang, Yan; Zhao, Hao-Jie; Bai, Yu
2017-06-01
In classical study on generalized viscoelastic fluid, the momentum equation was derived by considering the fractional constitutive model, while the energy equation was ignored its effect. This paper presents an investigation for the magnetohydrodynamic (MHD) flow and heat transfer of an incompressible generalized Burgers’ fluid due to an exponential accelerating plate with the effect of the second order velocity slip. The energy equation and momentum equation are coupled by the fractional Burgers’ fluid constitutive model. Numerical solutions for velocity, temperature and shear stress are obtained using the modified implicit finite difference method combined with the G1-algorithm, whose validity is confirmed by the comparison with the analytical solution. Our results show that the influences of the fractional parameters α and β on the flow are opposite each other, which is just like the effects of the two parameters on the temperature. Moreover, the impact trends of the relaxation time λ 1 and retardation time λ 3 on the velocity are opposite each other. Increasing the boundary parameter will promote the temperature, but has little effect on the temperature boundary layer thickness. Supported by the National Natural Science Foundations of China under Grant Nos. 21576023, 51406008, and the National Key Research Program of China under Grant Nos. 2016YFC0700601, 2016YFC0700603, and 2016YFE0115500
Flow structure around high-speed train in open air
田红旗; 黄莎; 杨明智
2015-01-01
According to the analysis of the turbulent intensity level around the high-speed train, the maximum turbulent intensity ranges from 0.2 to 0.5 which belongs to high turbulent flow. The flow field distribution law was studied and eight types of flow regions were proposed. They are high pressure with air stagnant region, pressure decreasing with air accelerating region, low pressure with high air flow velocity region I, turbulent region, steady flow region, low pressure with high air flow velocity region II, pressure increasing with air decelerating region and wake region. The analysis of the vortex structure around the train shows that the vortex is mainly induced by structures with complex mutation and large curvature change. The head and rear of train, the underbody structure, the carriage connection section and the wake region are the main vortex generating sources while the train body with even cross-section has rare vortexes. The wake structure development law studied lays foundation for the train drag reduction.
1995-02-01
The Diagnostic Instrumentation and Analysis Laboratory (DIAL) at Mississippi State University (MSU), under U.S. Department of Energy (DOE) Contract No. DE-AC02-80ET-15601, Diagnostic Development and Support of MHD Test Facilities, developed diagnostic instruments for magnetohydrodynamic (MHD) power train data acquisition and for support of MHD component development test facilities. Microprocessor-controlled optical instruments, initially developed for Heat Recovery/Seed Recovery (HRSR) support, were refined, and new systems to measure temperatures and gas-seed-slag stream characteristics were developed. To further data acquisition and analysis capabilities, the diagnostic systems were interfaced with DIAL`s computers. Technical support was provided for the diagnostic needs of the national MHD research effort. DIAL personnel also cooperated with government agencies and private industries to improve the transformation of research and development results into processes, products and services applicable to their needs. The initial contract, Testing and Evaluation of Heat Recovery/Seed Recovery, established a data base on heat transfer, slagging effects on heat transfer surfaces, metal durability, secondary combustor performance, secondary combustor design requirements, and other information pertinent to the design of HR/SR components at the Coal-Fired Flow Facility (CFFF). To accomplish these objectives, a combustion test stand was constructed that simulated MHD environments, and mathematical models were developed and evaluated for the heat transfer in hot-wall test sections. Two transitions occurred during the span of this contract. In May 1983, the objectives and title of the contract changed from Testing and Evaluation of Heat Recovery/Seed Recovery to Diagnostic Development and Support of MHD Test Facilities. In July 1988, the research laboratory`s name changed from the MHD Energy Center to the Diagnostic Instrumentation and Analysis Laboratory.
Magnetic levitation and MHD propulsion
Tixador, P.
1994-04-01
Magnetic levitation and MHD propulsion are now attracting attention in several countries. Different superconducting MagLev and MHD systems will be described concentrating on, above all, the electromagnetic aspect. Some programmes occurring throughout the world will be described. Magnetic levitated trains could be the new high speed transportation system for the 21st century. Intensive studies involving MagLev trains using superconductivity have been carried out in Japan since 1970. The construction of a 43 km long track is to be the next step. In 1991 a six year programme was launched in the United States to evaluate the performances of MagLev systems for transportation. The MHD (MagnetoHydroDynamic) offers some interesting advantages (efficiency, stealth characteristics, ...) for naval propulsion and increasing attention is being paid towards it nowadays. Japan is also up at the top with the tests of Yamato I, a 260 ton MHD propulsed ship. Depuis quelques années nous assistons à un redémarrage de programmes concernant la lévitation et la propulsion supraconductrices. Différents systèmes supraconducteurs de lévitation et de propulsion seront décrits en examinant plus particulièrement l'aspect électromagnétique. Quelques programmes à travers le monde seront abordés. Les trains à sustentation magnétique pourraient constituer un nouveau mode de transport terrestre à vitesse élevée (500 km/h) pour le 21^e siècle. Les japonais n'ont cessé de s'intéresser à ce système avec bobine supraconductrice. Ils envisagent un stade préindustriel avec la construction d'une ligne de 43 km. En 1991 un programme américain pour une durée de six ans a été lancé pour évaluer les performances des systèmes à lévitation pour le transport aux Etats Unis. La MHD (Magnéto- Hydro-Dynamique) présente des avantages intéressants pour la propulsion navale et un regain d'intérêt apparaît à l'heure actuelle. Le japon se situe là encore à la pointe des d
Misra, J C; Rath, H J
2010-01-01
Of concern in the paper is a study of steady incompressible viscoelastic and electrically conducting fluid flow and heat transfer in a parallel plate channel with stretching walls in the presence of a magnetic field applied externally. The flow is considered to be governed by Walter's liquid B fluid. The problem is solved by developing a suitable numerical method. The results are found to be in good agrement with those of earlier investigations reported in existing scientific literatures. The study reveals that a back flow occurs near the central line of the channel due to the stretching walls and further that this flow reversal can be stopped by applying a strong external magnetic field. The study also shows that with the increase in the strength of the magnetic field, the fluid velocity decreases but the temperature increases. Thus the study bears potential applications in the study of the haemodynamic flow of blood in the cardiovascular system when subjected to an external magnetic field.
El-Mistikawy, Tarek M A
2016-01-01
The equations governing the magnetohydrodynamic stagnation point flow toward a non-conducting, thermally insulated, nonporous, linearly stretching sheet are cast in a self similar form. Consistent boundary conditions on the velocity, magnetic field and temperature are invoked. The flow problem involves three parameters- the magnetic Prandtl number, the magnetic interaction number, and the ratio of the stretching rate to the strength of the stagnation point flow. The energy equation includes viscous dissipation and Joule heating, and introduces the Prandtl number as a fourth parameter. Numerical solutions are obtained and sample results are presented.
MHD mixed convection flow of power law non-Newtonian fluids over an isothermal vertical wavy plate
Mirzaei Nejad, Mehrzad; Javaherdeh, K.; Moslemi, M.
2015-09-01
Mixed convection flow of electrically conducting power law fluids along a vertical wavy surface in the presence of a transverse magnetic field is studied numerically. Prandtl coordinate transformation together with the spline alternating direction implicit method is employed to solve the boundary layer equations. The influences of both flow structure and dominant convection mode on the overall parameters of flow and heat transfer are well discussed. Also, the role of magnetic field in controlling the boundary layers is investigated. The variation of Nusselt number and skin friction coefficient are studied as functions of wavy geometry, magnetic field, buoyancy force and material parameters. Results reveal the interrelation of the contributing factors.
KHEM CHAND
2011-07-01
Full Text Available The heat transfer and hydromagnetic boundary layer flow of an electrically conducting viscous ,incompressible fluid over a continuous flat surface moving in a parallel free stream is investigated. The porous infinite surface is subjected to a slightly sinusoidal transverse suction velocity distribution. The flow becomes three dimensional due to this type of suction velocity without taking into account the induced magnetic field; the mathematical analysis is presented for the hydromagnetic laminar boundary layer flow. For the asymptotic flow condition, the components of the surface skin friction and the rate of heat transfer are obtained. During discussion it is found that with the increase of Hartmann number M, the skin friction factor F1 increase sharply for lower values of theReynolds number, but for the large value it increases steadily. But if the surface velocity is more than that of free stream velocity then the reverse trend is observed.
Qureshi, M. Zubair Akbar; Rubbab, Qammar; Irshad, Saadia; Ahmad, Salman; Aqeel, M.
2016-10-01
Energy generation is currently a serious concern in the progress of human civilization. In this regard, solar energy is considered as a significant source of renewable energy. The purpose of the study is to establish a thermal energy model in the presence of spherical Au-metallic nanoparticles. It is numerical work which studies unsteady magnetohydrodynamic (MHD) nanofluid flow through porous disks with heat and mass transfer aspects. Shaped factor of nanoparticles is investigated using small values of the permeable Reynolds number. In order to scrutinize variation of thermal radiation effects, a dimensionless Brinkman number is introduced. The results point out that heat transfer significantly escalates with the increase of Brinkman number. Partial differential equations that govern this study are reduced into nonlinear ordinary differential equations by means of similarity transformations. Then using a shooting technique, a numerical solution of these equations is constructed. Radiative effects on temperature and mass concentration are quite opposite. Heat transfer increases in the presence of spherical Au-metallic nanoparticles.
Sahin Ahmed
2013-01-01
Full Text Available The study of non-linear MHD flow with heat and mass transfer characteristics of an incompressible, viscous, electrically conducting and Newtonian fluid over a vertical oscillating porous plate embedded in a porous medium in presence of homogeneous chemical reaction of first order and thermal radiation effects have been analyzed. The fluid considered here is a gray, absorbing/emitting radiation, but a non-scattering medium. At timet>0, the plate temperature and concentration levels near the plate raised linearly with timet. The dimensionless governing coupled, non-linear boundary layer partial differential equations are solved by an efficient, accurate, and extensively validated and unconditionally stable finite difference scheme of the Crank-Nicolson type as well as by the Laplace Transform technique. An increase in porosity parameter (K is found to depress the fluid velocities and shear stress in the regime. Also it has been found that, when the conduction-radiation (R increased, the fluid velocities as well as temperature profiles were decreased. It has been found that, when the chemical reaction parameter(C_r increased, the fluid velocities as well as concentration profiles were decreased. Applications of the study arise in materials processing and solar energy collector systems.
Qureshi, M Zubair Akbar; Rubbab, Qammar; Irshad, Saadia; Ahmad, Salman; Aqeel, M
2016-12-01
Energy generation is currently a serious concern in the progress of human civilization. In this regard, solar energy is considered as a significant source of renewable energy. The purpose of the study is to establish a thermal energy model in the presence of spherical Au-metallic nanoparticles. It is numerical work which studies unsteady magnetohydrodynamic (MHD) nanofluid flow through porous disks with heat and mass transfer aspects. Shaped factor of nanoparticles is investigated using small values of the permeable Reynolds number. In order to scrutinize variation of thermal radiation effects, a dimensionless Brinkman number is introduced. The results point out that heat transfer significantly escalates with the increase of Brinkman number. Partial differential equations that govern this study are reduced into nonlinear ordinary differential equations by means of similarity transformations. Then using a shooting technique, a numerical solution of these equations is constructed. Radiative effects on temperature and mass concentration are quite opposite. Heat transfer increases in the presence of spherical Au-metallic nanoparticles.
MHD magnet technology development program summary, September 1982
1983-11-01
The program of MHD magnet technology development conducted for the US Department of Energy by the Massachusetts Institute of Technology during the past five years is summarized. The general strategy is explained, the various parts of the program are described and the results are discussed. Subjects covered include component analysis, research and development aimed at improving the technology base, preparation of reference designs for commercial-scale magnets with associated design evaluations, manufacturability studies and cost estimations, the detail design and procurement of MHD test facility magnets involving transfer of technology to industry, investigations of accessory subsystem characteristics and magnet-flow-train interfacing considerations and the establishment of tentative recommendations for design standards, quality assurance procedures and safety procedures. A systematic approach (framework) developed to aid in the selection of the most suitable commercial-scale magnet designs is presented and the program status as of September 1982 is reported. Recommendations are made for future work needed to complete the design evaluation and selection process and to provide a sound technological base for the detail design and construction of commercial-scale MHD magnets. 85 references.
Resistive MHD jet simulations with large resistivity
Cemeljic, Miljenko; Vlahakis, Nektarios; Tsinganos, Kanaris
2009-01-01
Axisymmetric resistive MHD simulations for radially self-similar initial conditions are performed, using the NIRVANA code. The magnetic diffusivity could occur in outflows above an accretion disk, being transferred from the underlying disk into the disk corona by MHD turbulence (anomalous turbulent diffusivity), or as a result of ambipolar diffusion in partially ionized flows. We introduce, in addition to the classical magnetic Reynolds number Rm, which measures the importance of resistive effects in the induction equation, a new number Rb, which measures the importance of the resistive effects in the energy equation. We find two distinct regimes of solutions in our simulations. One is the low-resistivity regime, in which results do not differ much from ideal-MHD solutions. In the high-resistivity regime, results seem to show some periodicity in time-evolution, and depart significantly from the ideal-MHD case. Whether this departure is caused by numerical or physical reasons is of considerable interest for nu...
Stanford Shateyi
2015-01-01
Full Text Available The present study investigates entropy generation on a magnetohydrodynamic flow and heat transfer of a Maxwell fluid using a spectral relaxation method. The method is based on simple iteration schemes formed by reduction of the order of the momentum equation followed by a rearrangement of the resulting governing nonlinear equation systems which are then solved using spectral methods. The velocity and temperature profiles are obtained numerically and used to generate the entropy generation number. Entropy generation increased with the Reynolds number, the magnetic parameter and the dimensionless group parameter while decreased for higher Prandtl numbers. The effect of the flow parameters on the velocity and temperature of the flow were also investigated. The results were validated using the bvp4c where the spectral relaxation method was found to be accurate and rapidly convergent to the numerical results.
MHD UNSTEADY FLOWS DUE TO NON-COAXIAL ROTATIONS OF A DISK AND A FLUID AT INFINITY
T.HAYAT; S.MUMTAZ; R.ELLAHI
2003-01-01
Exact analytical solution for flows of an electrically conducting fluid over an infinite oscillatory disk in the presence of a uniform transverse magnetic field is constructed.Both the disk and the fluid are in a state of non-coaxial rotation.Such a flow model has a great significance not only due to its own theoretical interest,but also due to applications to geophysics and engineering.The resulting initial value problem has been solved analytically by applying the Laplace transform technique and the explicit expressions for the velocity for steady and unsteady cases have been established.The analysis of the obtained results shows that the flow field is appreciably influenced by the applied magnetic field,the frequency and rotation parameters.
Kumar, Rakesh
2015-01-01
This investigation deals with the analysis of stagnation point heat transfer and corresponding flow features of hydromagnetic viscous incompressible fluid over a vertical shrinking sheet. The considered sheet is assumed to be permeable and subject to addition of stagnation point to control the generated vorticity in the boundary layer. The sheet is placed on the right side of the fluid saturated porous medium which is having permeability of specified form. Nonlinear convection waves in the flow field are realized due to the envisaged nonlinear relation between density and temperature. The equations governing the nonlinear convection boundary layer flow are modeled and simplified using similarity transformations. The economized equations are solved for numerical solutions by employing the implicit finite difference scheme also known as Keller-box method. The influence of the associated parameters of the problem on velocity and temperature distributions, skin friction and rate of heat transfer are presented thr...
MHD UNSTEADY FLOWS DUE TO NON—COAXIAL ROTATIONS OF A DISK AND A FLUID AT INFINITY
T.HAYAT
2003-01-01
Exact analytical solution for flows of an electrically conducting fluid over an infiniteoscillatory disk in the presence of a uniform transverse magnetic field is constructed. Both the disk andthe fluid are in a state of non-coaxial rotation. Such a flow model has a great significance not only clueto its own theoretical interest, but also clue to applications to geophysics and engineering. The resultinginitial value problem has been solved analytically by applying the Laplace transform technique and theexplicit expressions for the velocity for steady and unsteady cases have been established. The analysisof the obtained results shows that the flow field is appreciably influenced by the applied magnetic field,the frequency and rotation parameters.
HEAT AND MASS TRANSFER FOR VISCO-ELASTIC MHD BOUNDARY LAYER FLOW PAST A VERTICAL FLAT PLATE
Rita Choudhury
2012-07-01
Full Text Available The two-dimensional free convection flow of visco-elastic and electrically conducting fluid past a vertical impermeable flat plate is considered in presence of a uniform transverse magnetic field. The governing equations are reduced to ordinary differential equation by introducing appropriate co-ordinate transformation. The analytical expressions for the velocity, temperature and species concentration fields have been obtained. The corresponding expressions for the non-dimensional rates of heat transfer and mass transfer have beenobtained. The velocity profile and the shearing stress have been illustrated graphically, for various values of flow parameters involved in the solution to observe the effect of visco-elastic parameter.
Dr.Abhay Kumar Jha
2012-07-01
Full Text Available The objective of this paper is to study heat and mass transfer on an unsteady two dimensional hydromagnetic laminar mixed convective boundary layer flow of an incompressible fluid past a semi-infinite vertical plate with heat source/ sink. The plate moves with constant velocity in the direction of fluid flow while the free stream velocity follows an exponentially increasing small perturbation law. The dimensionless governing equations are solved analytically using two terms harmonic and non-harmonic functions .the results obtainedand discussed with help of graphs and tables to observe the effect of various parameter concerned in the problem under investigation.
MHD flow and heat transfer from continuous surface in uniform free stream of non-Newtonian fluid
无
2007-01-01
An analysis is carried out to study the steady flow and heat transfer characteristics from a continuous flat surface moving in a parallel free stream of an electrically conducting non-Newtonian viscoelastic fluid. The flow is subjected to a transverse uniform magnetic field. The constitutive equation of the fluid is modeled by that for a second grade fluid. Numerical results are obtained for the distribution of velocity and temperature profiles. The effects of various physical parameters like viscoelastic parameter, magnetic parameter and Prandtl number on various momentum and heat transfer characteristics are discussed in detail and shown graphically.
Penem Mohan KRISNA
2014-03-01
Full Text Available In this study, we analyze the effects of thermal radiation and chemical reaction on the steady 2 dimensional stagnation point flow of a viscous incompressible electrically conducting fluid over a stretching surface, with suction and heat generation. The partial differential equations governing the flow are solved numerically by using the shooting technique. The effects of various parameters on velocity, temperature, and concentration profiles, as well as Nusselt number, Skin friction coefficient, and Sherwood number, are examined, and presented graphically and through tables. It is found that velocity, temperature, and rate of heat transfer of the fluid are influenced more by radiation and chemical reaction parameters, along with applied magnetic field.
