Coupled heat transfer in high temperature transporting system with semitransparent/opaque material

International Nuclear Information System (INIS)

Du Shenghua; Xia Xinjin

2010-01-01

The heat transfer model of the aerodynamic heating coupled with radiative cooling was developed. The thermal protect system includes the higher heat flux region with high temperature semitransparent material, the heat transporting channel and the lower heat flux region with metal. The control volume method was combined with the Monte Carlo method to calculate the coupled heat transfer of the transporting system, and the thermal equilibrium equation for the transporting channel was solved simultaneously. The effect of the aeroheating flux radio, the area ratio of radiative surfaces, the convective heat transfer coefficient of the heat transporting channel on the radiative surface temperature and the fluid temperature in the heat transporting channel were analyzed. The effect of radiation and conduction in the semitransparent material was discussed. The result shows that to increase the convective heat transfer coefficient in heat flux channel can enhance the heat transporting ability of the system, but the main parameter to effect on the temperature of the heat transporting system is the area ratio of radiative surfaces. (authors)

Magnetically Modulated Heat Transport in a Global Simulation of Solar Magneto-convection

Energy Technology Data Exchange (ETDEWEB)

Cossette, Jean-Francois [Laboratory for Atmospheric and Space Physics, Campus Box 600, University of Colorado, Boulder, CO 80303 (United States); Charbonneau, Paul [Département de Physique, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, QC H3C 3J7 (Canada); Smolarkiewicz, Piotr K. [European Centre for Medium-Range Weather Forecasts, Reading, RG2 9AX (United Kingdom); Rast, Mark P., E-mail: Jean-Francois.Cossette@lasp.colorado.edu, E-mail: paulchar@astro.umontreal.ca, E-mail: smolar@ecmwf.int, E-mail: Mark.Rast@lasp.colorado.edu [Department of Astrophysical and Planetary Sciences, Laboratory for Atmospheric and Space Physics, Campus Box 391, University of Colorado, Boulder, CO 80303 (United States)

2017-05-20

We present results from a global MHD simulation of solar convection in which the heat transported by convective flows varies in-phase with the total magnetic energy. The purely random initial magnetic field specified in this experiment develops into a well-organized large-scale antisymmetric component undergoing hemispherically synchronized polarity reversals on a 40 year period. A key feature of the simulation is the use of a Newtonian cooling term in the entropy equation to maintain a convectively unstable stratification and drive convection, as opposed to the specification of heating and cooling terms at the bottom and top boundaries. When taken together, the solar-like magnetic cycle and the convective heat flux signature suggest that a cyclic modulation of the large-scale heat-carrying convective flows could be operating inside the real Sun. We carry out an analysis of the entropy and momentum equations to uncover the physical mechanism responsible for the enhanced heat transport. The analysis suggests that the modulation is caused by a magnetic tension imbalance inside upflows and downflows, which perturbs their respective contributions to heat transport in such a way as to enhance the total convective heat flux at cycle maximum. Potential consequences of the heat transport modulation for solar irradiance variability are briefly discussed.

Heat, mass, and momentum transport model for hydrogen diffusion flames in nuclear reactor containments

International Nuclear Information System (INIS)

Travis, J.R.

1985-01-01

It is now possible to analyze the time-dependent, fully three-dimensional behavior of hydrogen diffusion flames in nuclear reactor containments. This analysis involves coupling the full Navier-Stokes equations with multi-species transport to the global chemical kinetics of hydrogen combustion. A transport equation for the subgrid scale turbulent kinetic energy density is solved to produce the time and space dependent turbulent transport coefficients. The heat transfer coefficient governing the exchange of heat between fluid computational cells adjacent to wall cells is calculated by a modified Reynolds analogy formulation. The analysis of a MARK-III containment indicates very complex flow patterns that greatly influence fluid and wall temperatures and heat fluxes. 18 refs., 24 figs

Differential-algebraic solutions of the heat equation

OpenAIRE

Buchstaber, Victor M.; Netay, Elena Yu.

2014-01-01

In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of a special form. The ansatz for such solutions is called the $n$-ansatz, where $n+1$ is the order of the differential equation.

Study of the electron heat transport in Tore-Supra tokamak

International Nuclear Information System (INIS)

Harauchamps, E.

2004-01-01

This work presents analytical solutions to the electron heat transport equation involving a damping term and a convection term in a cylindrical geometry. These solutions, processed by Matlab, allow the determination of the evolution of the radial profile of electron temperature in tokamaks during heating. The modulated injection of waves around the electron cyclotron frequency is an efficient tool to study heat transport experimentally in tokamaks. The comparison of these analytical solutions with experimental results from Tore-Supra during 2 discharges (30550 and 31165) shows the presence of a sudden change for the diffusion and damping coefficients. The hypothesis of the presence of a pinch spread all along the plasma might explain the shape of the experimental temperature profiles. These analytical solutions could be used to determine the time evolution of plasma density as well or of any parameter whose evolution is governed by a diffusion-convection equation. (A.C.)