Khan Ilyas
2015-01-01
Full Text Available The present paper is concerned with the magnetohydrodynamic unsteady rotating flows of generalized Burgers' fluid with a porous medium. The flows are created by the plate oscillations. Modified Darcy's law has been employed to model the governing problem. Closed-form solutions corresponding to cosine and sine oscillations are obtained by the Laplace transform method. The performed calculations disclose that Hartmann number, porosity of the medium, angular frequency, and oscillating frequency have strong influence on the velocity. The graphs are presented for such influence and examined carefully.
The Effect of Heat Transfer on MHD Marangoni Boundary Layer Flow Past a Flat Plate in Nanofluid
D. R. V. S. R. K. Sastry
2013-01-01
Full Text Available The problem of heat transfer on the Marangoni convection boundary layer flow in an electrically conducting nanofluid is studied. Similarity transformations are used to transform the set of governing partial differential equations of the flow into a set of nonlinear ordinary differential equations. Numerical solutions of the similarity equations are then solved through the MATLAB “bvp4c” function. Different nanoparticles like Cu, Al2O3, and TiO2 are taken into consideration with water as base fluid. The velocity and temperature profiles are shown in graphs. Also the effects of the Prandtl number and solid volume fraction on heat transfer are discussed.
Sheikholeslami, R; Ashorynejad, H.R; Barari, Amin
2013-01-01
Purpose – The purpose of this paper is to analyze hydromagnetic flow between two horizontal plates in a rotating system. The bottom plate is a stretching sheet and the top one is a solid porous plate. Heat transfer in an electrically conducting fluid bounded by two parallel plates is also studied...
Srinivas Maripala
2015-06-01
Full Text Available An analysis is presented to study the forced convection in unsteady magnatohydrodynamic boundary layer flow of a nanofluid over a permeable shrinking sheet in the presence of thermal radiation and chemical reaction. A variable magnetic field is applied normal to the sheet. The nanofluid model includes Brownian motion and thermophoresis effects are also considered. The boundary layer equations governed by the partial differential equations are transformed into a set of ordinary differential equations the help of local similarity transformations. The coupled and nonlinear differential equations are solved by the implicit finite difference method along with the Thamous algorithm. We have explained the effect of various controlling flow parameters namely unsteadiness parameter A, magnetic parameter M, thermal radiation parameter R, Prandtl number Pr, Brownian motion parameter Nb, thermophoresis parameter Nt and Lewis number Le on the dimensionless velocity, temperature and nanoparticle volume fraction profiles are analyzed.
Mahanthesh, B.; Gireesha, B. J.; Shashikumar, N. S.; Shehzad, S. A.
2017-10-01
Present study addresses the Marangoni transport of dissipating SWCNT and MWCNT nanofluids under the influence of magnetic force and radiation. A novel exponential space dependent heat source is considered. The flow is generated due to a disk with surface tension created by thermal gradient. The partial differential equations system governing the flow of carbon-water nanoliquids and heat transfer through Marangoni convection is established. Subsequent system is reduced to nonlinear ordinary boundary value problem via generalized Karman transformations. Numerical solutions are developed of the arising nonlinear problem via Runge-Kutta based shooting approach. Impacts of embedded parameters are focused on Nusselt number, velocity and heat transport distributions through graphical illustrations. Our simulations figured out that the heat transfer rate increased via Marangoni convection; however it is decayed by applied magnetic force. The temperature of SWCNT-H2O nanoliquid dominates MWCNT-H2O nanoliquid.
M.M. Bhatti
2016-09-01
Full Text Available In this article, combine effects of Magnetohydrodynamics and partial slip on Blood flow of Ree–Eyring fluid through a porous medium have been investigated. The walls of the non-uniform porous channel are considered as compliant. The governing equation of Ree–Eyring fluid for blood flow are simplified using long wavelength and low Reynolds number approximation. The obtained resulting equation are solved analytically and exact solution has been obtained. The impact of different physical parameters such as Hartmann number, slip parameter, porous parameter, wall rigidity parameter, wall tension and mass characterization parameter are taken into account. It is found that velocity distribution increases due to slip effects while its behavior is opposite for Hartmann number. Trapping mechanism has also taken under consideration by drawing contour streamlines.
V. Rajesh
2016-01-01
Full Text Available In this paper, the problem of nanofluid flow and heat transfer due to the impulsive motion of a semi-infinite vertical plate in its own plane in the presence of magnetic field is analyzed by the implicit finite-difference numerical method. A range of nanofluids containing nanoparticles of aluminium oxide, copper, titanium oxide and silver with nanoparticle volume fraction range less than or equal to 0.04 are considered. The Tiwari-Das nanofluid model is employed. The velocity and temperature profiles as well as the skin friction coefficient and Nusselt number are examined for different parameters such as nanoparticle volume fraction, nanofluid type, magnetic parameter and thermal Grashof number. The present simulations are relevant to magnetic nanomaterials thermal flow processing in the chemical and metallurgical industries.
Soundalgekar, V.M. (Indian Inst. of Technology, Bombay); Shende, S.R. (Walchand Coll. of Engineering, Sangli, India)
1980-01-01
A two-dimensional unsteady flow of a viscous, incompressible, electrically conducting fluid past an infinite vertical porous plate has been carried out under the following conditions: (1) constant suction at the plate; (2) the wall temperature oscillating in time about a non-zero mean; (3) constant free-stream; and (4) transversely applied uniform magnetic field. Approximate solutions to coupled non-linear equations governing the flow have been derived for the transient velocity, the transient temperature, the amplitude and phase of the skin friction and the rate of heat transfer. The velocity and the temperature have been shown on graphs and the numerical values of the amplitude and phase are entered in tables. It has been observed that the amplitude of the skin friction and the rate of heat transfer decrease due to the application of the transverse magnetic field, but increase due to increasing the Grashof number.
Reza Hosseini
2012-01-01
Full Text Available The flow of an incompressible electrically conducting viscous fluid in convergent or divergent channels under the influence of an externally applied homogeneous magnetic field is studied both analytically and numerically. Navier-Stokes equations of fluid mechanics and Maxwell’s electromagnetism equations are reduced into highly non-linear ordinary differential equation. The resulting non-linear equation has been solved analytically using a very efficient technique, namely, differential transform method (DTM. The DTM solution is compared with the results obtained by a numerical method (shooting method, coupled with fourth-order Runge-Kutta scheme. The plots have revealed the physical characteristics of flow by changing angles of the channel, Hartmann and Reynolds numbers.
S. Sivasankaran
2013-03-01
Full Text Available This paper analyzes the influence of thermal radiation on the problem of unsteady magneto-convection flow of an electrically conducting fluid past a semi-infinite vertical porous plate embedded in a porous medium with time dependent suction. Perturbation technique is applied to transform the non-linear coupled governing partial differential equations in dimensionless form into a system of ordinary differential equations. The resulting equations are solved analytically and the solutions for the velocity and temperature fields are obtained. For different values of the flow parameters, the values for Nusselt number and skin-friction co-efficient are calculated. It is observed that the increase in the radiation parameter implies the decrease in the boundary layer thickness and enhances the rate of heat transfer. The velocity decreases as the existence of magnetic field becomes stronger.
Mostafa A.A. Mahmoud
2012-04-01
Full Text Available In this work, the effects of slip velocity on the flow and heat transfer for an electrically conducting micropolar fluid over a permeable stretching surface with variable heat flux in the presence of heat generation (absorption and a transverse magnetic field are investigated. The governing partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformation, which is solved numerically using the Chebyshev spectral method. The effects of the slip parameter on the flow, micro-rotation and temperature profiles as well as on the local skin-friction coefficient, the wall couple stress and the local Nusselt number are presented graphically. The numerical results of the local skin-friction coefficient, the wall couple stress and the local Nusselt number are given in a tabular form and discussed.
ABBAS Zaheer; MASOOD Tahmina; OLANREWAJU Philip Oladapo
2015-01-01
An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transverse magnetic field and generalized slip condition. Two flow problems corresponding to the planar and axisymmetric stretching/shrinking sheet were considered. By means of similarity transformations, the obtained resultant nonlinear ordinary differential equations were solved numerically using a shooting method for dual solutions of velocity and temperature profiles. Some important physical features of the flow and heat transfer in terms of the fluid velocity, the temperature distribution, the skin friction coefficient and the local Nusselt number for various values of the controlling governing parameters like velocity slip parameter, critical shear rate, magnetic field, ratio of stretching/shrinking rate to external flow rate and Prandtl number were analyzed and discussed. An increase of the critical shear rate decreases the fluid velocity whereas the local Nusselt number increases. The comparison of the present numerical results with the existing literature in a limiting case is given and found to be in an excellent agreement.
Yasmin Asia
2016-01-01
Full Text Available The unsteady laminar incompressible flow and heat transfer characteristics of an electrically conducting micropolar fluid in a porous channel with expanding or contracting walls is investigated. The relevant partial differential equations have been reduced to ordinary ones. The reduced system of ordinary differential equations (ODEs has been solved numerically by lower-upper (LU triangular factorization or Gaussian elimination and successive over relaxation (SOR method. The effects of some physical parameters such as magnetic parameter, micropolar parameters, wall expansion ratio, permeability Reynolds number and Prandtl number on the velocity, microrotation, temperature and the shear and couple stresses are discussed.
Letout, S; Duterrail, Y; Fautrelle, Y; Medina, M. , il.; Rey, F.; Laffont, G.
2015-01-01
International audience; The present paper deals with the analysis of the performances of a very large Annular Linear Induction Pumps (ALIP) for liquid sodium. This pump is able to provide high flow rates (more than 7,000 m3.h-1 with a pressure discharge of about 3.7 bar). Dimensions of pumping channel under the active part are of an average diameter of 966 mm and a length of 4,500 mm. It’s a double sided inductor pump. On the base of an imposed 2D axisymmetric geometry, performances (discharg...
Letout, S; Duterrail, Y; Fautrelle, Y; Medina, M. , il.; Rey, F.; Laffont, G.
2015-01-01
International audience; The present paper deals with the analysis of the behaviour of a very large Annular Linear Induction Pumps (ALIP) for liquid sodium. This pump is able to provide high flow rates (more than 7,000 m3/h with a pressure discharge of about 3.7 bar). Dimensions of pumping channel under the active part are of an average diameter of 966 mm and a length of 4,500 mm. The global and local stability of the pump are analyzed. It is found that in the nominal conditions, stable operat...
Ahmed Y. Ghaly
2002-01-01
Full Text Available We investigate the problem of free convection heat transfer near an isothermal stretching sheet. This has been done under the simultaneous action of buoyancy, radiation, and transverse magnetic field. The governing equations are solved by the shooting method. The velocity and temperature functions are represented graphically for various values of the flow parameters: radiation parameter F, free convection parameter Gr, magnetic parameter M, Prandtl number Pr, and the parameter of relative difference between the temperature of the sheet, and the temperature far away from the sheet r. The effects of the radiation and magnetic field parameters on the shear stress and heat flux are discussed.
Venkata Ramana Reddy Gurramapti
2016-01-01
Full Text Available The present paper concerns with the study of thermal radiation and magnetohydrodynamic effects on mixed convection flow of a viscous incompressible electrically-conducting fluid through a porous medium with variable permeability in the presence of oscillatory suction. The influence of a first-order homogeneous chemical reaction, heat source and Soret effects are analyzed. The resultant governing boundary layer equations are highly nonlinear and coupled form of partial differential equations which are solved analytically using two-term harmonic and non-harmonic functions. The effects of different physical parameters on the velocity, temperature and concentration fields are discussed in detail. The results are presented graphically and discussed qualitatively.
Chandrakala P.
2014-05-01
Full Text Available A numerical technique is employed to derive a solution to the transient natural convection flow of an incompressible viscous fluid past an impulsively started infinite isothermal vertical plate with uniform mass diffusion in the presence of a magnetic field and homogeneous chemical reaction of first order. The governing equations are solved using implicit finite-difference method. The effects of velocity, temperature and concentration for different parameters such as the magnetic field parameter, chemical reaction parameter, Prandtl number, Schmidt number, thermal Grashof number and mass Grashof number are studied. It is observed that the fluid velocity decreases with increasing the chemical reaction parameter and the magnetic field parameter.
Boričić Zoran
2005-01-01
Full Text Available This paper deals with laminar, unsteady flow of viscous, incompressible and electro conductive fluid caused by variable motion of flat plate. Fluid electro conductivity is variable. Velocity of the plate is time function. Plate moves in its own plane and in "still" fluid. Present external magnetic filed is perpendicular to the plate. Plate temperature is a function of longitudinal coordinate and time. Viscous dissipation, Joule heat, Hole and polarization effects are neglected. For obtaining of universal equations system general similarity method is used as well as impulse and energy equation of described problem.
Explosively-driven magnetohydrodynamic (MHD) generator studies
Agee, F.J.; Lehr, F.M. [Phillips Lab., Kirtland AFB, NM (United States); Vigil, M.; Kaye, R. [Sandia National Labs., Albuquerque, NM (United States); Gaudet, J.; Shiffler, D. [New Mexico Univ., Albuquerque, NM (United States)
1995-08-01
Plasma jet generators have been designed and tested which used an explosive driver and shocktube with a rectangular cross section that optimize the flow velocity and electrical conductivity. The latest in a series of designs has been tested using a reactive load to diagnose the electrical properties of the MHD generator/electromagnet combination. The results of these tests indicate that the plasma jet/MHD generator design does generate a flow velocity greater than 25 km/s and produces several gigawatts of pulsed power in a very small package size. A larger, new generator design is also presented.
MHD flow of Burger’s fluid over an off-centered rotating disk in a porous medium
Najeeb Alam Khan
2015-08-01
Full Text Available In this study, off-centered stagnation flow of three dimensional Burger’s fluid over an infinite rotating disk in a porous medium with a uniform magnetic field, which is applying normal to the disk, is investigated. A uniform suction/injection is applied through the surface of the porous disk. The structure has been modeled in the form of ordinary differential equations, which are reduced from partial differential equations by using the similarity transformation. Analytical solution is obtained by non-perturbation technique of homotopy analysis method (HAM. The influence of non-dimensional parameters on velocity profile is presented in graphical form and the numerical comparison is made with the viscous fluid as a special case.
Yasin, Mohd Hafizi Mat; Ishak, Anuar; Pop, Ioan
2015-12-09
The steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet with effects of viscous dissipation, Joule heating and partial velocity slip in the presence of a magnetic field is investigated. The partial differential equations are reduced to nonlinear ordinary differential equations by using a similarity transformation, before being solved numerically by shooting technique. Results indicate that the skin friction coefficient and the local Nusselt number increase as magnetic parameter increases. It is found that for the stretching sheet the solution is unique while for the shrinking sheet there exist nonunique solutions (dual solutions) in certain range of parameters. The stability analysis shows that the upper branch solution is stable while the lower branch solution is unstable.
Bhukta, D; Dash, G C; Mishra, S R
2014-01-01
An attempt has been made to study the heat and mass transfer effect in a boundary layer flow through porous medium of an electrically conducting viscoelastic fluid over a shrinking sheet subject to transverse magnetic field in the presence of heat source. Effects of radiation, viscous dissipation, and uniform heat sink on the heat transfer have been considered. The method of solution involves similarity transformation. The coupled nonlinear partial differential equations representing momentum, concentration, and nonhomogenous heat equation are reduced into a set of nonlinear ordinary differential equations. The transformed equations are solved by applying Kummer's function. The exact solution of temperature field is obtained for power-law surface temperature (PST) as well as power-law heat flux (PHF) boundary condition. The interaction of magnetic field is proved to be counterproductive in enhancing velocity and concentration distribution, whereas presence of porous matrix reduces the temperature field at all points.
Bilal, M.; Sagheer, M.; Hussain, S.; Mehmood, Y.
2017-06-01
The present study reveals the effect of homogeneous/hetereogeneous reaction on stagnation point flow of Williamson fluid in the presence of magnetohydrodynamics and heat generation/absorption coefficient over a stretching cylinder. Further the effects of variable thermal conductivity and thermal stratification are also considered. The governing partial differential equations are converted to ordinary differential equations with the help of similarity transformation. The system of coupled non-linear ordinary differential equations is then solved by shooting technique. MATLAB shooting code is validated by comparison with the previously published work in limiting case. Results are further strengthened when the present results are compared with MATLAB built-in function bvp4c. Effects of prominent parameters are deliberated graphically for the velocity, temperature and concentration profiles. Skin-friction coefficient and Nusselt number for the different parameters are investigated with the help of tables.
Sharma Pushkar Raj
2009-01-01
Full Text Available Aim of the paper is to investigate effects of ohmic heating and viscous dissipation on steady flow of a viscous incompressible electrically conducting fluid in the presence of uniform transverse magnetic field and variable free stream near a stagnation point on a stretching non-conducting isothermal sheet. The governing equations of continuity, momentum, and energy are transformed into ordinary differential equations and solved numerically using Runge-Kutta fourth order with shooting technique. The velocity and temperature distributions are discussed numerically and presented through graphs. Skin-friction coefficient and the Nusselt number at the sheet are derived, discussed numerically, and their numerical values for various values of physical parameters are compared with earlier results and presented through tables.
Rashidi, Mohammad M; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J; Freidoonimehr, Navid
2014-01-01
In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, [Formula: see text], local Nusselt number, [Formula: see text], and local Sherwood number [Formula: see text] are shown and explained through tables.
Mat Yasin, Mohd Hafizi; Ishak, Anuar; Pop, Ioan
2015-12-01
The steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet with effects of viscous dissipation, Joule heating and partial velocity slip in the presence of a magnetic field is investigated. The partial differential equations are reduced to nonlinear ordinary differential equations by using a similarity transformation, before being solved numerically by shooting technique. Results indicate that the skin friction coefficient and the local Nusselt number increase as magnetic parameter increases. It is found that for the stretching sheet the solution is unique while for the shrinking sheet there exist nonunique solutions (dual solutions) in certain range of parameters. The stability analysis shows that the upper branch solution is stable while the lower branch solution is unstable.
Jing Zhu; Lian-Cun Zheng; Xin-Xin Zhang
2011-01-01
This letter is concerned with the plane and axisymmetric stagnation-point flows and heat transfer of an electrically-conducting fluid past a stretching sheet in the presence of the thermal radiation and heat generation or absorption. The analytical solutions for the velocity distribution and dimensionless temperature profiles are obtained for the various values of the ratio of free stream velocity and stretching velocity,heat source parameter,Prandtl number,thermal radiation parameter,the suction and injection velocity parameter and magnetic parameter and dimensionality index in the series form with the help of homotopy analysis method(HAM). Convergence of the series is explicitly discussed. In addition,shear stress and heat flux at the surface are calculated.
Rana, B. M. Jewel; Ahmed, Rubel; Ahmmed, S. F.