Integral representation of nonlinear heat transport

International Nuclear Information System (INIS)

Kishimoto, Y.; Mima, K.; Haines, M.G.

1985-07-01

The electron distribution function in a plasma with steep temperature gradient is obtained from a Fokker-Planck equation by Green's function method. The formula describes the nonlocal effects on thermal transport over the range, λ e /L e /L → 0. As an example, the heat wave is analyzed numerically by the integral formula and it is found that the previous simulation results are well reproduced. (author)

The gBL transport equations

International Nuclear Information System (INIS)

Mynick, H.E.

1989-05-01

The transport equations arising from the ''generalized Balescu- Lenard'' (gBL) collision operator are obtained, and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases, having the same structure. The resultant theory offers potential explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/ΓT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy to neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest. 10 refs

A new bioheat equation and its application to peripheral tissue and whole limb heat transfer

International Nuclear Information System (INIS)

Weinbaum, S.

1987-01-01

Much of the mathematical modeling of heat transfer in perfused tissue over the past three decades has been based on the Pennes bioheat equation. This equation assumes that blood at the local arterial supply temperature reaches the capillaries where the primary thermal equilibration occurs because of the large surface area available for heat exchange. While this argument is correct for gas, water and solute transport, recent theoretical and experimental studies have shown that virtually no heat exchange occurs in vessels under 100 μm and that the primary mechanism for microvascular heat exchange is the imperfect heat exchange between the larger paired countercurrent microvessels that occur 3 to 6 generations prior to the capillaries. A new fundamental bioheat equations has been derived to describe this heat transfer mechanism. This equation contains a basic new expression for the thermal conductivity of perfused tissue which depends on the geometry and flow in the largest microvessels of the local tissue element and the direction of the vessels relative to the local tissue temperature gradient. Although the new equation appears to be complicated, it is shown that it can be applied with relative ease to a host of problems previously treated by the Pennes equation

Heat transport in two-dimensional materials by directly solving the phonon Boltzmann equation under Callaway's dual relaxation model

Science.gov (United States)

Guo, Yangyu; Wang, Moran

2017-10-01

The single mode relaxation time approximation has been demonstrated to greatly underestimate the lattice thermal conductivity of two-dimensional materials due to the collective effect of phonon normal scattering. Callaway's dual relaxation model represents a good approximation to the otherwise ab initio solution of the phonon Boltzmann equation. In this work we develop a discrete-ordinate-method (DOM) scheme for the numerical solution of the phonon Boltzmann equation under Callaway's model. Heat transport in a graphene ribbon with different geometries is modeled by our scheme, which produces results quite consistent with the available molecular dynamics, Monte Carlo simulations, and experimental measurements. Callaway's lattice thermal conductivity model with empirical boundary scattering rates is examined and shown to overestimate or underestimate the direct DOM solution. The length convergence of the lattice thermal conductivity of a rectangular graphene ribbon is explored and found to depend appreciably on the ribbon width, with a semiquantitative correlation provided between the convergence length and the width. Finally, we predict the existence of a phonon Knudsen minimum in a graphene ribbon only at a low system temperature and isotope concentration so that the average normal scattering rate is two orders of magnitude stronger than the intrinsic resistive one. The present work will promote not only the methodology for the solution of the phonon Boltzmann equation but also the theoretical modeling and experimental detection of hydrodynamic phonon transport in two-dimensional materials.

Integrated heat transport simulation of high ion temperature plasma of LHD

International Nuclear Information System (INIS)

Murakami, S.; Yamaguchi, H.; Sakai, A.

2014-10-01

A first dynamical simulation of high ion temperature plasma with carbon pellet injection of LHD is performed by the integrated simulation GNET-TD + TASK3D. NBI heating deposition of time evolving plasma is evaluated by the 5D drift kinetic equation solver, GNET-TD and the heat transport of multi-ion species plasma (e, H, He, C) is studied by the integrated transport simulation code, TASK3D. Achievement of high ion temperature plasma is attributed to the 1) increase of heating power per ion due to the temporal increase of effective charge, 2) reduction of effective neoclassical transport with impurities, 3) reduction of turbulence transport. The reduction of turbulence transport is most significant contribution to achieve the high ion temperature and the reduction of the turbulent transport from the L-mode plasma (normal hydrogen plasma) is evaluated to be a factor about five by using integrated heat transport simulation code. Applying the Z effective dependent turbulent reduction model we obtain a similar time behavior of ion temperature after the C pellet injection with the experimental results. (author)

Heat and damp transport in cavity bricks. Waerme- und Feuchtetransport in Hochlochziegeln