2017-06-01
An analysis is carried out to investigate the effects of variable viscosity, thermal radiation, absorption of radiation and cross diffusion past an inclined exponential accelerated plate under the influence of variable heat and mass transfer. A set of suitable transformations has been used to obtain the non-dimensional coupled governing equations. Explicit finite difference technique has been used to solve the obtained numerical solutions of the present problem. Stability and convergence of the finite difference scheme have been carried out for this problem. Compaq Visual Fortran 6.6a has been used to calculate the numerical results. The effects of various physical parameters on the fluid velocity, temperature, concentration, coefficient of skin friction, rate of heat transfer, rate of mass transfer, streamlines and isotherms on the flow field have been presented graphically and discussed in details.
Parvin, Salma; Siddiqua, Ayesha
2016-07-01
Mixed convective flow and heat transfer characteristics of nanofluid inside a double lid driven cavity with a square heat generating block is analyzed numerically based on heat line approach. The water- alumina nanofluid is chosen as the operational fluid through the enclosure. The governing partial differential equations with proper boundary conditions are solved by Finite Element Method using Galerkin's weighted residual scheme. Calculations are performed for different solid volume fraction (χ) of nanoparticles 0 ≤ χ ≤ 0.15. Results are shown in terms of stream lines, isothermal lines, heat lines, average Nusselt number, average velocity and average temperature. An enhancement in heat transfer rate is observed with the increase of nanoparticles volume fraction.
Rashidi, Mohammad M.; Kavyani, Neda; Abelman, Shirley; Uddin, Mohammed J.; Freidoonimehr, Navid
2014-01-01
In this study combined heat and mass transfer by mixed convective flow along a moving vertical flat plate with hydrodynamic slip and thermal convective boundary condition is investigated. Using similarity variables, the governing nonlinear partial differential equations are converted into a system of coupled nonlinear ordinary differential equations. The transformed equations are then solved using a semi-numerical/analytical method called the differential transform method and results are compared with numerical results. Close agreement is found between the present method and the numerical method. Effects of the controlling parameters, including convective heat transfer, magnetic field, buoyancy ratio, hydrodynamic slip, mixed convective, Prandtl number and Schmidt number are investigated on the dimensionless velocity, temperature and concentration profiles. In addition effects of different parameters on the skin friction factor, , local Nusselt number, , and local Sherwood number are shown and explained through tables. PMID:25343360
Swati Mukhopadhyay
2013-09-01
Full Text Available The boundary layer flow and heat transfer towards a porous exponential stretching sheet in presence of a magnetic field is presented in this analysis. Velocity slip and thermal slip are considered instead of no-slip conditions at the boundary. Thermal radiation term is incorporated in the temperature equation. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and energy equations into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by shooting method. It is found that the horizontal velocity decreases with increasing slip parameter as well as with the increasing magnetic parameter. Temperature increases with the increasing values of magnetic parameter. Temperature is found to decrease with an increase of thermal slip parameter. Thermal radiation enhances the effective thermal diffusivity and the temperature rises.
Final Report: "Large-Eddy Simulation of Anisotropic MHD Turbulence"
Zikanov, Oleg
2008-06-23
To acquire better understanding of turbulence in flows of liquid metals and other electrically conducting fluids in the presence of steady magnetic fields and to develop an accurate and physically adequate LES (large-eddy simulation) model for such flows. The scientific objectives formulated in the project proposal have been fully completed. Several new directions were initiated and advanced in the course of work. Particular achievements include a detailed study of transformation of turbulence caused by the imposed magnetic field, development of an LES model that accurately reproduces this transformation, and solution of several fundamental questions of the interaction between the magnetic field and fluid flows. Eight papers have been published in respected peer-reviewed journals, with two more papers currently undergoing review, and one in preparation for submission. A post-doctoral researcher and a graduate student have been trained in the areas of MHD, turbulence research, and computational methods. Close collaboration ties have been established with the MHD research centers in Germany and Belgium.
Abd Elazem, Nader Y.; Ebaid, Abdelhalim
2017-07-01
In this paper, the effect of partial slip boundary condition on the heat and mass transfer of the Cu-water and Ag-water nanofluids over a stretching sheet in the presence of magnetic field and radiation. Such partial slip boundary condition has attracted much attention due to its wide applications in industry and chemical engineering. The flow is basically governing by a system of partial differential equations which are reduced to a system of ordinary differential equations. This system has been exactly solved, where exact analytical expression has been obtained for the fluid velocity in terms of exponential function, while the temperature distribution, and the nanoparticles concentration are expressed in terms of the generalized incomplete gamma function. In addition, explicit formulae are also derived from the rates of heat transfer and mass transfer. The effects of the permanent parameters on the skin friction, heat transfer coefficient, rate of mass transfer, velocity, the temperature profile, and concentration profile have been discussed through tables and graphs.
Entropy analysis of convective MHD flow of third grade non-Newtonian fluid over a stretching sheet
M.M. Rashidi
2017-03-01
Full Text Available The purpose of this article is to study and analyze the convective flow of a third grade non-Newtonian fluid due to a linearly stretching sheet subject to a magnetic field. The dimensionless entropy generation equation is obtained by solving the reduced momentum and energy equations. The momentum and energy equations are reduced to a system of ordinary differential equations by a similarity method. The optimal homotopy analysis method (OHAM is used to solve the resulting system of ordinary differential equations. The effects of the magnetic field, Biot number and Prandtl number on the velocity component and temperature are studied. The results show that the thermal boundary-layer thickness gets decreased with increasing the Prandtl number. In addition, Brownian motion plays an important role to improve thermal conductivity of the fluid. The main purpose of the paper is to study the effects of Reynolds number, dimensionless temperature difference, Brinkman number, Hartmann number and other physical parameters on the entropy generation. These results are analyzed and discussed.
Hari R. Kataria
2016-03-01
Full Text Available Analytic expression for unsteady free convective hydromagnetic boundary layer Casson fluid flow past an oscillating vertical plate embedded through porous medium in the presence of uniform transverse magnetic field, thermal radiation and chemical reaction is obtained. Both isothermal and ramped wall temperatures are taken into account. The governing equations are solved using Laplace transform technique and the solutions are presented in closed form. The numerical values of Casson fluid velocity, temperature and concentration at the plate are presented graphically for several values of the pertinent parameters. Effect of governing parameters on Skin friction, Nusselt number and Sherwood number is also discussed. Casson parameter γ is inversely proportional to the yield stress and it is observed that for the large value of Casson parameter, the fluid is close to the Newtonian fluid where the velocity is less than the Non-Newtonian fluid. It is seen that velocity increases and Temperature decreases with increase in thermal radiation R. Radiation parameter R signifies the relative contribution of conduction heat transfer to thermal radiation transfer. Concentration decreases tendency with chemical reaction parameter R′.
T. Poornima
2016-01-01
Full Text Available A mathematical model is presented for an optically dense fluid past an isothermal circular cylinder with chemical reaction taking place in it. A constant, static, magnetic field is applied transverse to the cylinder surface. The cylinder surface is maintained at a constant temperature. New variables are introduced to transform the complex geometry into a simple shape and the boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, Crank-Nicolson finite difference scheme. Numerical computations are made and the effects of the various material parameters on the velocity, temperature and concentration as well as the surface skin friction and surface heat and mass transfer rates are illustrated graphs and tables. Increasing magnetohydrodynamic body force parameter (M is found to decelerate the flow but enhance temperatures. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing radiation parameter.
Ullah, Imran; Khan, Ilyas; Shafie, Sharidan
2016-11-01
In the present work, the effects of chemical reaction on hydromagnetic natural convection flow of Casson nanofluid induced due to nonlinearly stretching sheet immersed in a porous medium under the influence of thermal radiation and convective boundary condition are performed numerically. Moreover, the effects of velocity slip at stretching sheet wall are also examined in this study. The highly nonlinear-coupled governing equations are converted to nonlinear ordinary differential equations via similarity transformations. The transformed governing equations are then solved numerically using the Keller box method and graphical results for velocity, temperature, and nanoparticle concentration as well as wall shear stress, heat, and mass transfer rate are achieved through MATLAB software. Numerical results for the wall shear stress and heat transfer rate are presented in tabular form and compared with previously published work. Comparison reveals that the results are in good agreement. Findings of this work demonstrate that Casson fluids are better to control the temperature and nanoparticle concentration as compared to Newtonian fluid when the sheet is stretched in a nonlinear way. Also, the presence of suspended nanoparticles effectively promotes the heat transfer mechanism in the base fluid.
Masood Khan
Full Text Available In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies.
Khan, Masood; Hashim; Alshomrani, Ali Saleh
2016-01-01
In the present investigation we analyze the impact of magnetic field on the stagnation-point flow of a generalized Newtonian Carreau fluid. The convective surface boundary conditions are considered to investigate the thermal boundary layer. The leading partial differential equations of the current problem are altered to a set of ordinary differential equations by picking local similarity transformations. The developed non-linear ordinary differential equations are then numerically integrated via Runge-Kutta Fehlberg method after changing into initial value problems. This investigation explores that the momentum and thermal boundary layers are significantly influenced by various pertinent parameters like the Hartmann number M, velocity shear ratio parameter α, Weissenberg number We, power law index n, Biot number γ and Prandtl number Pr. The analysis further reveals that the fluid velocity as well as the skin friction is raised by the velocity shear ratio parameter. Moreover, strong values of the Hartmann number correspond to thinning of the momentum boundary layer thickness while quite the opposite is true for the thermal boundary layer thickness. Additionally, it is seen that the numerical computations are in splendid consent with previously reported studies.
Uddin, Md Jashim; Khan, Waqar A; Ismail, A I Md
2013-01-01
A two-dimensional steady forced convective flow of a Newtonian fluid past a convectively heated permeable vertically moving plate in the presence of a variable magnetic field and radiation effect has been investigated numerically. The plate moves either in assisting or opposing direction to the free stream. The plate and free stream velocities are considered to be proportional to x(m) whilst the magnetic field and mass transfer velocity are taken to be proportional to x((m-1)/2) where x is the distance along the plate from the leading edge of the plate. Instead of using existing similarity transformations, we use a linear group of transformations to transform the governing equations into similarity equations with relevant boundary conditions. Numerical solutions of the similarity equations are presented to show the effects of the controlling parameters on the dimensionless velocity, temperature and concentration profiles as well as on the friction factor, rate of heat and mass transfer. It is found that the rate of heat transfer elevates with the mass transfer velocity, convective heat transfer, Prandtl number, velocity ratio and the magnetic field parameters. It is also found that the rate of mass transfer enhances with the mass transfer velocity, velocity ratio, power law index and the Schmidt number, whilst it suppresses with the magnetic field parameter. Our results are compared with the results existing in the open literature. The comparisons are satisfactory.
Ullah, Imran; Khan, Ilyas; Shafie, Sharidan
2016-12-01
In the present work, the effects of chemical reaction on hydromagnetic natural convection flow of Casson nanofluid induced due to nonlinearly stretching sheet immersed in a porous medium under the influence of thermal radiation and convective boundary condition are performed numerically. Moreover, the effects of velocity slip at stretching sheet wall are also examined in this study. The highly nonlinear-coupled governing equations are converted to nonlinear ordinary differential equations via similarity transformations. The transformed governing equations are then solved numerically using the Keller box method and graphical results for velocity, temperature, and nanoparticle concentration as well as wall shear stress, heat, and mass transfer rate are achieved through MATLAB software. Numerical results for the wall shear stress and heat transfer rate are presented in tabular form and compared with previously published work. Comparison reveals that the results are in good agreement. Findings of this work demonstrate that Casson fluids are better to control the temperature and nanoparticle concentration as compared to Newtonian fluid when the sheet is stretched in a nonlinear way. Also, the presence of suspended nanoparticles effectively promotes the heat transfer mechanism in the base fluid.
SAFETY CONSIDERATIONS WITH BLOOD FLOW RESTRICTED RESISTANCE TRAINING
Alan Kacin
2015-11-01
Full Text Available Blood flow restricted resistance (BFRR training with pneumatic tourniquet has been suggested as an alternative for conventional weight training due to the proven benefits for muscle strength and hypertrophy using relatively low resistance, hence reducing the mechanical stress across a joint. As such, it has become an important part of rehabilitation programs used in either injured or operated athletes. Despite a general consensus on effectiveness of BFRR training for muscle conditioning, there are several uncertainties regarding the interplay of various extrinsic and intrinsic factors on its safety and efficiency, which are being reviewed from a clinical perspective. Among extrinsic factors tourniquet cuff pressure, size and shape have been identified as key for safety and efficiency. Among intrinsic factors, limb anthropometrics, patient history and presence of cardiac, vascular, metabolic or peripheral neurologic conditions have been recognized as most important. Though there are a few potential safety concerns connected to BFRR training, the following have been identified as the most probable and health-hazardous: (a mechanical injury to the skin, muscle, and peripheral nerves, (b venous thrombosis due to vascular damage and disturbed hemodynamics and (c augmented arterial blood pressure responses due to combined high body exertion and increased peripheral vascular resistance. Based on reviewed literature and authors’ personal experience with the use of BFRR training in injured athletes, some guidelines for its safe application are outlined. Also, a comprehensive risk assessment tool for screening of subjects prior to their inclusion in a BFRR training program is being introduced.
Om Prakash
2011-06-01
Full Text Available The present paper is concerned with the study of MHD free convective flow of a visco-elastic (Kuvshinski type dusty gas through a porous medium induced by the motion of a semi-infinite flat plate under the influence of radiative heat transfer moving with velocity decreasing exponentially with time. The expressions for velocity distribution of a dusty gas and dust particles, concentration profile and temperature field are obtained. The effect of Schmidt number (Sc, Magnetic field parameter (M and Radiation parameter (N on velocity distribution of dusty gas and dust particles, concentration and temperature distribution are discussed graphically.
Schnack, Dalton D.
In this lecture we will examine some simple examples of MHD equilibrium configurations. These will all be in cylindrical geometry. They form the basis for more complicated equilibrium states in toroidal geometry.
Properties of train traffic flow in a moving block system
Wang Min; Zeng Jun-Wei; Qian Yong-Sheng; Li Wen-Jun; Yang Fang; Jia Xin-Xin
2012-01-01
The development direction of railways is toward the improvement of capacity and service quality,where the service quality includes safety,schedule,high speed,and comfort.In light of the existing cellular automaton models,in this paper,we develop a model to analyze the mixed running processes of trains with maximal speeds of 500 km/h and 350 km/h respectively in the moving block system.In the proposed model,we establish some sound rules to control the running processes of a train,where the rules include the departure rules in the intermediate stations,the overtaking rules,and the conditions of speed limitation for a train stopping at a station or passing through a station.With the consideration of the mixed ratio and the distance between two adjacent stations,the properties of the train traffic flow (including capacity and average speed) are simulated.The numerical results show that the interactions among different trains will affect the capacity,and a proper increase of the spatial distance between two adjacent stations can enhance the capacity and the average speed under the moving block.
Metallurgical technologies, energy conversion, and magnetohydrodynamic flows
Branover, H.; Unger, Y.
1993-01-01
The present volume discusses metallurgical applications of MHD, R D on MHD devices employing liquid working medium for process applications, electromagnetic (EM) modulation of molten metal flow, EM pump performance of superconducting MHD devices, induction EM alkali-metal pumps, a physical model for EM-driven flow in channel-induction furnaces, grain refinement in Al alloys via EM vibrational method, dendrite growth of solidifying metal in dc magnetic field, MHD for mass and heat transfer in single-crystal melt growth, inverse EM shaping, and liquid-metal MHD development in Israel. Also discussed are the embrittlement of steel by lead, an open cycle MHD disk generator, the acceleration of gas-liquid piston flows for molten-metal MHD generators, MHD flow around a cylinder, new MHD drag coefficients, liquid-metal MHD two-phase flow, and two-phase liquid gas mixers for MHD energy conversion.
K. GANGADHAR
2015-01-01
Full Text Available This study is devoted to investigate the radiation, heat generation viscous dissipation and magnetohydrodynamic effects on the laminar boundary layer about a flat-plate in a uniform stream of fluid (Blasius flow, and about a moving plate in a quiescent ambient fluid (Sakiadis flow both under a convective surface boundary condition. Using a similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting technique alongside with the forth order of Runge-Kutta method and the variations of dimensionless surface temperature and fluid-solid interface characteristics for different values of Magnetic field parameter M, Grashof number Gr, Prandtl number Pr, radiation parameter NR, Heat generation parameter Q, Convective parameter and the Eckert number Ec, which characterizes our convection processes are graphed and tabulated. Quite different and interesting behaviors were encountered for Blasius flow compared with a Sakiadis flow. A comparison with previously published results on special cases of the problem shows excellent agreement.
Analogue Kerr-like geometries in a MHD inflow
Noda, Sousuke; Takahashi, Masaaki
2016-01-01
We present a model of the analogue black hole in magnetohydrodynamic (MHD) flow. For a two dimensional axisymmetric stationary trans-magnetosonic inflow with a sink, using the dispersion relation of the MHD waves, we introduce the effective geometries for magnetoacoustic waves propagating in the MHD flow. Investigating the properties of the effective potentials for magnetoacoustic rays, we find that the effective geometries can be classified into five types which include analogue spacetimes of the Kerr black hole, ultra spinning stars with ergoregions and spinning stars without ergoregions. We address the effects of the magnetic pressure and the magnetic tension on each magnetoacoustic geometries.
MHD equilibria of astrospheric flows
Nickeler, Dieter Horst
2005-01-01
The hot gas cavities around stars which have a stellar wind are called astrospheres. Between the outer interstellar medium and the stellar wind there forms a contact surface or boundary surface which is called an astropause. In this thesis the geometrical shape of such an astrosphere/astropause regi
The Statistical Mechanics of Ideal MHD Turbulence
Shebalin, John V.
2003-01-01
Turbulence is a universal, nonlinear phenomenon found in all energetic fluid and plasma motion. In particular. understanding magneto hydrodynamic (MHD) turbulence and incorporating its effects in the computation and prediction of the flow of ionized gases in space, for example, are great challenges that must be met if such computations and predictions are to be meaningful. Although a general solution to the "problem of turbulence" does not exist in closed form, numerical integrations allow us to explore the phase space of solutions for both ideal and dissipative flows. For homogeneous, incompressible turbulence, Fourier methods are appropriate, and phase space is defined by the Fourier coefficients of the physical fields. In the case of ideal MHD flows, a fairly robust statistical mechanics has been developed, in which the symmetry and ergodic properties of phase space is understood. A discussion of these properties will illuminate our principal discovery: Coherent structure and randomness co-exist in ideal MHD turbulence. For dissipative flows, as opposed to ideal flows, progress beyond the dimensional analysis of Kolmogorov has been difficult. Here, some possible future directions that draw on the ideal results will also be discussed. Our conclusion will be that while ideal turbulence is now well understood, real turbulence still presents great challenges.