Energy Technology Data Exchange (ETDEWEB)

Elsner, M

1987-11-19

The aim of this work is a systematic measurement of the structural effect of cavity bricks on the thermal insulation and thermal storage values depending on the material values of the bricks and the mortar. The arrangement and orientation of the hollow spaces and their dimensions should be varied. Brick shapes with socalled handle slots, which give more convenient handling, and with mortar pockets instead of mortar gaps, should be taken into account in the investigation. Special attention should be paid to the heat transport mechanism in the hollow spaces, where thermal conduction, thermal radiation and convection heat transport are superimposed on one another. The second main aim of the work is the calculation of the coupled heat and damp transport in hollow bricks. The heat and damp transport is described by a coupled system of differential equations, where the decisive transport coefficients should be shown as a function of the variables determining the transport processes. (orig./MM).

Moment approach to neoclassical flows, currents and transport in auxiliary heated tokamaks

International Nuclear Information System (INIS)

Kim, Yil Bong.

1988-02-01

The moment approach is utilized to derive the full complement of neoclassical transport processes in auxiliary heated tokamaks. The effects of auxiliary heating [neutral beam injection (NBI) and ion cyclotron resonance heating (ICRH)] considered arise from the collisional interaction between the background plasma species and the fast-ion-tail species. From a known fast ion distribution function we evaluate the parallel (to the magnetic field) momentum and heat flow inputs to the background plasma. Then, through the momentum and heat flow balance equations, we can determine the induced parallel flows (and current) and radial transpot fluxes in ''equilibrium'' (on the time scale much longer than the collisional relaxation time, i.e., t >> 1ν/sub ii/). In addition to the fast-ion-induced current, the total neoclassical current includes the boostap current, which is driven by the pressure and temperature gradients, the Pfirsch-Schlueter current which is required for charge neutrality, and the neoclassical (including trapped particle effects) Spitzer current due to the parallel electric field. The radial transport fluxes also include off-diagonal compnents in the transport matrix which correspond to the Ware (neoclassical) pinch due to the inductive applied electric field an the fast-ion-induced radial fluxes, in addition to the usual pressure- and temperature-gradient-driven fluxes (particle diffusion and heat conduction). Once the tranport coefficient are completely determined, the radial fluxes and the heat fluxes can be substituted into the density and energy evolution equations to provide a complete description of ''equilibrium'' (δδt << ν/sub ii/) neoclassical transport processes in a plasma. 47 refs., 14 figs

Development of interfacial area transport equation

International Nuclear Information System (INIS)

Kim, Seung Jin; Ishii, Mamoru; Kelly, Joseph

2005-01-01

The interfacial area transport equation dynamically models the changes in interfacial structures along the flow field by mechanistically modeling the creation and destruction of dispersed phase. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport mechanism for various sizes of bubbles, the transport equation is formulated for two characteristic groups of bubbles. The group 1 equation describes the transport of small-dispersed bubbles, whereas the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. To evaluate the feasibility and reliability of interfacial area transport equation available at present, it is benchmarked by an extensive database established in various two-phase flow configurations spanning from bubbly to churn-turbulent flow regimes. The geometrical effect in interfacial area transport is examined by the data acquired in vertical air-water two-phase flow through round pipes of various sizes and a confined flow duct, and by those acquired in vertical co-current downward air-water two-phase flow through round pipes of two different sizes

The influence of meridional ice transport on Europa's ocean stratification and heat content

Science.gov (United States)

Zhu, P.; Manucharyan, G.; Thompson, A. F.; Goodman, J. C.; Vance, S.

2017-12-01

Jupiter's moon Europa likely hosts a saltwater ocean beneath its icy surface. Geothermal heating and rotating convection in the ocean may drive a global overturning circulation that redistributes heat vertically and meridionally, preferentially warming the ice shell at the equator. Here we assess thepreviously unconstrained influence of ocean-ice coupling on Europa's ocean stratification and heat transport. We demonstrate that a relatively fresh layer can form at the ice-ocean interface due to a meridional ice transport forced by the differential ice shell heating between the equator and the poles. We provide analytical and numerical solutions for the layer's characteristics, highlighting their sensitivity to critical ocean parameters. For a weakly turbulent and highly saline ocean, a strong buoyancy gradient at the base of the freshwater layer can suppress vertical tracer exchange with the deeper ocean. As a result, the freshwater layer permits relatively warm deep ocean temperatures.

Subcooled He II heat transport in the channel with abrupt contractions/enlargements

International Nuclear Information System (INIS)

Maekawa, R.; Iwamoto, A.; Hamaguchi, S.; Mito, T.