张秀杰; 潘传杰; 许增裕
2013-01-01
建立了液态金属膜流MHD流动的数学物理模型，开发了相关数值模拟程序。首先，通过相关实验结果对该程序进行了校验。然后，对液态金属锂膜流在横向强磁场中的MHD流动进行了模拟，给出了入口流速、入口膜厚、底壁宽度、壁面粗糙度对其MHD流动的影响。模拟结果表明，存在唯一入口流速和唯一底壁宽度使得膜流MHD流动稳定；存在两个入口膜厚值使得膜流MHD流动稳定；壁面粗糙度对膜流MHD流动影响较小。最后，通过膜流MHD流动平衡分析，初步给出了其MHD稳定性的物理机制。分析结果表明，增加底壁宽度有利于降低电磁阻力，增加膜流的MHD稳定性；膜流的稳定流速随入口膜厚的增加先增大后减小，同时其最大稳定流速值相对于无磁场的情况减小很多。%A mathematical and physical modeling of the liquid metal MHD film flow has been built and a related numerical code has been developed. Firstly, the code is validated by the related experimental results. Secondly, numerical simulation of the liquid metal MHD film flow is carried out by this code. The effects of the inlet velocity, the initial film thickness, the width of the bottom wall and the wall roughness on the flow state are presented. It is indicated that there is only one value of the inlet velocity and the substrate width when the film flow state is stable, and two initial film thickness values exist at the stable state, the wall roughness has little effect on the film flow state. In the end, the preliminary stable mechanism of the film MHD flow based on a equilibrium analysis is described, it is indicated that the increase of the substrate width is helpful to reduce the electromagnetic resistance and increase the MHD stability;the stable velocity firstly increases then decreases with the increase of the initial film thickness and it is greatly reduced compared to the no magnetic field case.
陈瑞锋; 魏志军; 王宁飞
2012-01-01
为了快速分析磁流体管流,采用涡轮喷气发动机模型对磁流体管流进行类比分析,引入变截面管流理论和修改过的多变效率表达式,推导了磁流体发电器和加速器的准一维模型,采用二维数值方法验证了准一维模型的可行性,利用该准一维模型对磁流体管流进行了性能分析,结果表明,多变效率的引入使准一维模型更加完整,当负载系数不变时,磁流体装置中的平均马赫数越低,其等熵效率越高。%For the Purpose of quick analysis for the magnetohydrodynamic （MHD） flow, quasi-one-dimensional models for the MHD equipments have been deduced using the turbojet engine model, the variable cross-section pipe flow theory and the expressions of modified polytropie efficiencies. The feasibility of the quasi-one-dimensional models have been validated with the 2D numerical method. Then, the performance analysis has been performed with these quasi-one-dimensional models, which shows that the modified polytropic efficiencies make the models improved, and when the load factors is kept to be constant, the effieiencies of the MHD flow increase by decreasing the average Mach number.
李俊峰; 倪明玖
2011-01-01
在低磁场雷诺数条件下,基于电势泊松方程,发展了交错网格下可以精确计算电流和洛伦兹力(电磁力)的相容守恒格式.采用压力为变量的原始变量法求解不可压缩Navier-Stokes方程,所计算的电流满足电荷守恒定律,所计算的电磁力满足动量守恒定律.对金属流体在Hartmann数50～5000范围内验证了格式的精确性.交错网格下相容守恒格式的发展为后续MHD稳定性分析、湍流的大涡模拟及直接数值模拟提供很好的选择.%A consistent and conservative scheme has been extended and developed on a staggered grid system for liquid metal MHD flow at a low magnetic Reynolds number by solving electrical potential Poisson equation based on the Ohm's law and the charge conservation law. The consistent scheme is used to ensure the calculated current density conserves the charge, and the divergence formula of the Lorentz force is used to ensure the momentum conservation. Simulation of liquid metal flows in a three-dimensional straight channel is conducted and compared with the analytical solutions from Shercliff's and Hunt's. The numerical results are in good agreement with analytical solutions for the Hartmann numbers from 50 to 5000. A fully conservative scheme on a staggered grid, which can conserve mass, momentum and kinetic energy and charge, is then developed with the central-symmetrical scheme for the convective term and the pressure term and with the consistent and conservative scheme for the calculation of the current density and the Lorentz force. A fully conservative scheme can be a good tool for numerical analysis of MHD flow instability, large eddy simulation (LES) and direct-numerical simulation (DNS) of MHD turbulence.
Lowery, Ryan P; Joy, Jordan M; Loenneke, Jeremy P; de Souza, Eduardo O; Machado, Marco; Dudeck, Joshua E; Wilson, Jacob M
2014-07-01
Resistance training in combination with practical blood flow restriction (pBFR) is thought to stimulate muscle hypertrophy by increasing muscle activation and muscle swelling. Most previous studies used the KAATSU device; however, little long-term research has been completed using pBFR. To investigate the effects of pBFR on muscle hypertrophy. Twenty college-aged male participants with a minimum of 1 year of resistance training experience were recruited for this study. Our study consisted of a randomized, crossover protocol consisting of individuals either using pBFR for the elbow flexors during the first 4 weeks (BFR-HI) or the second 4 weeks (HI-BFR) of an 8-week resistance training programme. Direct ultrasound-determined bicep muscle thickness was assessed collectively at baseline and at the end of weeks 4 and 8. There were no differences in muscle thickness between groups at baseline (P = 0·52). There were time (Pmuscle thickness in which the combined values of both groups increased on average from week 0 (3·66 ± 0·06) to week 4 (3·95 ± 0·05) to week 8 (4·11 ± 0·07). However, both the BFR-HI and HI-BFR increased significantly from baseline to week 4 (6·9% and 8·6%, Pmuscle hypertrophy to the same degree to that of high-intensity resistance training. © 2013 Scandinavian Society of Clinical Physiology and Nuclear Medicine. Published by John Wiley & Sons Ltd.
Wu, C.; Chang, T.
2010-12-01
A new method in describing the multifractal characteristics of intermittent events was introduced by Cheng and Wu [Chang T. and Wu C.C., Physical Rev, E77, 045401(R), 2008]. The procedure provides a natural connection between the rank-ordered spectrum and the idea of one-parameter scaling for monofractals. This technique has been demonstrated using results obtained from a 2D MHD simulation. It has also been successfully applied to in-situ solar wind observations [Chang T., Wu, C.C. and Podesta, J., AIP Conf Proc. 1039, 75, 2008], and the broadband electric field oscillations from the auroral zone [Tam, S.W.Y. et al., Physical Rev, E81, 036414, 2010]. We take the next step in this procedure. By using the ROMA spectra and the scaled probability distribution functions (PDFs), raw PDFs can be calculated, which can be compared directly with PDFs from observations or simulation results. In addition to 2D MHD simulation results and in-situ solar wind observation, we show clearly using the ROMA analysis the multifractal character of the 3D fluid simulation data obtained from the JHU turbulence database cluster at http://turbulence.pha.jhu.edu. In particular, we show the scaling of the non-symmetrical PDF for the parallel-velocity fluctuations of this 3D fluid data.
Application of ADER Scheme in MHD Simulation
ZHANG Yanyan; FENG Xueshang; JIANG Chaowei; ZHOU Yufen
2012-01-01
The Arbitrary accuracy Derivatives Riemann problem method（ADER） scheme is a new high order numerical scheme based on the concept of finite volume integration,and it is very easy to be extended up to any order of space and time accuracy by using a Taylor time expansion at the cell interface position.So far the approach has been applied successfully to flow mechanics problems.Our objective here is to carry out the extension of multidimensional ADER schemes to multidimensional MHD systems of conservation laws by calculating several MHD problems in one and two dimensions： （ⅰ） Brio-Wu shock tube problem,（ⅱ） Dai-Woodward shock tube problem,（ⅲ） Orszag-Tang MHD vortex problem.The numerical results prove that the ADER scheme possesses the ability to solve MHD problem,remains high order accuracy both in space and time,keeps precise in capturing the shock.Meanwhile,the compared tests show that the ADER scheme can restrain the oscillation and obtain the high order non-oscillatory result.
Numerical simulation of MHD duct flow about laminar and turbulence model%磁流体管流的层流与湍流模型数值模拟
侯俊; 毛洁; 潘华辰
2013-01-01
采用FLUENT软件分别对外加均匀横向磁场的等截面三维充分发展液态金属管流的层流模型和低雷诺数湍流Lam/Bremhost(LB)模型进行了数值模拟,分析了外加磁场对普通方管LB模型速度分布和压降的影响.比较在相同哈特曼数下,层流和湍流模型方管截面上速度分布和管道中MHD压降.其中,对电流的计算采用磁感应方程来求得.数值模拟结果证明了用低雷诺数LB湍流模型解决方管磁流体流动的可行性.通过层流模型和湍流模型的对比可知,层流模型有较短的入口长度,但管内流体的压降却很大；而湍流模型管内速度更加平均化,管内压降较小,但管内入口长度较长.%The numerical analysis of full-developed flow of a liquid metal in a rectangular duct of constant cross-section with a uniform transverse magnetic field was proceeded in laminar and low-Reynolds number Lam/Bremhost turbulence model (for short LB model) using FLUENT software. The paper analyzed the influence of external magnetic field for velocity distribution and MHD pressure drop in turbulence model. Under the same Hartmann number conductions, the paper compared the velocity distribution and MHD pressure drop of laminar model and turbulent model. The solution of current density was obtained by means of induced magnetic field formulation. The result of numerical simulation proved that this was a feasible scheme to use the low-Reynolds LB turbulence model to calculate MHD duct flow. Comparison between laminar model and turbulent model show that laminar model made shorter entrance length, but the pressure drop in the duct increased. Turbulent model had more average speed and smaller pressure drop, but entrance length was longer.
MHD Integrated Topping Cycle Project
1992-07-01
This seventeenth quarterly technical progress report of the MHD Integrated Topping Cycle Project presents the accomplishments during the period August 1, 1991 to October 31, 1991. Manufacturing of the prototypical combustor pressure shell has been completed including leak, proof, and assembly fit checking. Manufacturing of forty-five cooling panels was also completed including leak, proof, and flow testing. All precombustor internal components (combustion can baffle and swirl box) were received and checked, and integration of the components was initiated. A decision was made regarding the primary and backup designs for the 1A4 channel. The assembly of the channel related prototypical hardware continued. The cathode wall electrical wiring is now complete. The mechanical design of the diffuser has been completed.
Proceedings of the workshop on nonlinear MHD and extended MHD
NONE
1998-12-01
Nonlinear MHD simulations have proven their value in interpreting experimental results over the years. As magnetic fusion experiments reach higher performance regimes, more sophisticated experimental diagnostics coupled with ever expanding computer capabilities have increased both the need for and the feasibility of nonlinear global simulations using models more realistic than regular ideal and resistive MHD. Such extended-MHD nonlinear simulations have already begun to produce useful results. These studies are expected to lead to ever more comprehensive simulation models in the future and to play a vital role in fully understanding fusion plasmas. Topics include the following: (1) current state of nonlinear MHD and extended-MHD simulations; (2) comparisons to experimental data; (3) discussions between experimentalists and theorists; (4) /equations for extended-MHD models, kinetic-based closures; and (5) paths toward more comprehensive simulation models, etc. Selected papers have been indexed separately for inclusion in the Energy Science and Technology Database.
MHD thrust vectoring of a rocket engine
Labaune, Julien; Packan, Denis; Tholin, Fabien; Chemartin, Laurent; Stillace, Thierry; Masson, Frederic
2016-09-01
In this work, the possibility to use MagnetoHydroDynamics (MHD) to vectorize the thrust of a solid propellant rocket engine exhaust is investigated. Using a magnetic field for vectoring offers a mass gain and a reusability advantage compared to standard gimbaled, elastomer-joint systems. Analytical and numerical models were used to evaluate the flow deviation with a 1 Tesla magnetic field inside the nozzle. The fluid flow in the resistive MHD approximation is calculated using the KRONOS code from ONERA, coupling the hypersonic CFD platform CEDRE and the electrical code SATURNE from EDF. A critical parameter of these simulations is the electrical conductivity, which was evaluated using a set of equilibrium calculations with 25 species. Two models were used: local thermodynamic equilibrium and frozen flow. In both cases, chlorine captures a large fraction of free electrons, limiting the electrical conductivity to a value inadequate for thrust vectoring applications. However, when using chlorine-free propergols with 1% in mass of alkali, an MHD thrust vectoring of several degrees was obtained.
K.C. Saha
2015-04-01
Full Text Available The effects of MHD free convection heat and mass transfer of power-law Non-Newtonian fluids along a stretching sheet with viscous dissipation has been analyzed. This has been done under the simultaneous action of suction, thermal radiation and uniform transverse magnetic field. The stretching sheet is assumed to continuously moving with a power-law velocity and maintaining a uniform surface heat-flux. The governing non-linear partial differential equations are transformed into non-linear ordinary differential equations, using appropriate similarity transformations and the resulting problem is solved numerically using Nachtsheim-Swigert shooting iteration technique along with sixth order Runge-Kutta integration scheme. A parametric study of the parameters arising in the problem such as the Eckert number due to viscous dissipation, radiation number, buoyancy parameter, Schmidt number, Prandtl number etc are studied and the obtained results are shown graphically and the physical aspects of the problem are discussed.
Frutos-Alfaro, Francisco
2015-01-01
A program to generate codes in Fortran and C of the full Magnetohydrodynamic equations is shown. The program used the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the MHD equations to obtain a code that can be used as a seed for a MHD code for numerical applications. As an example, we present part of output of our programs for Cartesian coordinates and how to do the discretization.
MHD equilibria with diamagnetic effects
Tessarotto, M.; Zorat, R.; Johnson, J. L.; White, R. B.
1997-11-01
An outstanding issue in magnetic confinement is the establishment of MHD equilibria with enhanced flow shear profiles for which turbulence (and transport) may be locally effectively suppressed or at least substantially reduced with respect to standard weak turbulence models. Strong flows develop in the presence of equilibrium E× B-drifts produced by a strong radial electric field, as well as due to diamagnetic contributions produced by steep equilibrium radial profiles of number density, temperature and the flow velocity itself. In the framework of a kinetic description, this generally requires the construction of guiding-center variables correct to second order in the relevant expansion parameter. For this purpose, the Lagrangian approach developed recently by Tessarotto et al. [1] is adopted. In this paper the conditions of existence of such equilibria are analyzed and their basic physical properties are investigated in detail. 1 - M. Pozzo, M. Tessarotto and R. Zorat, in Theory of fusion Plasmas, E.Sindoni et al. eds. (Societá Italiana di Fisica, Editrice Compositori, Bologna, 1996), p.295.
UPWIND SCHEME FOR IDEAL 2-D MHD FLOWS BASED ON UNSTRUCTURED MESH%非结构网格二维理想MHD绕流逆风格式解法
潘勇; 王江峰; 伍贻兆
2007-01-01
An upwind scheme based on the unstructured mesh is developed to solve ideal 2-D magnetohydrodynamics(MHD) equations. The inviscid fluxes are approximated by using the modified advection upstream splitting method(AUSM) scheme, and a 5-stage explicit Runge-Kutta scheme is adopted in the time integration. To avoid the influence of the magnetic field divergence created during the simulation, the hyperbolic divergence cleaning method is introduced. The shock-capturing properties of the method are verified by solving the MHD shock-tube problem. Then the 2-D nozzle flow with the magnetic field is numerically simulated on the unstructured mesh. Computational results demonstrate the effects of the magnetic field and agree well with those from references.%在非结构网格上发展了针对二维理想磁流体方程组的逆风格式求解方法.控制方程中的对流项采用AUSM格式处理,时间推进采用显式5步龙格-库塔方法.为了消除计算中产生的磁场散度的影响,引入了双曲型散度清除方法.通过对磁流体激波管问题的求解验证了该方法对激波的捕捉能力,对有均匀磁场干扰下的喷管流动情况进行了数值模拟,并与文献中结果进行了对比.计算结果显示了磁场对磁流体流动的干扰效应,该结果与参考文献中的数值模拟结果相吻合.
Process flows for cyber forensic training and operations
Venter, JP
2006-02-01
Full Text Available In this paper the development and testing of Cyber First Responder Process Flows is discussed. A generic process flow framework is presented and design principles and layout characteristics as well as important points within the process flows...
Nonlinear MHD dynamo operating at equipartition
Archontis, V.; Dorch, Bertil; Nordlund, Åke
2007-01-01
Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy-equipartition a......Context.We present results from non linear MHD dynamo experiments with a three-dimensional steady and smooth flow that drives fast dynamo action in the kinematic regime. In the saturation regime, the system yields strong magnetic fields, which undergo transitions between an energy......-equipartition and a turbulent state. The generation and evolution of such strong magnetic fields is relevant for the understanding of dynamo action that occurs in stars and other astrophysical objects. Aims.We study the mode of operation of this dynamo, in the linear and non-linear saturation regimes. We also consider...... the effect of varying the magnetic and fluid Reymolds number on the non-linear behaviour of the system. Methods.We perform three-dimensional non-linear MHD simulations and visualization using a high resolution numerical scheme. Results.We find that this dynamo has a high growth rate in the linear regime...
Frutos-Alfaro, Francisco; Carboni-Mendez, Rodrigo
2015-01-01
A program to generate codes in Fortran and C of the full Magnetohydrodynamic equations is shown. The program used the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the MHD equations to obtain a c...
G. García Segura
2000-01-01
Full Text Available Se presenta un escenario auto consistente para explicar la morfolog a de las nebulosas planetarias. El escenario es consistente con la distribuci on Gal actica de los diferentes tipos morfol ogicos. Este trabajo resuelve, por medio de efectos MHD, algunas de las caracter sticas controversiales que aparecen en las nebulosas planetarias. Estas caracter sticas incluyen la presencia de ujos axisim etricos y colimados, con una cinem atica que aumenta linealmente con la distancia y la existencia de morfolog as asim etricas tales como las de las nebulosas con simetr a de punto.
Muthuraj R.
2012-01-01
Full Text Available A mathematical model is developed to examine the effect of chemical reaction on MHD mixed convective heat and mass transfer flow of a couple-stress fluid in vertical porous space in the presence of temperature dependent heat source with travelling thermal waves. The dimensionless governing equations are assumed to be made up of two parts: a mean part corresponding to the fully developed mean flow, and a small perturbed part, using amplitude as a small parameter. The analytical solution of perturbed part have been carried out by using the long-wave approximation. The expressions for the zeroth-order and the first order solutions are obtained and the results of the heat and mass transfer characteristics are presented graphically for various values of parameters entering into the problem. It is noted that velocity of the fluid increases with the increase of the couple stress parameter and increasing the chemical reaction parameter leads suppress the velocity of the fluid. Cross velocity decreases with an increase of the phase angle. The increase of the chemical reaction parameter and Schmidt number lead to decrease the fluid concentration. The hydrodynamic case for a non-porous space in the absence of the temperature dependent heat source for Newtonian fluid can be captured as a limiting case of our analysis by taking, and α1→0, Da→∞, a→∞.
Retallick, F.D.
1978-04-01
This document establishes criteria to be utilized for the design of a pilot-scale (150 to 300 MW thermal) open cycle, coal-fired MHD/steam plant. Criteria for this Engineering Test Facility (ETF) are presented relative to plant siting, plant engineering and operations, MHD-ETF testing, costing and scheduling.
MHD turbulence and distributed chaos
Bershadskii, A
2016-01-01
It is shown, using results of recent direct numerical simulations, that spectral properties of distributed chaos in MHD turbulence with zero mean magnetic field are similar to those of hydrodynamic turbulence. An exception is MHD spontaneous breaking of space translational symmetry, when the stretched exponential spectrum $\\exp(-k/k_{\\beta})^{\\beta}$ has $\\beta=4/7$.
High-Order Finite Difference GLM-MHD Schemes for Cell-Centered MHD
Mignone, A; Bodo, G
2010-01-01
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different reconstruction techniques based on recently improved versions of the weighted essentially non-oscillatory (WENO) schemes, monotonicity preserving (MP) schemes as well as slope-limited polynomial reconstruction. The proposed numerical methods are highly accurate in smooth regions of the flow, avoid loss of accuracy in proximity of smooth extrema and provide sharp non-oscillatory transitions at discontinuities. We suggest a numerical formulation based on a cell-centered approach where all of the primary flow variables are discretized at the zone center. The divergence-free condition is enforced by augmenting the MHD equations with a generalized Lagrange multiplier yielding a mixed hyperbolic/parabolic correction, as in Dedner et al. (J. Comput. Phys. 175 (2002) 645-673). The resulting...
XUZenyu; KANGWeishan; PANChuanjie; DENHongyin; ZHANGYanxu
2003-01-01
In lost paper of magneto-hydrodynamic instability analysis of liquid metal free surface jet flow (Part Ⅰ), the magneto-hydrodynamic instability was analyzed for the jet flow in a transverse non-uniform magnetic field, BT. But, as all known, for the real conditions of liquid metal limiter-divertor plasma-facing components are in toroidal and poloidal fields. So, we try to analyze the magneto-hydrodynamic instability of the jet flow (hereby only for circular shape cross section jet flow) in the zone of non-uniform magnetic fields,
A Numerical Study of Resistivity and Hall Effects for a Compressible MHD Model
Yee, H. C.; Sjogreen, B.
2005-01-01
The effect of resistive, Hall, and viscous terms on the flow structure compared with compressible ideal MHD is studied numerically for a one-fluid non-ideal MHD model. The goal of the present study is to shed some light on the emerging area of non-ideal MHD modeling and simulation. Numerical experiments are performed on a hypersonic blunt body flow with future application to plasma aerodynamics flow control in reentry vehicles. Numerical experiments are also performed on a magnetized time-developing mixing layer with possible application to magnetic/turbulence mixing.
MHD discontinuities in solar flares: continuous transitions and plasma heating
Ledentsov, L S
2015-01-01
The boundary conditions for the ideal MHD equations on a plane dis- continuity surface are investigated. It is shown that, for a given mass flux through a discontinuity, its type depends only on the relation between inclina- tion angles of a magnetic field. Moreover, the conservation laws on a surface of discontinuity allow changing a discontinuity type with gradual (continu- ous) changes in the conditions of plasma flow. Then there are the so-called transition solutions that satisfy simultaneously two types of discontinuities. We obtain all transition solutions on the basis of the complete system of boundary conditions for the MHD equations. We also found the expression describing a jump of internal energy of the plasma flowing through the dis- continuity. Firstly, this allows constructing a generalized scheme of possible continuous transitions between MHD discontinuities. Secondly, it enables the examination of the dependence of plasma heating by plasma density and configuration of the magnetic field near t...
Steady-State Axisymmetric MHD Solutions with Various Boundary Conditions
Wang, Lile
2014-01-01
Axisymmetric magnetohydrodynamics (MHD) can be invoked for describing astrophysical magnetized flows and formulated to model stellar magnetospheres including main sequence stars (e.g. the Sun), compact stellar objects [e.g. magnetic white dwarfs (MWDs), radio pulsars, anomalous X-ray pulsars (AXPs), magnetars, isolated neutron stars etc.], and planets as a major step forward towards a full three-dimensional model construction. Using powerful and reliable numerical solvers based on two distinct finite-difference method (FDM) and finite-element method (FEM) schemes of algorithm, we examine axisymmetric steady-state or stationary MHD models in Throumoulopoulos & Tasso (2001), finding that their separable semi-analytic nonlinear solutions are actually not unique given their specific selection of several free functionals and chosen boundary conditions. The multiplicity of nonlinear steady MHD solutions gives rise to differences in the total energies contained in the magnetic fields and flow velocity fields as ...
Course 1: Accretion and Ejection-Related MHD
Heyvaerts, Jean
This lecture is an introduction to MHD. Relevant equations, both in the classical and special-relativistic regimes are derived. The magnetic field evolution is considered both in the perfect-MHD limit and when weak resistivity is present, giving rise to reconnection flows. A short section gives a flavour of dynamo theory. Examples of simple stationnary flows and equilibria are then presented. Stationnary, axisymmetric, rotating perfect-MHD winds and jets are discussed in some more detail. Their asymptotic structure is described. The last sections deal with small motions about an equilibrium and stability. These issues are illustrated by a few classical examples. The last section discusses linear aspects of the magneto-rotationnal instability.
2013-01-01
M.Comm. (Industrial Psychology) There is ample evidence to suggest that optimal experience (flow), happiness and life satisfaction are related to one another in the creative culinary training environment. In this study, the effect of time management behaviour on these relationships was investigated within the hospitality training environment. Furthermore, the mediating role of perceived control of time on flow was explored, as well as the direct effect of happiness and life satisfaction on...
S.K Ghosh
2015-01-01
Full Text Available The purpose of present investigation is to analyse bouyancy-driven radiation-convection flow past a moving vertical plate with reference to an optically dense medium in the presence of mass concentration, using Rosseland approximation permeated by a magnetic field. The flow is considered to be gray in the presence of free convection, mass transfer and radiation. An exact solution of the governing equations is obtained by applying the Laplace transform method. Numerical results of velocity distributions, shear stress, temperature distribution and mass concentration are presented graphically to give physical insight into the flow pattern.
J. Siva Ram Prasad
2016-01-01
Full Text Available We analyzed in this paper the problem of mixed convection along a vertical plate in a non-Newtonian fluid saturated non-Darcy porous medium in the presence of melting and thermal dispersion-radiation effects for aiding and opposing external flows. Similarity solution for the governing equations is obtained for the flow equations in steady state. The equations are numerically solved by using Runge-kutta fourth order method coupled with shooting technique. The effects of melting (M, thermal dispersion (D, radiation (R, magnetic field (MH, viscosity index (n and mixed convection (Ra/Pe on fluid velocity and temperature are examined for aiding and opposing external flows.
Fernanda R. Roque
2011-01-01
Full Text Available OBJECTIVES: Aerobic exercise training prevents cardiovascular risks. Regular exercise promotes functional and structural adaptations that are associated with several cardiovascular benefits. The aim of this study is to investigate the effects of swimming training on coronary blood flow, adenosine production and cardiac capillaries in normotensive rats. METHODS: Wistar rats were randomly divided into two groups: control (C and trained (T. An exercise protocol was performed for 10 weeks and 60 min/day with a tail overload of 5% bodyweight. Coronary blood flow was quantified with a color microsphere technique, and cardiac capillaries were quantified using light microscopy. Adenine nucleotide hydrolysis was evaluated by enzymatic activity, and protein expression was evaluated by western blot. The results are presented as the means ± SEMs (p<0.05. RESULTS: Exercise training increased the coronary blood flow and the myocardial capillary-to-fiber ratio. Moreover, the circulating and cardiac extracellular adenine nucleotide hydrolysis was higher in the trained rats than in the sedentary rats due to the increased activity and protein expression of enzymes, such as E-NTPDase and 59- nucleotidase. CONCLUSIONS: Swimming training increases coronary blood flow, number of cardiac capillaries, and adenine nucleotide hydrolysis. Increased adenosine production may be an important contributor to the enhanced coronary blood flow and angiogenesis that were observed in the exercise-trained rats; collectively, these results suggest improved myocardial perfusion.
Giri, Shib Sankar; Das, Kalidas; Kundu, Prabir Kumar
2017-02-01
The present paper investigates the effect of Stefan blowing on the hydro-magnetic bioconvection of a water-based nanofluid flow containing gyrotactic microorganisms through a permeable surface. Also we studied both actively and passively the controlled flux of nanoparticles and the effect of a surface slip at the wall. We adopt a similarity approach to reduce the leading partial differential equations into ordinary differential equations along with two separate boundary conditions (active and passive) and solve the resulting equations numerically by employing the RK-4 method through the shooting technique to perform the flow analysis. Discussions on the effect of emerging flow parameter on the flow characteristic are made properly through graphs and charts. We observed that the effects of the traditional Lewis number and suction/blowing parameter on temperature distribution and microorganism concentration are converse to each other. A fair result comparison of the present paper with formerly obtained results is given.
Low-Load Resistance Training with Blood Flow Occlusion as a Countermeasure to Disuse Atrophy
Ploutz-Snyder, L. L.; Cook, S. B.
2009-01-01
Decreases in strength and neuromuscular function are observed following prolonged disuse. Exercise countermeasures to prevent muscle dysfunction during disuse typically involve high intensity resistance training. The purpose of the study is to evaluate the effectiveness of low-load resistance training with a blood flow occlusion to mitigate muscle loss and dysfunction during 30 days of unilateral lower limb suspension (ULLS).
Normobaric hypoxia training: the effects of breathing-gas flow rate on symptoms.
Artino, Anthony R; Folga, Richard V; Vacchiano, Charles
2009-06-01
The U.S. Navy has replaced segments of refresher low-pressure chamber instruction with normobaric hypoxia training using a reduced oxygen breathing device (ROBD). A previous training evaluation revealed that this alternative instructional paradigm is a preferred means of training experienced jet aviators to recognize and recover from hypoxia. However, findings from this earlier work also indicated that air hunger was the most commonly reported symptom during ROBD training. This finding raised concern that air hunger could have resulted from a training artifact caused by the lower breathing-gas flow rate produced by the ROBD when compared to more familiar jet aircraft breathing systems. In an effort to address this issue, a software change was made that increased ROBD mask flow from 30 to 50 L x min(-1) (LPM). The purpose of this retrospective study was to determine if there are differences in the hypoxia symptoms reported by aviators trained on the ROBD upgrade (ROBD-50) compared to those trained on the original device (ROBD-30). Hypoxia training was provided to 156 aviators using the ROBD-50, and survey results were compared to those obtained from 121 aviators trained on the ROBD-30. There was a significant decrease in the number of aviators who reported experiencing air hunger while training on the ROBD-50 (44.2%) as compared to the ROBD-30 (59.4%) [Pearson chi2 (1) = 5.45, P training fidelity.
A. M. Salem
2013-01-01
Full Text Available A numerical model is developed to study the effects of temperature-dependent viscosity on heat and mass transfer flow of magnetohydrodynamic(MHD micropolar fluids with medium molecular weight along a permeable stretching surface embedded in a non-Darcian porous medium in the presence of viscous dissipation and chemical reaction. The governing boundary equations for momentum, angular momentum (microrotation, and energy and mass transfer are transformed to a set of nonlinear ordinary differential equations by using similarity solutions which are then solved numerically by shooting technique. A comparison between the analytical and the numerical solutions has been included. The effects of the various physical parameters entering into the problem on velocity, microrotation, temperature and concentration profiles are presented graphically. Finally, the effects of pertinent parameters on local skin-friction coefficient, local Nusselt number and local Sherwood number are also presented graphically. One important observation is that for some kinds of mixtures (e.g., H2, air with light and medium molecular weight, the magnetic field and temperature-dependent viscosity effects play a significant role and should be taken into consideration as well.
Kunimatsu, Taketoshi; Hirai, Chikara; Tomii, Norio
In order to evaluate train timetables from passengers' points of view, it is indispensable to estimate the disutilities of passengers. This can be done by estimating the movements of passengers and trains accurately. In particular, when there are many passengers, an interaction between the passengers and trains must be considered. To this end, we have developed a microsimulation system to simulate both train operation and passengers' train choice behavior. The system can simulate train choice behaviors of more than one million passengers as well as their positions in trains. It is possible to estimate the delays caused by congestion in trains as well. The system is based on models of different attitudes of the passengers with respect to the train choice behavior, with includes the choice of the earliest train, transfer avoidance, and congestion avoidance; a passengers' train choice behavior reflects his/her preferences. We applied this system to an actual railway line in a metropolitan area and evaluated two train schedules by calculating the generalized cost that reflects each passenger's disutility in his/her experience. Through the numerical experiments, we have confirmed that the proposed method is very useful for evaluating timetables from passengers' points of view.
Annular MHD Physics for Turbojet Energy Bypass
Schneider, Steven J.
2011-01-01
The use of annular Hall type MHD generator/accelerator ducts for turbojet energy bypass is evaluated assuming weakly ionized flows obtained from pulsed nanosecond discharges. The equations for a 1-D, axisymmetric MHD generator/accelerator are derived and numerically integrated to determine the generator/accelerator performance characteristics. The concept offers a shockless means of interacting with high speed inlet flows and potentially offers variable inlet geometry performance without the complexity of moving parts simply by varying the generator loading parameter. The cycle analysis conducted iteratively with a spike inlet and turbojet flying at M = 7 at 30 km altitude is estimated to have a positive thrust per unit mass flow of 185 N-s/kg. The turbojet allowable combustor temperature is set at an aggressive 2200 deg K. The annular MHD Hall generator/accelerator is L = 3 m in length with a B(sub r) = 5 Tesla magnetic field and a conductivity of sigma = 5 mho/m for the generator and sigma= 1.0 mho/m for the accelerator. The calculated isentropic efficiency for the generator is eta(sub sg) = 84 percent at an enthalpy extraction ratio, eta(sub Ng) = 0.63. The calculated isentropic efficiency for the accelerator is eta(sub sa) = 81 percent at an enthalpy addition ratio, eta(sub Na) = 0.62. An assessment of the ionization fraction necessary to achieve a conductivity of sigma = 1.0 mho/m is n(sub e)/n = 1.90 X 10(exp -6), and for sigma = 5.0 mho/m is n(sub e)/n = 9.52 X 10(exp -6).
Pressure Distribution Characters of Flow Field around High-Speed Train
无
2000-01-01
Based on incompressible viscous fluid Navier-Stokes equation and k-ε 2-equationsturbulent model, an investigation on 3D turbulent flow field around four kinds of train models has been made by finite element method. From the calculation, the pressure distribution characters of flow field around high-speed trains have been obtained. It is significant for strength design of the high-speed train body, for resisting wind design of the facilities beside the high-speed railways and for determining the aerodynamic force of induced air to the human body near the railways.
G. K. Ramesh
2012-01-01
Full Text Available This paper presents the study of momentum and heat transfer characteristics in a hydromagnetic flow of dusty fluid over an inclined stretching sheet with non-uniform heat source/sink, where the flow is generated due to a linear stretching of the sheet. Using a similarity transformation, the governing equations of the problem are reduced to a coupled third-order nonlinear ordinary differential equations and are solved numerically by Runge-Kutta-Fehlberg fourth-fifth-order method using symbolic software Maple. Our numerical solutions are shown to agree with the available results in the literature and then employ the numerical results to bring out the effects of the fluid-particle interaction parameter, local Grashof number, angle of inclination, heat source/sink parameter, Chandrasekhar number, and the Prandtl number on the flow and heat transfer characteristics. The results have possible technological applications in liquid-based systems involving stretchable materials.
Ferdows, M.
2017-03-10
A steady two-dimensional free convective flow of a viscous incompressible fluid along a vertical stretching sheet with the effect of magnetic field, radiation and variable thermal conductivity in porous media is analyzed. The nonlinear partial differential equations, governing the flow field under consideration, have been transformed by a similarity transformation into a systemof nonlinear ordinary differential equations and then solved numerically. Resulting non-dimensional velocity and temperature profiles are then presented graphically for different values of the parameters. Finally, the effects of the pertinent parameters, which are of physical and engineering interest, are examined both in graphical and tabular form.
Shivaiah S.
2012-01-01
Full Text Available The objective of this paper is to analyze the effect of chemical reaction on unsteady magneto hydrodynamic free convective fluid flow past a vertical porous plate in the presence of suction or injection. The governing equations of the flow field are solved numerically by a finite element method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-friction coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.
Prabhakar Reddy B.
2016-02-01
Full Text Available In this paper, a numerical solution of mass transfer effects on an unsteady free convection flow of an incompressible electrically conducting viscous dissipative fluid past an infinite vertical porous plate under the influence of a uniform magnetic field considered normal to the plate has been obtained. The non-dimensional governing equations for this investigation are solved numerically by using the Ritz finite element method. The effects of flow parameters on the velocity, temperature and concentration fields are presented through the graphs and numerical data for the skin-friction, Nusselt and Sherwood numbers are presented in tables and then discussed.
An Extended Cellular Automaton Model for Train Traffic Flow on the Dedicated Passenger Lines
Wenbo Zhao
2014-01-01
Full Text Available As one of the key components for the railway transportation system, the Train Operation Diagram can be greatly influenced by many extrinsic and intrinsic factors. Therefore, the railway train flow has shown the strong nonlinear characteristics, which makes it quite difficult to take further relative studies. Fortunately, the cellular automaton model has its own advantages in solving nonlinear problems and traffic flow simulation. Considering the mixed features of multispeed running trains on the passenger dedicated lines, this paper presents a new train model under the moving block system with different types of trains running with the cellular automaton idea. By analyzing such key factors as the maintenance skylight, the proportion of the multispeed running trains, and the distance between adjacent stations and departure intervals, the corresponding running rules for the cellular automaton model are reestablished herewith. By means of this CA model, the program of train running system is designed to analyze the potential impact on railway carrying capacity by various factors; the model can also be implemented to simulate the actual train running process and to draw the train operation diagram by computers. Basically the theory can be applied to organize the train operation on the dedicated passenger lines.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Tataronis, J. A.
2004-06-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfvkn continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named “accumulation continuum” and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory.