2002-01-01

Heat transport mechanisms for subcooled He II in the channel with abrupt contractions and/or enlargements have been investigated under steady state conditions. The channel, made of G-10, contains various contraction geometries to simulate the cooling channel of a superconducting magnet. In other words, contractions are periodically placed along the channel to simulate the spacers within the magnet winding. A copper block heater inputs the heat to the channel from one end, while the other end is open to the He II bath. Temperature profiles were measured with temperature sensors embedded in the channel as a function of heat input. Calculations were performed using a simple one-dimensional turbulent heat transport equation and with geometric factor consideration. The effects on heat transport mechanisms in He II caused by abrupt change of channel geometry and size are discussed

Thickness Optimisation of Textiles Subjected to Heat and Mass Transport during Ironing

Directory of Open Access Journals (Sweden)

Korycki Ryszard

2016-09-01

Full Text Available Let us next analyse the coupled problem during ironing of textiles, that is, the heat is transported with mass whereas the mass transport with heat is negligible. It is necessary to define both physical and mathematical models. Introducing two-phase system of mass sorption by fibres, the transport equations are introduced and accompanied by the set of boundary and initial conditions. Optimisation of material thickness during ironing is gradient oriented. The first-order sensitivity of an arbitrary objective functional is analysed and included in optimisation procedure. Numerical example is the thickness optimisation of different textile materials in ironing device.

The 'generalized Balescu-Lenard' transport equations

International Nuclear Information System (INIS)

Mynick, H.E.

1990-01-01

The transport equations arising from the 'generalized Balescu-Lenard' collision operator are obtained and some of their properties examined. The equations contain neoclassical and turbulent transport as two special cases having the same structure. The resultant theory offers a possible explanation for a number of results not well understood, including the anomalous pinch, observed ratios of Q/ΓT on TFTR, and numerical reproduction of ASDEX profiles by a model for turbulent transport invoked without derivation, but by analogy with neoclassical theory. The general equations are specialized to consideration of a number of particular transport mechanisms of interest. (author). Letter-to-the-editor. 10 refs

Study of electronic heat transport in plasma through diagnosis based on modulated electron cyclotron heating; Etudes de transport de la chaleur electronique par injection modulee d'ondes a la frequence cyclotronique electronique

Energy Technology Data Exchange (ETDEWEB)

Clemencon, A.; Guivarch, C

2003-07-01

In order to make nuclear fusion energetically profitable, it is crucial to heat and confine the plasma efficiently. Studying the behavior of the heat diffusion coefficient is a key issue in this matter. The use of modulated electron cyclotron heating as a diagnostic has suggested the existence of a transport barrier under certain plasma conditions. We have determined the solution to the heat transport equation, for several heat diffusion coefficient profiles. By comparing the analytical solutions with experimental data; we are able to study the heat diffusion coefficient profile. Thus, in certain experiments, we can confirm that the heat diffusion coefficient switches from low to high values at the radius where the electron cyclotron heat deposition is made. (authors)

The heat and moisture transport properties of wet porous media

International Nuclear Information System (INIS)

Wang, B.X.; Fang, Z.H.; Yu, W.P.

1989-01-01

Existing methods for determining heat and moisture transport properties in porous media are briefly reviewed, and their merits and deficiencies are discussed. Emphasis is placed on research in developing new transient methods undertaken in China during the recent years. An attempt has been made to relate the coefficients in the heat and mass transfer equations with inherent properties of the liquid and matrix and then to predict these coefficients based on limited measurements

Numerical study of the influence of the convective heat transport on acoustic streaming in a standing wave.

Science.gov (United States)

Červenka, Milan; Bednařík, Michal

2018-02-01

Within this work, acoustic streaming in an air-filled cylindrical resonator with walls supporting a temperature gradient is studied by means of numerical simulations. A set of equations based on successive approximations is derived from the Navier-Stokes equations. The equations take into account the acoustic-streaming-driven convective heat transport; as time-averaged secondary-field quantities are directly calculated, the equations are much easier to integrate than the original fluid-dynamics equations. The model equations are implemented and integrated employing commercial software COMSOL Multiphysics. Numerical calculations are conducted for the case of a resonator with a wall-temperature gradient corresponding to the action of a thermoacoustic effect. It is shown that due to the convective heat transport, the streaming profile is considerably distorted even in the case of weak wall-temperature gradients. The numerical results are consistent with available experimental data.

The Laplace transformation of adjoint transport equations

International Nuclear Information System (INIS)

Hoogenboom, J.E.

1985-01-01

A clarification is given of the difference between the equation adjoint to the Laplace-transformed time-dependent transport equation and the Laplace-transformed time-dependent adjoint transport equation. Proper procedures are derived to obtain the Laplace transform of the instantaneous detector response. (author)

Paleoclassical electron heat transport

International Nuclear Information System (INIS)

Callen, J.D.