R.K. Luz
2011-08-01
Full Text Available The effects of different water flow rates and feed training on the production of "pacamã" Lophiosilurus alexandri juveniles were evaluated. In the first experiment, nine day post-hatch larvae (n= 2,400 were stocked at a density of 5 larvae/L. Different water flow (F rates were tested: F1 = 180; F2 = 600; F3 = 1,300; and F4 = 2,600mL/min. Artemia nauplii were offered as food during the first 15 days of active feeding. In the second experiment for feed training, 720 juveniles (total length of 22.2mm were stocked at a density of 1.5 juveniles/L. A water flow rate similar to F1 was used. The use of extruded dry diet was tested, and feed training was done with and without other enhanced flavors (Artemia nauplii or Scott emulsion. The water flow rates did not influence the survival or growth of L. alexandri. Cannibalism occurred during feed training. The worst survival, specific growth rate and high mortality were found with the use of extruded dry diet, while similar values were registered with the different feed training diets used. Reduced water flow rate can be used to lower water consumption during larviculture and feed training of L. alexandri.
Shock Train and Pseudo-shock Phenomena in Supersonic Internal Flows
Kazuyasu Matsuo
2003-01-01
When a normal shock wave interacts with a boundary layer along a wall surface in supersonic internal flows and the shock is strong enough to separate the boundary layer, the shock is bifurcated and a series of shocks called "shock train" is formed. The flow is decelerated from supersonic to subsonic through the whole interaction region that is referred to as "pseudo-shock". In the present paper some characteristics of the shock train and pseudo-shock and some examples of the pseudo-shocks in some flow devices are described.
Karimipour, Arash; Taghipour, Abdolmajid [Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad (Iran, Islamic Republic of); Malvandi, Amir, E-mail: amirmalvandi@aut.ac.ir [Department of Mechanical Engineering, Neyshabur Branch, Islamic Azad University, Neyshabur (Iran, Islamic Republic of)
2016-12-01
This paper aims to investigate magnetic field and slip effects on developing laminar forced convection of nanofluids in the microchannels. A novel mixture of water and FMWNT carbon nanotubes is used as the working fluid. To do this, fluid flow and heat transfer through a microchannel is simulated by a computer code in FORTRAN language. The mixture of FMWNT carbon nanotubes suspended in water is considered as the nanofluid. Slip velocity is supposed as the hydrodynamic boundary condition while the microchannel's lower wall is insulated and the top wall is under the effect of a constant heat flux. Moreover, the flow field is subjected to a magnetic field with a constant strength. The results are presented as the velocity, temperature and Nusselt number profiles. It is observed that nanofluid composed of water and carbon nanotubes (FMWNT) can work well to increase the heat transfer rate along the microchannel walls. Furthermore, it is indicated that imposing the magnetic field is very effective at the thermally developing region. In contrast, the magnetic field effect at fully developed region is insignificant, especially at low values of Reynolds number. - Highlights: • Simulation of water/FMWNT carbon nanotubes flow in a microchannel. • The effects of magnetic field strength on nanofluid's slip velocity. • The effects of Ha, Re, ϕ and slip coefficient on averaged Nusselt number. • Magnetic field effect at developing flow region is significant.
A.NAYAK; S.PANDA; D.K.PHUKAN
2014-01-01
This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme-able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of the stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations and solved numerically by the Runge-Kutta fourth order scheme in as-sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph-ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.
Khan Najeeb Alam
2017-03-01
Full Text Available An investigation is performed for an alyzing the effect of entropy generation on the steady, laminar, axisymmetric flow of an incompressible Powell-Eyring fluid. The flow is considered in the presence of vertically applied magnetic field between radially stretching rotating disks. The Energy and concentration equation is taking into account to investigate the heat dissipation, Soret, Dufour and Joule heating effects. To describe the considered flow non-dimensionalized equations, an exact similarity function is used to reduce a set of the partial differential equation into a system of non-linear coupled ordinary differential equation with the associated boundary conditions. Using homotopy analysis method (HAM, an analytic solution for velocity, temperature and concentration profiles are obtained over the entire range of the imperative parameters. The velocity components, concentration and temperature field are used to determine the entropy generation. Plots illustrate important results on the effect of physical flow parameters. Results obtained by means of HAM are then compared with the results obtained by using optimized homotopy analysis method (OHAM. They are in very good agreement.
P. Bala Anki Reddy
2016-09-01
Full Text Available In this paper, the prediction of the magnetohydrodynamic boundary layer slip flow over a permeable stretched cylinder with chemical reaction is investigated by using some mathematical techniques, namely Runge–Kutta fourth order method along with shooting technique and artificial neural network (ANN. A numerical method is implemented to approximate the flow of heat and mass transfer characteristics as a function of some input parameters, explicitly the curvature parameter, magnetic parameter, permeability parameter, velocity slip, Grashof number, solutal Grashof number, Prandtl number, temperature exponent, Schmidt number, concentration exponent and chemical reaction parameter. The non-linear partial differential equations of the governing flow are converted into a system of highly non-linear ordinary differential equations by using the suitable similarity transformations, which are then solved numerically by a Runge–Kutta fourth order along with shooting technique and then ANN is applied to them. The Back Propagation Neural Network is applied for forecasting the desired outputs. The reported numerical values and the ANN values are in good agreement than those published works on various special cases. According to the findings of this study, the ANN approach is reliable, effective and easily applicable for simulating heat and mass transfer flow over a stretched cylinder.
An advanced implicit solver for MHD
Udrea, Bogdan
A new implicit algorithm has been developed for the solution of the time-dependent, viscous and resistive single fluid magnetohydrodynamic (MHD) equations. The algorithm is based on an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on a staggered grid for the parabolic fluxes. The algorithm employs a locally aligned coordinate system that allows the solution to the Riemann problems to be solved in a natural direction, normal to cell interfaces. The result is an original scheme that is robust and reduces the complexity of the flux formulas. The evaluation of the parabolic fluxes is also implemented using a locally aligned coordinate system, this time on the staggered grid. The implicit formulation employed by WARP3 is a two level scheme that was applied for the first time to the single fluid MHD model. The flux Jacobians that appear in the implicit scheme are evaluated numerically. The linear system that results from the implicit discretization is solved using a robust symmetric Gauss-Seidel method. The code has an explicit mode capability so that implementation and test of new algorithms or new physics can be performed in this simpler mode. Last but not least the code was designed and written to run on parallel computers so that complex, high resolution runs can be per formed in hours rather than days. The code has been benchmarked against analytical and experimental gas dynamics and MHD results. The benchmarks consisted of one-dimensional Riemann problems and diffusion dominated problems, two-dimensional supersonic flow over a wedge, axisymmetric magnetoplasmadynamic (MPD) thruster simulation and three-dimensional supersonic flow over intersecting wedges and spheromak stability simulation. The code has been proven to be robust and the results of the simulations showed excellent agreement with analytical and experimental results. Parallel performance studies showed that the code performs as expected when run on parallel
GANGA B; SARANYA S; VISHNU GANESH N; ABDUL HAKEEM A K
2015-01-01
In this paper we analyzed the effects of space and temperature dependent internal heat generation/absorption (non-uniform heat source/sink) on magnetohydrodynamic boundary layer flow of water based nanofluid over a stretching sheet with different nanoparticles. The flow is generated due to linear stretching of the sheet and influenced by uniform magnetic field, which is applied normally to the stretching sheet. A scaling group of transformation is used to reduce the governing momentum and energy equations into non-linear ordinary differential equations. The resulting differential equations are solved analytically using hypergeometric functions and numerically by the fourth order Runge-Kutta method with shooting technique. The influence of nanoparticle volume fraction, magnetic field, Prandtl number, non uniform heat source/sink, local skin friction coefficient and reduced Nusselt number are investigated for different nanoparticles.
N. Sandeep
2015-12-01
Full Text Available The aim of the present study is to investigate the influence of non-uniform heat source/sink, mass transfer and chemical reaction on an unsteady mixed convection boundary layer flow of a magneto-micropolar fluid past a stretching/shrinking sheet in the presence of viscous dissipation and suction/injection. The governing equations of the flow, heat and mass transfer are transformed into system of nonlinear ordinary differential equations by using similarity transformation and then solved numerically using Shooting technique with Matlab Package. The influence of non-dimensional governing parameters on velocity, microrotation, temperature and concentration profiles are discussed and presented with the help of their graphical representations. Also, friction factor, heat and mass transfer rates have been computed and presented through tables. Under some special conditions, present results are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.
N. Bhaskar Reddy
2014-01-01
Full Text Available An analysis is carried out to investigate the influence of variable thermal conductivity and partial velocity slip on hydromagnetic two-dimensional boundary layer flow of a nanofluid with Cu nanoparticles over a stretching sheet with convective boundary condition. Using similarity transformation, the governing boundary layer equations along with the appropriate boundary conditions are transformed to a set of ordinary differential equations. Employing Runge-kutta fourth-order method along with shooting technique, the resultant system of equations is solved. The influence of various pertinent parameters such as nanofluid volume fraction parameter, the magnetic parameter, radiation parameter, thermal conductivity parameter, velocity slip parameter, Biot number, and suction or injection parameter on the velocity of the flow field and heat transfer characteristics is computed numerically and illustrated graphically. The present results are compared with the existing results for the case of regular fluid and found an excellent agreement.
Motsa Sandile Sydney
2015-01-01
Full Text Available The behaviour of unsteady non-Darcian magnetohydrodynamic fluid flow past an impulsively started vertical porous surface is investigated. The effect of thermophoresis due to migration of colloidal particles in response to a macroscopic temperature gradient is taken into account. It is assumed that both dynamic viscosity and thermal conductivity are linear functions of temperature. The governing equations are non-dimensionalized by using suitable similarity transformation which can unravel the behaviour of the flow at short time and long time periods. A novel iteration scheme, called bivariate spectral local linearization method is developed for solving the corresponding systems of highly non-linear partial differential equations. The results of the numerical solutions obtained are presented graphically and analyzed for the effects of the various important parameters entering into the problem on velocity, temperature, and concentration field within the boundary layer.
K. GANGADHAR
2013-01-01
Full Text Available A mathematical model is presented for a two-dimensional, steady, incompressible electrically conducting, laminar free convection boundary layer flow of a continuously moving vertical porous plate in a chemically reactive and porous medium in the presence of a transverse magnetic field. The basic equations governing the flow are in the form of partial differential equations and have been reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations. The problem is tackled numerically using shooting techniques with the forth order Runga-Kutta method. Pertinent results with respect to embedded parameters are displayed graphically for the velocity,temperature and concentration profiles and were discussed quantitatively.
Zhu, Jianyue; Hu, Zhiwei; Thompson, David
2017-01-01
Dataset for the main results of paper entitled 'The flow and flow-induced noise behaviour of a simplified high-speed train bogie in a cavity and including a fairing' published in Journal of Rail and Rapid Transit.
Kandasamy, R., E-mail: future990@gmail.com [Computational Fluid Dynamics, FSSW, Universiti Tun Hussein Onn Malaysia (Malaysia); Loganathan, P.; Arasu, P. Puvi [Department of Mathematics, Anna University, Tamil Nadu (India)
2011-06-15
Highlights: > A nanofluid is a new class of heat transfer fluids that contain a base fluid and nanoparticles. > The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. > In nanofluid systems, thermophoresis particle deposition in the presence of magnetic field with Brownian motion has a substantial effect on the flow field. - Abstract: The problem of laminar fluid flow which results from the stretching of a vertical surface with variable stream conditions in a nanofluid has been investigated numerically. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of magnetic field. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. An exact solution is obtained for translation symmetry and numerical solutions for scaling symmetry. This solution depends on a Lewis number, magnetic field, Brownian motion parameter and thermophoretic parameter. The conclusion is drawn that the flow field and temperature and nanoparticle volume fraction profiles are significantly influenced by these parameters.
Linga Raju, T.; Neela Rao, B.
2016-08-01
The paper aims to analyze the heat transfer aspects of a two-layered fluid flow in a horizontal channel under the action of an applied magnetic and electric fields, when the whole system is rotated about an axis perpendicular to the flow. The flow is driven by a common constant pressure gradient in the channel bounded by two parallel porous insulating plates, one being stationary and the other one oscillatory. The fluids in the two regions are considered electrically conducting, and are assumed to be incompressible with variable properties, namely, different densities, viscosities, thermal and electrical conductivities. The transport properties of the two fluids are taken to be constant and the bounding plates are maintained at constant and equal temperature. The governing partial differential equations are then reduced to the ordinary linear differential equations by using a two-term series. The temperature distributions in both fluid regions of the channel are derived analytically. The results are presented graphically to discuss the effect on the heat transfer characteristics and their dependence on the governing parameters, i.e., the Hartmann number, Taylor number, porous parameter, and ratios of the viscosities, heights, electrical and thermal conductivities. It is observed that, as the Coriolis forces become stronger, i.e., as the Taylor number increases, the temperature decreases in the two fluid regions. It is also seen that an increase in porous parameter diminishes the temperature distribution in both the regions.
A Sri Sailam
2014-04-01
Full Text Available The study of unsteady hydro magnetic free convective flow of viscous incompressible and electrically conducting fluids past an infinite vertical porous plate in the presence of constant suction and heat absorbing sinks has been made. Appropriate solutions have been derived for the velocity and temperature fields, skin friction and rate of heat transfer using Galerkin finite element method. It is observed that increase in magnetic field strength decreases the velocity of the fluid. Also the skin friction and rate of heat transfer of the conducting fluid decrease with increase in magnetic field strength.
RAKESH KUMAR,
2011-04-01
Full Text Available The purpose of this paper is to present a theoretical analysis of an unsteady hydromagnetic free convection flow of viscoelastic fluid (Walter’s B’ past an infinite vertical porous flat plate through porous medium. The temperature is assumed to be oscillating with time and the effect of the Hall current is taken into account. Assuming constant suction at the plate, closed form solutions have been obtained for velocity and temperature profiles. The effect of the various parameters, entering into the problem, on the primary, secondary velocity profiles, the axial and transverse components of skin-friction are shown graphically followed by quantitative discussion.
Dhanai, Ruchika; Rana, Puneet; Kumar, Lokendra
2016-05-01
The motivation behind the present analysis is to focus on magneto-hydrodynamic flow and heat transfer characteristics of non-Newtonian fluid (Sisko fluid) past a permeable nonlinear shrinking sheet utilizing nanoparticles involving convective boundary condition. The non-homogenous nanofluid transport model considering the effect of Brownian motion, thermophoresis, suction/injection and no nanoparticle flux at the sheet with convective boundary condition has been solved numerically by the RKF45 method with shooting technique. Critical points for various pertinent parameters are evaluated in this study. The dual solutions (both first and second solutions) are captured in certain range of material constant (ncthermophoresis parameter.
D. R. V. S. R. K. Sastry
2013-01-01
Full Text Available The problem of unsteady magnetohydrodynamic convective flow with radiation and chemical reaction past a flat porous plate moving through a binary mixture in an optically thin environment is considered. The governing boundary layer equations are converted to nonlinear ordinary differential equations by similarity transformation and then solved numerically by MATLAB “bvp4c” routine. The velocity, temperature, and concentration profiles are presented graphically for various values of the material parameters. Also a numerical data for the local skin friction coefficient, the local Nusselt number, and local Sherwood number is presented in tabular forms.
Yirga, Y.; Shankar, B.
2015-09-01
This article investigates the convective heat and mass transfer in nanofluid flow through a porous media due to a stretching sheet subjected to magnetic field, viscous dissipation, chemical reaction, and Soret effects. The governing equations are reduced to ordinary differential equations using similarity transformations and then solved numerically by the Keller box method. Numerical results are obtained for the skin friction coefficient, Nusselt number, Sherwood number, as well as for the velocity, temperature, and concentration profiles for selected values of the governing parameters. Excellent validation of the present numerical results has been achieved with the earlier studies in the literature.
Khan, Sujit Kumar; Abel, M. Subhas [Department of Mathematics, Gulbarga University, Gulbarga - 585 106, Karnataka (India); Sonth, Ravi M. [Department of Mathematics, K.C.T. Engineering College, Gulbarga - 585 104, Karnataka (India)
2003-12-01
The present paper deals with the study of momentum, heat and mass transfer characteristics in a viso-elastic fluid flow over a porous sheet, where the flow is generated due to linear stretching of the sheet and influenced by a uniform magnetic field applied vertically and a continuous injection of the fluid through porous boundary. In the flow region, heat balance is maintained with a temperature dependent heat source/sink, viscous dissipation, dissipation due to elastic deformation and stress work produced as the result of magnetic field on the non-Newtonian fluid. In mass transfer analysis we have taken into account the loss of mass of the chemically reactive diffusive species by means of first order chemical conversion rate. Using suitable similarity transformations on the highly non-linear partial differential equations we derive several closed form analytical solutions for non-dimensional temperature, concentration, heat flux, mass flux profiles in the form of confluent hyper geometric (Kummer's) functions and some other elementary functions as its special form, for two different cases of the boundary conditions, namely, (i) wall with prescribed second order power law temperature (PST) and prescribed second order power law concentration (ii) wall with prescribed second order power law heat flux (PHF) and prescribed second order power law mass flux. The effect of the non-dimensional magnetic parameter on momentum, heat and mass transfer characteristics for non-isothermal boundary condition and different physical situations of the fluid, having various degrees of visco-elasticity, Prandtl number, heat source/sink strength and Schmidt number, are discussed in detail. Some of the several important findings reported in this paper are: (i) The combined effect of magnetic field, visco-elasticity and impermeability of the wall is to increase skin-friction largely at the wall; (ii) maximum enhancement of wall-temperature profile due to the application of
Muhaimin; R. Kandasamy; Azme B. Khamis
2008-01-01
This work is concerned with Magnetohydrodynamic viscous flow due to a shrinking sheet in the presence of suction. The cases of two dimensional and axisymmetric shrinking are discussed. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are numerically solved by using an advanced numeric technique. Favorability comparisons with previously published work are presented. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.
Islam M. Eldesoky
2012-01-01
Full Text Available Unsteady pulsatile flow of blood through porous medium in an artery has been studied under the influence of periodic body acceleration and slip condition in the presence of magnetic field considering blood as an incompressible electrically conducting fluid. An analytical solution of the equation of motion is obtained by applying the Laplace transform. With a view to illustrating the applicability of the mathematical model developed here, the analytic explicit expressions of axial velocity, wall shear stress, and fluid acceleration are given. The slip condition plays an important role in shear skin, spurt, and hysteresis effects. The fluids that exhibit boundary slip have important technological applications such as in polishing valves of artificial heart and internal cavities. The effects of slip condition, magnetic field, porous medium, and body acceleration have been discussed. The obtained results, for different values of parameters into the problem under consideration, show that the flow is appreciably influenced by the presence of Knudsen number of slip condition, permeability parameter of porous medium, Hartmann number of magnetic field, and frequency of periodic body acceleration. The study is useful for evaluating the role of porosity and slip condition when the body is subjected to magnetic resonance imaging (MRI.
Mahmoud, Mostafa A. A.; Megahed, Ahmed M.