2005-01-01

Radial electron heat transport in low collisionality, magnetically-confined toroidal plasmas is shown to result from paleoclassical Coulomb collision processes (parallel electron heat conduction and magnetic field diffusion). In such plasmas the electron temperature equilibrates along magnetic field lines a long length L, which is the minimum of the electron collision length and a maximum effective half length of helical field lines. Thus, the diffusing field lines induce a radial electron heat diffusivity M ≅ L/(πR 0q ) ∼ 10 >> 1 times the magnetic field diffusivity η/μ 0 ≅ ν e (c/ω p ) 2 . The paleoclassical electron heat flux model provides interpretations for many features of 'anomalous' electron heat transport: magnitude and radial profile of electron heat diffusivity (in tokamaks, STs, and RFPs), Alcator scaling in high density plasmas, transport barriers around low order rational surfaces and near a separatrix, and a natural heat pinch (or minimum temperature gradient) heat flux form. (author)

NON-LINEAR TRANSIENT HEAT CONDUCTION ANALYSIS OF INSULATION WALL OF TANK FOR TRANSPORTATION OF LIQUID ALUMINUM

Directory of Open Access Journals (Sweden)

Miroslav M Živković

2010-01-01

Full Text Available This paper deals with transient nonlinear heat conduction through the insulation wall of the tank for transportation of liquid aluminum. Tanks designed for this purpose must satisfy certain requirements regarding temperature of loading and unloading, during transport. Basic theoretical equations are presented, which describe the problem of heat conduction finite element (FE analysis, starting from the differential equation of energy balance, taking into account the initial and boundary conditions of the problem. General 3D problem for heat conduction is considered, from which solutions for two- and one-dimensional heat conduction can be obtained, as special cases. Forming of the finite element matrices using Galerkin method is briefly described. The procedure for solving equations of energy balance is discussed, by methods of resolving iterative processes of nonlinear transient heat conduction. Solution of this problem illustrates possibilities of PAK-T software package, such as materials properties, given as tabular data, or analytical functions. Software also offers the possibility to solve nonlinear and transient problems with incremental methods. Obtained results for different thicknesses of the tank wall insulation materials enable its comparison in regards to given conditions

Role of ocean heat transport in climates of tidally locked exoplanets around M dwarf stars.

Science.gov (United States)

Hu, Yongyun; Yang, Jun

2014-01-14

The distinctive feature of tidally locked exoplanets is the very uneven heating by stellar radiation between the dayside and nightside. Previous work has focused on the role of atmospheric heat transport in preventing atmospheric collapse on the nightside for terrestrial exoplanets in the habitable zone around M dwarfs. In the present paper, we carry out simulations with a fully coupled atmosphere-ocean general circulation model to investigate the role of ocean heat transport in climate states of tidally locked habitable exoplanets around M dwarfs. Our simulation results demonstrate that ocean heat transport substantially extends the area of open water along the equator, showing a lobster-like spatial pattern of open water, instead of an "eyeball." For sufficiently high-level greenhouse gases or strong stellar radiation, ocean heat transport can even lead to complete deglaciation of the nightside. Our simulations also suggest that ocean heat transport likely narrows the width of M dwarfs' habitable zone. This study provides a demonstration of the importance of exooceanography in determining climate states and habitability of exoplanets.

Study of the electron heat transport in Tore-Supra tokamak; Etude du transport de la chaleur electronique dans le Tokamak Tore Supra

Energy Technology Data Exchange (ETDEWEB)

Harauchamps, E

2004-07-01

This work presents analytical solutions to the electron heat transport equation involving a damping term and a convection term in a cylindrical geometry. These solutions, processed by Matlab, allow the determination of the evolution of the radial profile of electron temperature in tokamaks during heating. The modulated injection of waves around the electron cyclotron frequency is an efficient tool to study heat transport experimentally in tokamaks. The comparison of these analytical solutions with experimental results from Tore-Supra during 2 discharges (30550 and 31165) shows the presence of a sudden change for the diffusion and damping coefficients. The hypothesis of the presence of a pinch spread all along the plasma might explain the shape of the experimental temperature profiles. These analytical solutions could be used to determine the time evolution of plasma density as well or of any parameter whose evolution is governed by a diffusion-convection equation. (A.C.)

Probabilistic Representations of Solutions to the Heat Equation

Indian Academy of Sciences (India)

In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition , is given by the convolution of with the heat kernel (Gaussian density). Our results also extend the ...

ELECTRON TEMPERATURE FLUCTUATIONS AND CROSS-FIELD HEAT TRANSPORT IN THE EDGE OF DIII-D

International Nuclear Information System (INIS)

RUDAKOV, DL; BOEDO, JA; MOYER, RA; KRASENINNIKOV, S; MAHDAVI, MA; McKEE, GR; PORTER, GD; STANGEBY, PC; WATKINS, JG; WEST, WP; WHYTE, DG.

2003-01-01

OAK-B135 The fluctuating E x B velocity due to electrostatic turbulence is widely accepted as a major contributor to the anomalous cross-field transport of particles and heat in the tokamak edge and scrape-off layer (SOL) plasmas. This has been confirmed by direct measurements of the turbulent E x B transport in a number of experiments. Correlated fluctuations of the plasma radial velocity v r , density n, and temperature T e result in time-average fluxes of particles and heat given by (for electrons): Equation 1--Λ r ES = r > = 1/B varφ θ ; Equation 2--Q r ES = e (tilde v) r > ∼ 3/2 kT e Λ r ES + 3 n e /2 B varφ e (tilde E) θ > Q conv + Q cond . The first term in Equation 2 is referred to as convective and the second term as conductive heat flux. Experimental determination of fluxes given by Equations 1 and 2 requires simultaneous measurements of the density, temperature and poloidal electric field fluctuations with high spatial and temporal resolution. Langmuir probes provide most readily available (if not the only) tool for such measurements. However, fast measurements of electron temperature using probes are non-trivial and are not always performed. Thus, the contribution of the T e fluctuations to the turbulent fluxes is usually neglected. Here they report results of the studies of T e fluctuations and their effect on the cross-field transport in the SOL of DIII-D

Neutron transport equation - indications on homogenization and neutron diffusion

International Nuclear Information System (INIS)

Argaud, J.P.

1992-06-01

In PWR nuclear reactor, the practical study of the neutrons in the core uses diffusion equation to describe the problem. On the other hand, the most correct method to describe these neutrons is to use the Boltzmann equation, or neutron transport equation. In this paper, we give some theoretical indications to obtain a diffusion equation from the general transport equation, with some simplifying hypothesis. The work is organised as follows: (a) the most general formulations of the transport equation are presented: integro-differential equation and integral equation; (b) the theoretical approximation of this Boltzmann equation by a diffusion equation is introduced, by the way of asymptotic developments; (c) practical homogenization methods of transport equation is then presented. In particular, the relationships with some general and useful methods in neutronic are shown, and some homogenization methods in energy and space are indicated. A lot of other points of view or complements are detailed in the text or the remarks

Numerical resolution of Navier-Stokes equations coupled to the heat equation

International Nuclear Information System (INIS)

Zenouda, Jean-Claude

1970-08-01

The author proves a uniqueness theorem for the time dependent Navier-Stokes equations coupled with heat flow in the two-dimensional case. He studies stability and convergence of several finite - difference schemes to solve these equations. Numerical experiments are done in the case of a square domain. (author) [fr

Analysis for Heat Transfer in a High Current-Passing Carbon Nanosphere Using Nontraditional Thermal Transport Model.

Science.gov (United States)

Hol C Y; Chen, B C; Tsai, Y H; Ma, C; Wen, M Y

2015-11-01

This paper investigates the thermal transport in hollow microscale and nanoscale spheres subject to electrical heat source using nontraditional thermal transport model. Working as supercapacitor electrodes, carbon hollow micrometer- and nanometer-sized spheres needs excellent heat transfer characteristics to maintain high specific capacitance, long cycle life, and high power density. In the nanoscale regime, the prediction of heat transfer from the traditional heat conduction equation based on Fourier's law deviates from the measured data. Consequently, the electrical heat source-induced heat transfer characteristics in hollow micrometer- and nanometer-sized spheres are studied using nontraditional thermal transport model. The effects of parameters on heat transfer in the hollow micrometer- and nanometer-sized spheres are discussed in this study. The results reveal that the heat transferred into the spherical interior, temperature and heat flux in the hollow sphere decrease with the increasing Knudsen number when the radius of sphere is comparable to the mean free path of heat carriers.

Bounds on heat transport in rapidly rotating Rayleigh–Bénard convection

International Nuclear Information System (INIS)

Grooms, Ian; Whitehead, Jared P

2015-01-01

The heat transport in rotating Rayleigh–Bénard convection is considered in the limit of rapid rotation (small Ekman number E) and strong thermal forcing (large Rayleigh number Ra). The analysis proceeds from a set of asymptotically reduced equations appropriate for rotationally constrained dynamics; the conjectured range of validity for these equations is Ra ≲ E −8/5 . A rigorous bound on heat transport of Nu ⩽ 20.56Ra 3 E 4 is derived in the limit of infinite Prandtl number using the background method. We demonstrate that the exponent in this bound cannot be improved on using a piece-wise monotonic background temperature profile like the one used here. This is true for finite Prandtl numbers as well, i.e. Nu ≲ Ra 3 is the best upper bound for this particular setup of the background method. The feature that obstructs the availability of a better bound in this case is the appearance of small-scale thermal plumes emanating from (or entering) the thermal boundary layer. The derived upper bound is consistent with, although significantly higher than the observed behaviour in simulations of the reduced equations, which find at most Nu ∼ Ra 2 E 8/3 . (paper)