2017-10-01
Theoretical and numerical outcomes of the non-Newtonian Casson liquid thin film fluid flow owing to an unsteady stretching sheet which exposed to a magnetic field, Ohmic heating and slip velocity phenomena is reported here. The non-Newtonian thermal conductivity is imposed and treated as it vary with temperature. The nonlinear partial differential equations governing the non-Newtonian Casson thin film fluid are simplified into a group of highly nonlinear ordinary differential equations by using an adequate dimensionless transformations. With this in mind, the numerical solutions for the ordinary conservation equations are found using an accurate shooting iteration technique together with the Runge-Kutta algorithm. The lineaments of the thin film flow and the heat transfer characteristics for the pertinent parameters are discussed through graphs. The results obtained here detect many concern for the local Nusselt number and the local skin-friction coefficient in which they may be beneficial for the material processing industries. Furthermore, in some special conditions, the present problem has an excellent agreement with previously published work.
Karimipour, Arash; Taghipour, Abdolmajid; Malvandi, Amir
2016-12-01
This paper aims to investigate magnetic field and slip effects on developing laminar forced convection of nanofluids in the microchannels. A novel mixture of water and FMWNT carbon nanotubes is used as the working fluid. To do this, fluid flow and heat transfer through a microchannel is simulated by a computer code in FORTRAN language. The mixture of FMWNT carbon nanotubes suspended in water is considered as the nanofluid. Slip velocity is supposed as the hydrodynamic boundary condition while the microchannel's lower wall is insulated and the top wall is under the effect of a constant heat flux. Moreover, the flow field is subjected to a magnetic field with a constant strength. The results are presented as the velocity, temperature and Nusselt number profiles. It is observed that nanofluid composed of water and carbon nanotubes (FMWNT) can work well to increase the heat transfer rate along the microchannel walls. Furthermore, it is indicated that imposing the magnetic field is very effective at the thermally developing region. In contrast, the magnetic field effect at fully developed region is insignificant, especially at low values of Reynolds number.
Navid Freidoonimehr
2015-01-01
Full Text Available The main purpose of this study is to present dual solutions for the problem of magneto-hydrodynamic Jeffery–Hamel nano-fluid flow in non-parallel walls. To do so, we employ a new analytical technique, Predictor Homotopy Analysis Method (PHAM. This effective method is capable to calculate all branches of the multiple solutions simultaneously. Moreover, comparison of the PHAM results with numerical results obtained by the shooting method coupled with a Runge-Kutta integration method illustrates the high accuracy for this technique. For the current problem, it is found that the multiple (dual solutions exist for some values of governing parameters especially for the convergent channel cases (α = -1. The fluid in the non-parallel walls, divergent and convergent channels, is the drinking water containing different nanoparticles; Copper oxide (CuO, Copper (Cu and Silver (Ag. The effects of nanoparticle volume fraction parameter (φ, Reynolds number (Re, magnetic parameter (Mn, and angle of the channel (α as well as different types of nanoparticles on the flow characteristics are discussed.
T. M. Agbaje
2015-06-01
Full Text Available In this study, the spectral perturbation method (SPM is utilized to solve the momentum, heat and mass transfer equations describing the unsteady MHD mixed convection flow over an impulsively stretched vertical surface in the presence of chemical reaction effect. The governing partial differential equations are reduced into a set of coupled non similar equations and then solved numerically using the SPM. The SPM combines the standard perturbation method idea with the Chebyshev pseudo-spectral collocation method. In order to demonstrate the accuracy and efficiency of the proposed method, the spectral perturbation (SPM numerical results are compared with numerical results generated using the spectral relaxation method (SRM and a good agreement between the two methods is observed up to a minimum of eight decimal digits. Several simulation are conducted to ascertain the accuracy of the SPM and the SRM. The computational speed of the SPM is demonstrated by comparing the SPM computational time with the SRM computational time. A residual error analysis is also conducted for the SPM and the SRM in order to further assess the accuracy of the SPM. The study shows that the spectral perturbation method (SPM is more efficient in terms of computational speed when compared with the SRM. The study also shows that the SPM can be used as an efficient and reliable tool for solving strongly nonlinear boundary value partial differential equation problems that are defined under the Williams and Rhyne [3] transformation. In addition, the study shows that accurate results can be obtained using the perturbation method and thus, the conclusions earlier drawn by researchers regarding the accuracy of perturbation methods is corrected.
微极流体向受热面的MHD驻点流动%MHD Stagnation Point Flow of a Micropolar Fluid Towards a Heated Surface
M·M·阿斯拉夫
2011-01-01
The problem of two dimensional stagnation point flow of an electrically conducting micropolar fluid impinging normally on a heated surface in the presence of a uniform transverse magnetic field was analyzed. The governing continuity, momentum, angular momentum, and heat equations together with the associated boundary conditions were reduced to dimensionless form using suitable similarity transformations. The reduced self similar non-linear equations were then solved numerically by an algorithm based on finite difference discretization. The results were further refined by Richardson' s extrapolation. The effects of the magnetic parameter, the micropolar parameters, and the Prandtl number on the flow and temperature fields were predicted in tabular and graphical forms to show the important features of the solution.The study shows that the velocity and thermal boundary layers become thinner as the magnetic parameter is increased. The micropolar fluids display more reduction in shear stress as well as heat transfer rate than that exhibited by Newtonian fluids, which is beneficial in the flow and thermal control of polymeric processing.%分析了有均匀横向磁场作用时,导电微极流体垂直冲击受热面时形成的二维驻点流动问题.应用适当的相似转换,将连续、动量、角动量及热量的控制方程,及其相应的边界条件,简化为无量纲形式.然后,利用以有限差分离散化为基础的算法,求解简化了的自相似非线性方程.用Richardson外推法,进一步求精其结果.以图表形式表示磁场参数、微极性参数、Prandtl数对流动和温度场的影响,说明了其解的重要特性.研究表明,随着磁场参数的增大,速度和热边界层厚度变小了.与Newton流体相比较,微极流体的剪应力和传热率出现明显的减少,这对聚合物生产过程中流体的流动和热量控制是有益的.
Nickeler, D H; Nickeler, Dieter H.; Fahr, Hans-Joerg
2005-01-01
We make some remarks on reconnection in plasmas and want to present some calculations related to the problem of finding velocity fields which conserve magnetic flux or at least magnetic field lines. Hereby we start from views and definitions of ideal and non-ideal flows on one hand, and of reconnective and non-reconnective plasma dynamics on the other hand. Our considerations give additional insights into the discussion on violations of the frozen--in field concept which started recently with the papers by Baranov & Fahr (2003a; 2003b). We find a correlation between the nonidealness which is given by a generalized form of the Ohm's law and a general transporting velocity, which is field line conserving.
Prasad Ramachandra V.
2007-01-01
Full Text Available An unsteady, two-dimensional, hydromagnetic, laminar free convective boundary-layer flow of an incompressible, Newtonian, electrically-conducting and radiating fluid past an infinite heated vertical porous plate with heat and mass transfer is analyzed, by taking into account the effect of viscous dissipation. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. Numerical evaluation of the analytical results is performed and graphical results for velocity, temperature and concentration profiles within the boundary layer and tabulated results for the skin-friction coefficient, Nusselt number and Sherwood number are presented and discussed. It is observed that, when the radiation parameter increases, the velocity and temperature decrease in the boundary layer, whereas when thermal and solutal Grashof increases the velocity increases.
Winifred Nduku Mutuku-Njane
2013-01-01
Full Text Available We examine the effect of magnetic field on boundary layer flow of an incompressible electrically conducting water-based nanofluids past a convectively heated vertical porous plate with Navier slip boundary condition. A suitable similarity transformation is employed to reduce the governing partial differential equations into nonlinear ordinary differential equations, which are solved numerically by employing fourth-order Runge-Kutta with a shooting technique. Three different water-based nanofluids containing copper (Cu, aluminium oxide (Al2O3, and titanium dioxide (TiO2 are taken into consideration. Graphical results are presented and discussed quantitatively with respect to the influence of pertinent parameters, such as solid volume fraction of nanoparticles (φ, magnetic field parameter (Ha, buoyancy effect (Gr, Eckert number (Ec, suction/injection parameter (fw, Biot number (Bi, and slip parameter (β, on the dimensionless velocity, temperature, skin friction coefficient, and heat transfer rate.
Reddy Gnaneswara M.
2012-01-01
Full Text Available In this paper, an analysis has been carried out to study heat and mass transfer effects on steady two-dimensional flow of an electrically conducting incompressible dissipating fluid past an inclined semi-infinite porous surface with heat generation. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation, and two secondorder ordinary differential equations corresponding to energy and diffusion equations are derived. The coupled ordinary differential equations along with the boundary conditions are solved numerically. Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity, temperature and concentration profiles. Comparisons with previously published work are performed and the results are found to be in very good agreement.
Acharya, Nilankush; Das, Kalidas; Kumar Kundu, Prabir
2016-09-01
The present investigation reveals the effect of variable thickness on the steady two-dimensional boundary layer flows of a TiO2-water and Ag-water nanofluid through a slendering stretching sheet. The whole analysis has been performed in the presence of variable magnetic field and variable surface temperature. Similarity transformation has been introduced to renovate the non-linear partial differential equations into ordinary ones and then they were solved using the innovative technique of Natural decomposition method (NDM). The influence of pertinent parameters on velocity and temperature distribution has been illustrated by means of graphs and tables approach. Our analysis conveys that the temperature of the nanofluid reduces due to enhancing of the variable thickness parameter. The rate of heat transfer is significantly reduced for the Ag-water nanofluid with the positive impact of nanoparticle volume fraction.
Zaib, Aurang; Shafie, Sharidan
2015-09-01
The effect of slip and thermophoresis on an unsteady magnetohydrodynamic stagnation-point-flow micropolar fluid with heat and mass transfer towards a shrinking sheet has been investigated. The governing equations are reduced to a system of non-dimensional partial differential equations by using similarity transformation, before being solved numerically using the Keller-box method. The effects of various physical parameters on the velocity, microrotation, temperature, and concentration profiles as well as the reduced skin friction, the reduced Nusselt number, and the reduced Sherwood number are analyzed and discussed graphically. It is found that the concentration boundary layer thickness decreases with increasing values of the thermophoresis. Comparison with previously published results under the limiting cases is made and found to be in excellent agreement.
Kandasamy, R.; Jeyabalan, C.; Sivagnana Prabhu, K. K.
2016-02-01
This article examines the influence of thermophoresis, Brownian motion of the nanoparticles with variable stream conditions in the presence of magnetic field on mixed convection heat and mass transfer in the boundary layer region of a semi-infinite porous vertical plate in a nanofluid under the convective boundary conditions. The transformed boundary layer ordinary differential equations are solved numerically using Maple 18 software with fourth-fifth order Runge-Kutta-Fehlberg method. Numerical results are presented both in tabular and graphical forms illustrating the effects of these parameters with magnetic field on momentum, thermal, nanoparticle volume fraction and solutal concentration boundary layers. The numerical results obtained for the velocity, temperature, volume fraction, and concentration profiles reveal interesting phenomenon, some of these qualitative results are presented through plots. It is interesting to note that the magnetic field plays a dominant role on nanofluid flow under the convective boundary conditions.
El-Aziz, Mohamed Abd; Afify, Ahmed A.
2016-10-01
In the present work, the hydromagnetic boundary layer flow and heat transfer of Casson fluid in a thin liquid film over an unsteady stretching sheet in the presence of variable thermal conductivity, thermal radiation, and viscous dissipation is investigated numerically. The Casson fluid model is applied to characterize the non-Newtonian fluid behavior. Similarity equations are derived and then solved numerically by using a shooting method with fourth order Runge-Kutta integration scheme. Comparisons with previous literature are accomplished and obtained an excellent agreement. The influences of parameters governing a thin liquid film of Casson fluid and heat transfer characteristics are presented graphically and analyzed. It is observed that the heat transfer rate diminishes with a rise in thermal conductivity parameter and Eckert number. Further, the opposite influence is found with an increase in radiation parameter.
M. Kayalvizhi
2016-06-01
Full Text Available In the present article, we discussed the velocity slip effects on the heat and mass fluxes of a viscous electrically conducting fluid flow over a stretching sheet in the presence of viscous dissipation, Ohmic dissipation and thermal radiation. A system of governing nonlinear PDEs is converted into a set of nonlinear ODEs by suitable similarity transformations. The numerical and analytical solutions are presented for the governing non-dimensional ODEs using shooting method and hypergeometric function respectively. The results are discussed for skin friction coefficient, concentration field, non-dimensional wall temperature and non-dimensional wall concentration. The non-dimensional wall concentration increases with slip and magnetic parameters and decreases with Schmidt number. Furthermore, comparisons are found to be good with bench mark solutions.
Khan, Md Shakhaoath; Karim, Ifsana; Ali, Lasker Ershad; Islam, Ariful
2012-10-01
In this work, we study the unsteady free convection boundary-layer flow of a nanofluid along a stretching sheet with thermal radiation in the presence of magnetic field. To obtain non-similar equations, continuity, momentum, energy, and concentration equations have been non-dimensionalized by usual transformation. The non-similar solutions are considered here which depend on the magnetic parameter M, radiation parameter R, Prandtl number P r, Eckert number E c, Lewis number L e, Brownian motion parameter N b, thermophoresis parameter N t, and Grashof number G r. The obtained equations have been solved by an explicit finite difference method with stability and convergence analysis. The velocity, temperature, and concentration profiles are discussed for different time steps and for the different values of the parameters of physical and engineering interest.
Rajesh Vemula
2016-01-01
Full Text Available In the present study, the effects of chemical reaction on unsteady free convection flow of a viscous, electrically conducting, and incompressible fluid past a moving semi-infinite vertical cylinder with mass transfer and temperature oscillation is studied. The dimensionless governing partial differential equations are solved using an implicit finite-difference method of Crank–Nicolson type, which is stable and convergent. The transient velocity, transient temperature, and transient concentration profiles are studied for various parameters. The local as well as average skin-friction, Nusselt number, and Sherwood number are also analyzed and presented graphically. The results are compared with available computations in the literature, and are found to be in good agreement.
S. S. Motsa
2012-01-01
Full Text Available The problem of magnetomicropolar fluid flow, heat, and mass transfer with suction through a porous medium is numerically analyzed. The problem was studied under the effects of chemical reaction, Hall, ion-slip currents, and variable thermal diffusivity. The governing fundamental conservation equations of mass, momentum, angular momentum, energy, and concentration are converted into a system of nonlinear ordinary differential equations by means of similarity transformation. The resulting system of coupled nonlinear ordinary differential equations is the then solved using a fairly new technique known as the successive linearization method together with the Chebyshev collocation method. A parametric study illustrating the influence of the magnetic strength, Hall and ion-slip currents, Eckert number, chemical reaction and permeability on the Nusselt and Sherwood numbers, skin friction coefficients, velocities, temperature, and concentration was carried out.
Uwanta, Ime Jimmy; Usman, Halima
2014-01-01
The present paper investigates the combined effects of Soret and Dufour on free convective heat and mass transfer on the unsteady one-dimensional boundary layer flow over a vertical channel in the presence of viscous dissipation and constant suction. The governing partial differential equations are solved numerically using the implicit Crank-Nicolson method. The velocity, temperature, and concentration distributions are discussed numerically and presented through graphs. Numerical values of the skin-friction coefficient, Nusselt number, and Sherwood number at the plate are discussed numerically for various values of physical parameters and are presented through tables. It has been observed that the velocity and temperature increase with the increase in the viscous dissipation parameter and Dufour number, while an increase in Soret number causes a reduction in temperature and a rise in the velocity and concentration.
Reddy, G. J.; Raju, R. S.; Rao, J. A.; Gorla, R. S. R.
2017-02-01
An unsteady magnetohydromagnetic natural convection on the Couette flow of electrically conducting water at 4°C (Pr = 11.40) in a rotating system has been considered. A Finite Element Method (FEM) was employed to find the numerical solutions of the dimensionless governing coupled boundary layer partial differential equations. The primary velocity, secondary velocity and temperature of water at 4°C as well as shear stresses and rate of heat transfer have been obtained for both ramped temperature and isothermal plates. The results are independent of the mesh (grid) size and the present numerical solutions through the Finite Element Method (FEM) are in good agreement with the existing analytical solutions by the Laplace Transform Technique (LTT). These are shown in tabular and graphical forms.
Reddy G.J.
2017-02-01
Full Text Available An unsteady magnetohydromagnetic natural convection on the Couette flow of electrically conducting water at 4°C (Pr = 11.40 in a rotating system has been considered. A Finite Element Method (FEM was employed to find the numerical solutions of the dimensionless governing coupled boundary layer partial differential equations. The primary velocity, secondary velocity and temperature of water at 4°C as well as shear stresses and rate of heat transfer have been obtained for both ramped temperature and isothermal plates. The results are independent of the mesh (grid size and the present numerical solutions through the Finite Element Method (FEM are in good agreement with the existing analytical solutions by the Laplace Transform Technique (LTT. These are shown in tabular and graphical forms.
M. M. Rashidi
2012-01-01
Full Text Available In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations are obtained and solved analytically by using homotopy analysis method (HAM with two auxiliary parameters for two classes of visco-elastic fluid (Walters’ liquid B and second-grade fluid. It is clear that by the use of second auxiliary parameter, the straight line region in ℏ-curve increases and the convergence accelerates. This research is performed by considering two different boundary conditions: (a prescribed surface temperature (PST and (b prescribed heat flux (PHF. The effect of involved parameters on velocity and temperature is investigated.
Hussain, S.; Mehmood, K.; Sagheer, M.
2016-12-01
In the present study, entropy generation due to mixed convection in a partially heated square double lid driven cavity filled with Al2O3 -water nanofluid under the influence of inclined magnetic field is numerically investigated. At the lower wall of the cavity two heat sources are fixed, with the condition that the remaining part of the bottom wall is kept insulated. Top wall and vertically moving walls are maintained at constant cold temperature. Buoyant force is responsible for the flow along with the two moving vertical walls. Governing equations are discretized in space using LBB-stable finite element pair Q2 / P1disc which lead to 3rd and 2nd order accuracy in the L2-norm for the velocity/temperature and pressure, respectively and the fully implicit Crank-Nicolson scheme of 2nd order accuracy is utilized for the temporal discretization. The discretized systems of nonlinear equations are treated by using the Newton method and the associated linear subproblems are solved by means of Guassian elimination method. Numerical results are presented and analyzed by means of streamlines, isotherms, tables and some useful plots. Impacts of emerging parameters on the flow, in specific ranges such as Reynolds number (1 ≤ Re ≤ 100) , Richardson number (1 ≤ Ri ≤ 50) , Hartman number (0 ≤ Ha ≤ 100) , solid volume fraction (0 ≤ ϕ ≤ 0.2) as well as the angles of inclined magnetic field (0 ° ≤ γ ≤ 90 °) are investigated and the findings are exactly of the same order as that of the previously performed analysis. Calculation of average Nusselt number, entropy generation due to heat transfer, fluid friction and magnetic field, total entropy generation, Bejan number and kinetic energy are the main focus of our study.