Maximal stochastic transport in the Lorenz equations

Energy Technology Data Exchange (ETDEWEB)

Agarwal, Sahil, E-mail: sahil.agarwal@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Wettlaufer, J.S., E-mail: john.wettlaufer@yale.edu [Program in Applied Mathematics, Yale University, New Haven (United States); Departments of Geology & Geophysics, Mathematics and Physics, Yale University, New Haven (United States); Mathematical Institute, University of Oxford, Oxford (United Kingdom); Nordita, Royal Institute of Technology and Stockholm University, Stockholm (Sweden)

2016-01-08

We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh–Bénard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

An alternative treatment of heat flow for charge transport in semiconductor devices

International Nuclear Information System (INIS)

Grupen, Matt

2009-01-01

A unique thermodynamic model of Fermi gases suitable for semiconductor device simulation is presented. Like other models, such as drift diffusion and hydrodynamics, it employs moments of the Boltzmann transport equation derived using the Fermi-Dirac distribution function. However, unlike other approaches, it replaces the concept of an electron thermal conductivity with the heat capacity of an ideal Fermi gas to determine heat flow. The model is used to simulate a field-effect transistor and show that the external current-voltage characteristics are strong functions of the state space available to the heated Fermi distribution.

Swarm analysis by using transport equations

International Nuclear Information System (INIS)

Dote, Toshihiko.

1985-01-01

As the basis of weak ionization plasma phenomena, the motion, i.e. swarm, of charged particles in the gas is analyzed by use of the transport equations, from which basic nature of the swarm is discussed. The present report is an overview of the studies made in the past several years. Described are principally the most basic aspects concerning behaviors of the electrons and positive ions, that is, the basic equations and their significance, characteristics of the behaviors of the electron and positive ion swarms as revealed by solving the equations, and various characteristics of the swarm parameters. Contents are: Maxwell-Boltzmann's transport equations, behavior of the electron swarm, energy loss of the electrons, and behavior of the positive ion swarm. (Mori, K.)

Low frequency turbulence, particle and heat transport in the Wisconsin levitated octupole

International Nuclear Information System (INIS)

Garner, H.R.

1982-01-01

Low frequency turbulence in the drift frequency range and its relation to the observed particle transport in the Wisconsin Levitated Octupole has been studied with a microwave scattering apparatus. The experimental parameters were T/sub e/ approx. T/sub i/ 13 cm -3 , 200 G < B/sub p-average/ < 1.25 kG. The effect of shear on the transport was studied by the addition of a small toroidal field. By matching experimentally measured density profiles to those given by numerical solutions of the transport equations, diffusion coefficients were obtained. Time dependent density fluctuation spectra were measured with an 8 mm microwave scattering diagnostic to correlate the drift wave portion of the spectrum with the observed diffusion. The density fluctuation spectrum of low frequency (1 kHz < ω < 6 MHz) turbulence was measured for several values of perpendicular wavenumber, k/sub perpendicular to/. Electron heat transport was studied by fitting experimentally measured electron temperature profiles to those predicted by numerical solutions of electron energy transport equation

Transport equation solving methods

International Nuclear Information System (INIS)

Granjean, P.M.

1984-06-01

This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method [fr

Range of validity of transport equations

International Nuclear Information System (INIS)

Berges, Juergen; Borsanyi, Szabolcs

2006-01-01

Transport equations can be derived from quantum field theory assuming a loss of information about the details of the initial state and a gradient expansion. While the latter can be systematically improved, the assumption about a memory loss is not known to be controlled by a small expansion parameter. We determine the range of validity of transport equations for the example of a scalar g 2 Φ 4 theory. We solve the nonequilibrium time evolution using the three-loop 2PI effective action. The approximation includes off-shell and memory effects and assumes no gradient expansion. This is compared to transport equations to lowest order (LO) and beyond (NLO). We find that the earliest time for the validity of transport equations is set by the characteristic relaxation time scale t damp =-2ω/Σ ρ (eq) , where -Σ ρ (eq) /2 denotes the on-shell imaginary-part of the self-energy. This time scale agrees with the characteristic time for partial memory loss, but is much shorter than thermal equilibration times. For times larger than about t damp the gradient expansion to NLO is found to describe the full results rather well for g 2 (less-or-similar sign)1

Saturation and linear transport equation

International Nuclear Information System (INIS)

Kutak, K.

2009-03-01

We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)

Poloidal profiles and transport during turbulent heating

International Nuclear Information System (INIS)

Mascheroni, P.L.