Uddin Ziya
2014-01-01
Full Text Available In this paper a numerical model is developed to examine the effect of thermal radiation on magnetohydrodynamic heat transfer flow of a micropolar fluid past a non-conducting wedge in presence of heat source/sink. In the model it is assumed that the fluid is viscous, incompressible and electrically conducting. The Hall and ion slip effects have also been taken into consideration. The model contains highly non-linear coupled partial differential equations which have been converted into ordinary differential equation by using the similarity transformations. These equations are then solved numerically by Shooting technique along with the Runge-Kutta-Fehlberg integration scheme for entire range of parameters with appropriate boundary conditions. The effects of various parameters involved in the problem have been studied with the help of graphs. Numerical values of skin friction coefficients and Nusselt number are presented in tabular form. The results showed that the micropolar fluids are better to reduce local skin drag as compared to Newtonian fluids and the presence of heat sink increases the heat transfer rate.
Ali, M.; Alim, M. A.; Nasrin, R.; Alam, M. S.
2016-07-01
An analysis is performed to study the free convection heat and mass transfer flow of an electrically conducting incompressible viscous fluid about a semi-infinite inclined porous plate under the action of radiation, chemical reaction in presence of magnetic field with variable viscosity. The dimensionless governing equations are steady, two-dimensional coupled and non-linear ordinary differential equation. Nachtsgeim-Swigert shooting iteration technique along with Runge-Kutta integration scheme is used to solve the non-dimensional governing equations. The effects of magnetic parameter, viscosity parameter and chemical reaction parameter on velocity, temperature and concentration profiles are discussed numerically and shown graphically. Therefore, the results of velocity profile decreases for increasing values of magnetic parameter and viscosity parameter but there is no effect for reaction parameter. The temperature profile decreases in presence of magnetic parameter, viscosity parameter and Prandtl number but increases for radiation parameter. Also, concentration profile decreases for the increasing values of magnetic parameter, viscosity parameter and reaction parameter. All numerical calculations are done with respect to salt water and fixed angle of inclination of the plate.
B.I. Olajuwon
2014-12-01
Full Text Available Heat and mass transfer effects on unsteady flow of a viscoelastic micropolar fluid over an infinite moving permeable plate in a saturated porous medium in the presence of a transverse magnetic field with Hall effect and thermal radiation are studied. The governing system of partial differential equations is transformed to dimensionless equations using dimensionless variables. The dimensionless equations are then solved analytically using perturbation technique to obtain the expressions for velocity, microrotation, temperature and concentration. With the help of graphs, the effects of magnetic field parameter M, thermal radiation parameter Nr, Hall current parameter m, K, viscoelastic parameter a, and slip parameter h on the velocity, microrotation, temperature and concentration fields within the boundary layer are discussed. The result showed that increase in Nr and m increases translational velocity across the boundary layer while (a decreases translational velocity in the vicinity of the plate but the reverse happens when away from the plate. As h increases the translational velocity across the boundary layer increases. The higher the values of Nr, the higher the micro-rotational velocity effect while m lowers it. Also the effects n, a, m, Nr, Pr and Sc on the skin friction coefficient, Nusselt number and Sherwood numbers are presented numerically in tabular form. The result also revealed that increase in n reduces the skin friction coefficient. Pr enhances the rate of heat transfer while Sc enhances the rate of mass transfer.
Machireddy Gnaneswara Reddy
2014-01-01
Full Text Available A two-dimensional mathematical model is presented for the laminar heat and mass transfer of an electrically-conducting, viscous and Joule (Ohmic heating fluid over an inclined radiate isothermal permeable surface in the presence of the variable thermal conductivity, thermophoresis and heat generation. The Talbot- Cheng-Scheffer-Willis formulation (1980 is used to introduce a thermophoretic coefficient into the concentration boundary layer equation. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations, in a single independent variable . The resulting coupled nonlinear equations are solved under appropriate transformed boundary conditions using the Runge-Kutta fourth order along with shooting method. Comparisons with previously published work are performed and the results are found to be in very good agreement. Computations are performed for a wide range of the governing flow parameters, viz., magnetic field parameter, thermophoretic coefficient (a function of Knudsen number, Eckert number (viscous heating effect, angle of inclination, thermal conductivity parameter, heat generation parameter and Schmidt number. The present problem finds applications in optical fiber fabrication, aerosol filter precipitators, particle deposition on hydronautical blades, semiconductor wafer design, thermo-electronics and magnetohydrodynamic energy generators.
Ali, M., E-mail: ali.mehidi93@gmail.com [Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000 (Bangladesh); Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong-4349 (Bangladesh); Alim, M. A., E-mail: maalim@math.buet.ac.bd; Nasrin, R., E-mail: rehena@math.buet.ac.bd [Department of Mathematics, Bangladesh University of Engineering and Technology, Dhaka-1000 (Bangladesh); Alam, M. S., E-mail: shahalammaths@gmail.com [Department of Mathematics, Chittagong University of Engineering and Technology, Chittagong-4349 (Bangladesh)
2016-07-12
An analysis is performed to study the free convection heat and mass transfer flow of an electrically conducting incompressible viscous fluid about a semi-infinite inclined porous plate under the action of radiation, chemical reaction in presence of magnetic field with variable viscosity. The dimensionless governing equations are steady, two-dimensional coupled and non-linear ordinary differential equation. Nachtsgeim-Swigert shooting iteration technique along with Runge-Kutta integration scheme is used to solve the non-dimensional governing equations. The effects of magnetic parameter, viscosity parameter and chemical reaction parameter on velocity, temperature and concentration profiles are discussed numerically and shown graphically. Therefore, the results of velocity profile decreases for increasing values of magnetic parameter and viscosity parameter but there is no effect for reaction parameter. The temperature profile decreases in presence of magnetic parameter, viscosity parameter and Prandtl number but increases for radiation parameter. Also, concentration profile decreases for the increasing values of magnetic parameter, viscosity parameter and reaction parameter. All numerical calculations are done with respect to salt water and fixed angle of inclination of the plate.
Fazle Mabood
2016-01-01
Full Text Available This study presents a numerical analysis on the effects of Soret, variable thermal conductivity, viscous-Ohmic dissipation, non-uniform heat sources, on steady two-dimensional hydromagnetic mixed convective heat and mass transfer flow of a micropolar fluid over a stretching sheet embedded in a non-Darcian porous medium with thermal radiation and chemical reaction. The governing differential equations are transformed into a set of non-linear coupled ordinary differential equations which are then solved numerically by using the fifth-order Runge-Kutta-Fehlberg method with shooting technique. Numerical solutions are obtained for the velocity, angular velocity, temperature and concentration profiles for various parametric values, and then results are presented graphically as well as skin-friction coefficient, and also local Nusselt number and local Sherwood number for different physical parameters are shown graphically and in tabular form. A critical analysis with earlier published papers was done, and the results were found to be in accordance with each other.
Rahman Abdel-Gamal M.
2013-01-01
Full Text Available The unsteady flow and heat transfer in an incompressible laminar, electrically conducting and non-Newtonian fluid over a non-isothermal stretching sheet with the variation in the viscosity and thermal conductivity in a porous medium by the influence of an external transverse magnetic field have been obtained and studied numerically. By using similarity analysis the governing differential equations are transformed into a set of non-linear coupled ordinary differential equations which are solved numerically. Numerical results were presented for velocity and temperature profiles for different parameters of the problem as power law parameter, unsteadiness parameter, radiation parameter, magnetic field parameter, porous medium parameter, temperature buoyancy parameter, Prandtl parameter, modified Eckert parameter, Joule heating parameter , heat source/sink parameter and others. A comparison with previously published work has been carried out and the results are found to be in good agreement. Also the effects of the pertinent parameters on the skin friction and the rate of heat transfer are obtained and discussed numerically and illustrated graphically.
Muscular adaptations after two different volumes of blood flow-restricted training.
Martín-Hernández, J; Marín, P J; Menéndez, H; Ferrero, C; Loenneke, J P; Herrero, A J
2013-03-01
This study aimed to gain an insight into the adaptations of muscle strength and skeletal muscle thickness after two different volumes of blood flow restriction training (BFRT), and compare them with high-intensity training. The sample was divided into four groups: low-volume, low-intensity BFRT (BFRT LV); high-volume, low-intensity BFRT (BFRT HV); traditional high-intensity resistance training (HIT); and a control group, which maintained their routine activities (CON). Leg extension one repetition maximum (1RM), isokinetic peak knee extension, and flexion torques at 60°/s and 180°/s as well as muscle thickness of the rectus femoris (RF) and vastus lateralis (VL) were assessed at baseline and after 5 weeks of training BFRT LV (7.03%, P muscular size or strength. Although similar increases in muscle thickness were observed between training groups, HIT increased 1RM performance to a greater extent compared to either volume of BFRT.
Problems in nonlinear resistive MHD
Turnbull, A.D.; Strait, E.J.; La Haye, R.J.; Chu, M.S.; Miller, R.L. [General Atomics, San Diego, CA (United States)
1998-12-31
Two experimentally relevant problems can relatively easily be tackled by nonlinear MHD codes. Both problems require plasma rotation in addition to the nonlinear mode coupling and full geometry already incorporated into the codes, but no additional physics seems to be crucial. These problems discussed here are: (1) nonlinear coupling and interaction of multiple MHD modes near the B limit and (2) nonlinear coupling of the m/n = 1/1 sawtooth mode with higher n gongs and development of seed islands outside q = 1.
Magnetohydrodynamic (MHD) channel corner seal
Spurrier, Francis R.
1980-01-01
A corner seal for an MHD duct includes a compressible portion which contacts the duct walls and an insulating portion which contacts the electrodes, sidewall bars and insulators. The compressible portion may be a pneumatic or hydraulic gasket or an open-cell foam rubber. The insulating portion is segmented into a plurality of pieces of the same thickness as the electrodes, insulators and sidewall bars and aligned therewith, the pieces aligned with the insulator being of a different size from the pieces aligned with the electrodes and sidewall bars to create a stepped configuration along the corners of the MHD channel.
Direct numerical simulations of helical dynamo action: MHD and beyond
D. O. Gómez
2004-01-01
Full Text Available Magnetohydrodynamic dynamo action is often invoked to explain the existence of magnetic fields in several astronomical objects. In this work, we present direct numerical simulations of MHD helical dynamos, to study the exponential growth and saturation of magnetic fields. Simulations are made within the framework of incompressible flows and using periodic boundary conditions. The statistical properties of the flow are studied, and it is found that its helicity displays strong spatial fluctuations. Regions with large kinetic helicity are also strongly concentrated in space, forming elongated structures. In dynamo simulations using these flows, we found that the growth rate and the saturation level of magnetic energy and magnetic helicity reach an asymptotic value as the Reynolds number is increased. Finally, extensions of the MHD theory to include kinetic effects relevant in astrophysical environments are discussed.
Branover, Herman; Mond, Michael; Unger, Yeshajahu
The present collection of papers on MHD-related uses of liquid metal flows and their applications discusses topics in laminar MHD flows, MHD power generation, metallurgical MHD applications, and two-phase MHD flows. Attention is given to MHD flows with closed streamlines, nonlinear waves in liquid metals under a transverse magnetic field, liquid-metal MHD conversion of nuclear energy to electricity, the testing of optimized MHD conversion ('OMACON') systems, and aspects of a liquid-metal induction generator. Also discussed are MHD effects in liquid-metal breeder reactors, a plasma-driven MHD powerplant, modeling the recirculating flows in channel-induction surfaces, the hydrodynamics of aluminum reduction cells, free-surface determination in a levitation-melting process, the parametric interactions of waves in bubbly liquid metals, and the occurrence of cavitation in water jets.
Three-dimensional fluid and electrodynamic modeling for MHD DCW channels
Liu, B. L.; Lineberry, J. T.; Schmidt, H. J.
1983-01-01
A three dimensional, numerical solution for modeling diagonal conducting wall (DCW) magnetohydrodynamic (MHD) generators is developed and discussed. Cross plane gasdynamic and electrodynamic profiles are computed considering coupled MHD flow and electrical phenomena. A turbulent transport model based on the mixing length theory is used to deal with wall roughness generated turbulence effects. The infinitely fine electrode segmentation formulation is applied to simplify the governing electrical equations. Calculations show the development of distorted temperature and velocity profiles under influence of magnetohydrodynamic interaction. Since both sidewall and electrode wall boundary losses are treated, the results furnish a realistic representation of MHD generator behavior.
Delayed Effect of Blood-Flow-Restricted Resistance Training on Rapid Force Capacity
Nielsen, Jakob Lindberg; Frandsen, Ulrik; Prokhorova, Tatyana
2017-01-01
PURPOSE: The aim of the present study was to investigate the effect and time course of high-frequent low-load resistance training with blood-flow restriction (BFR) on rapid force capacity (i.e. rate of torque development (RTD)). METHODS: Ten male subjects (22.8±2.3 years) performed four sets...... and rapid force capacity (e.g. RTD) as well as evoked twitch contractile parameters was assessed before (Pre) and 5 and 12 days after training (Post5, Post12). Muscle biopsies were obtained Pre, after 8 days (Mid8) and 3 and 10 days post training (Post3, Post10) to examine changes in myofiber area...... exercise performed with blood-flow restriction leads to marked increases in rapid force capacity (RTD). However, a general delayed adaptive response was observed for voluntary contractile parameters (including RTD) in parallel with a decline and subsequent recovery in evoked contractile properties...
Extended MHD Effects in High Energy Density Experiments
Seyler, Charles
2016-10-01
The MHD model is the workhorse for computational modeling of HEDP experiments. Plasma models are inheritably limited in scope, but MHD is expected to be a very good model for studying plasmas at the high densities attained in HEDP experiments. There are, however, important ways in which MHD fails to adequately describe the results, most notably due to the omission of the Hall term in the Ohm's law (a form of extended MHD or XMHD). This talk will discuss these failings by directly comparing simulations of MHD and XMHD for particularly relevant cases. The methodology is to simulate HEDP experiments using a Hall-MHD (HMHD) code based on a highly accurate and robust Discontinuous Galerkin method, and by comparison of HMHD to MHD draw conclusions about the impact of the Hall term. We focus on simulating two experimental pulsed power machines under various scenarios. We examine the MagLIF experiment on the Z-machine at Sandia National Laboratories and liner experiments on the COBRA machine at Cornell. For the MagLIF experiment we find that power flow in the feed leads to low density plasma ablation into the region surrounding the liner. The inflow of this plasma compresses axial magnetic flux onto the liner. In MHD this axial flux tends to resistively decay, whereas in HMHD a force-free current layer sustains the axial flux on the liner leading to a larger ratio of axial to azimuthal flux. During the liner compression the magneto-Rayleigh-Taylor instability leads to helical perturbations due to minimization of field line bending. Simulations of a cylindrical liner using the COBRA machine parameters can under certain conditions exhibit amplification of an axial field due to a force-free low-density current layer separated by some distance from the liner. This results in a configuration in which there is predominately axial field on the liner inside the current layer and azimuthal field outside the layer. We are currently attempting to experimentally verify the simulation
Information Flow in Training Exercises with the Combined Arms Tactical Training Simulator (CATTS)
1977-11-01
A 4 12 16 G & S 10 6 16 A & S 0 2 2 A & G & S 5 3 8 Fabrication 2 1 3 Total 41 44 85 aData are based on one training group. 17 example...position (0A14) . Feedback A The team commander reported that his unit was in " big trouble". He indicated that he would not be
Effect of training level and blood flow restriction on thermal parameters: Preliminary study
Sampaio, Lucas; Bezerra, Ewertton; Paladino, Kayo; dos Santos, João Otacílio Libardoni; Priego Quesada, Jose I.; Rossato, Mateus
2016-11-01
Training with blood flow restriction could lead to an effect on skin temperature. Additionally, this effect could be higher in people with lower physical fitness level due to their lower capacity of heat loss. The aim of this preliminary study was therefore to evaluate the effects of training experience on the acute and chronic thermal skin responses after performing exercise with and without blood flow restriction. The study included ten men, of these, five were trained. All subjects performed tests and re-tests for maximum strength (1 repetition maximum) through unilateral leg extensions (right thigh at 45 ± 6.7 kg and left thigh at 45.5 ± 8.1 kg, p > 0.05). The protocol consisted of four sets to concentric failure, with one-minute rest intervals between sets at an intensity corresponding to 40% of 1 RM. There were 7-day intervals between experimental sessions (150 mmHg versus unrestricted flow restriction). The thermal images were made before the protocol (pre), immediately after the end of the series (post), and 24 h afterward (post 24 h). When comparing temperature variation (Δ exercise and Δ 24 h) between groups, it was observed that the trained participants showed a greater drop in temperature 24 h after exercise with 150 mmHg restriction (confidence interval: 95% of Δ 24 h [-0.2 to -0.9 °C]) compared to untrained subjects (p = 0.006 and ES > 1.5, confidence interval: 95% Δ 24 h [-0.1 to 0.6 °C].) In conclusion, this preliminary study showed that training experience interferes with the chronic cutaneous thermal temperature of the anterior thigh when strength training associated with blood flow restriction 150 mmHg was performed.
Adaptation of Perceptual Responses to Low-Load Blood Flow Restriction Training.
Martín-Hernández, Juan; Ruiz-Aguado, Jorge; Herrero, Azael J; Loenneke, Jeremy P; Aagaard, Per; Cristi-Montero, Carlos; Menéndez, Héctor; Marín, Pedro J
2017-03-01
Martín-Hernández, J, Ruiz-Aguado, J, Herrero, AJ, Loenneke, JP, Aagaard, P, Cristi-Montero, C, Menéndez, H, and Marín, PJ. Adaptation of perceptual responses to low-load blood flow restriction training. J Strength Cond Res 31(3): 765-772, 2017-The purpose of this study was to determine the adaptive response of ratings of perceived exertion (RPE) and pain over 6 consecutive training sessions. Thirty subjects were assigned to either a blood flow restriction training (BFRT) group or a high-intensity resistance training (HIT) group. Blood flow-restricted training group performed 4 sets (30 + 15 + 15 + 15, respectively) of unilateral leg extension at an intensity of 20% one repetition maximum (1RM) while a restrictive cuff was applied to the most proximal part of the leg. The HIT group performed 3 sets of 8 repetitions with 85% 1RM. Ratings of perceived exertion and pain were assessed immediately after each exercise set along the 6 training sessions and were then averaged to obtain the overall RPE and pain per session. Statistical analyses showed significant main effects for group (p ≤ 0.05) and time (p values dropped from session 1 to session 6 in both BFRT (8.12 ± 1.3 to 5.7 ± 1.1, p training, comparable with that observed with HIT. However, this response becomes attenuated with continuous practice, leading to moderate values of RPE and pain. Perceptual responses may not limit the application of BFRT to highly motivated individuals.