1977-01-01

The current penetration stage of a turbulently heated tokamak is modeled. The basic formulae are written in slab geometry since the dominant anomalous transport has a characteristic frequency much larger than the bounce frequency. Thus, the basic framework is provided by the Maxwell and fluid equations, with classical and anomalous transport. Quasi-neutrality is used. It is shown that the anomalous collision frequency dominates the anomalous viscosity and thermal conductivity, and that the convective wave transport can be neglected. For these numerical estimates, the leading term in the quasi-linear series is used. During the current penetration stage the distribution function for the particles will depart from a single Maxwellian type. Hence, the first objective was to numerically compare calculated poloidal magnetic field profiles with measured, published poloidal profiles. The poloidal magnetic field has been calculated using a code which handles the anomalous collision frequency self-consistently. The agreement is good, and it is concluded that the current penetration stage can be satisfactorily described by this model

Gradient estimates on the weighted p-Laplace heat equation

Science.gov (United States)

Wang, Lin Feng

2018-01-01

In this paper, by a regularization process we derive new gradient estimates for positive solutions to the weighted p-Laplace heat equation when the m-Bakry-Émery curvature is bounded from below by -K for some constant K ≥ 0. When the potential function is constant, which reduce to the gradient estimate established by Ni and Kotschwar for positive solutions to the p-Laplace heat equation on closed manifolds with nonnegative Ricci curvature if K ↘ 0, and reduce to the Davies, Hamilton and Li-Xu's gradient estimates for positive solutions to the heat equation on closed manifolds with Ricci curvature bounded from below if p = 2.

Large-Eddy Simulation of Flow and Pollutant Transport in Urban Street Canyons with Ground Heating

OpenAIRE

Li, Xian-Xiang; Britter, Rex E.; Koh, Tieh Yong; Norford, Leslie Keith; Liu, Chun-Ho; Entekhabi, Dara; Leung, Dennis Y. C.

2009-01-01

Our study employed large-eddy simulation (LES) based on a one-equation subgrid-scale model to investigate the flow field and pollutant dispersion characteristics inside urban street canyons. Unstable thermal stratification was produced by heating the ground of the street canyon. Using the Boussinesq approximation, thermal buoyancy forces were taken into account in both the Navier–Stokes equations and the transport equation for subgrid-scale turbulent kinetic energy (TKE). The LESs were valida...

SWIFT, 3-D Fluid Flow, Heat Transfer, Decay Chain Transport in Geological Media

International Nuclear Information System (INIS)

Cranwell, R.M.; Reeves, M.

2003-01-01

1 - Description of problem or function: SWIFT solves the coupled or individual equations governing fluid flow, heat transport, brine displacement, and radionuclide displacement in geologic media. Fluid flow may be transient or steady-state. One, two, or three dimensions are available and transport of radionuclides chains is possible. 4. Method of solution: Finite differencing is used to discretize the partial differential equations in space and time. The user may choose centered or backward spatial differencing, coupled with either central or backward temporal differencing. The matrix equations may be solved iteratively (two line successive-over-relaxation) or directly (special matrix banding and Gaussian elimination). 5. Restrictions on the complexity of the problem: On the CDC7600 in direct solution mode, the maximum number of grid blocks allowed is approximately 1400

Heat transport in the XXZ spin chain: from ballistic to diffusive regimes and dephasing enhancement

International Nuclear Information System (INIS)

Mendoza-Arenas, J J; Al-Assam, S; Clark, S R; Jaksch, D

2013-01-01

In this work we study the heat transport in an XXZ spin-1/2 Heisenberg chain with homogeneous magnetic field, incoherently driven out of equilibrium by reservoirs at the boundaries. We focus on the effect of bulk dephasing (energy-dissipative) processes in different parameter regimes of the system. The non-equilibrium steady state of the chain is obtained by simulating its evolution under the corresponding Lindblad master equation, using the time evolving block decimation method. In the absence of dephasing, the heat transport is ballistic for weak interactions, while being diffusive in the strongly interacting regime, as evidenced by the heat current scaling with the system size. When bulk dephasing takes place in the system, diffusive transport is induced in the weakly interacting regime, with the heat current monotonically decreasing with the dephasing rate. In contrast, in the strongly interacting regime, the heat current can be significantly enhanced by dephasing for systems of small size. (paper)

Parallel heat transport in integrable and chaotic magnetic fields

Energy Technology Data Exchange (ETDEWEB)

Castillo-Negrete, D. del; Chacon, L. [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-8071 (United States)

2012-05-15

The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion, space plasmas, and astrophysics research. Three issues make this problem particularly challenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), {chi}{sub ||} , and the perpendicular, {chi}{sub Up-Tack }, conductivities ({chi}{sub ||} /{chi}{sub Up-Tack} may exceed 10{sup 10} in fusion plasmas); (ii) Nonlocal parallel transport in the limit of small collisionality; and (iii) Magnetic field lines chaos which in general complicates (and may preclude) the construction of magnetic field line coordinates. Motivated by these issues, we present a Lagrangian Green's function method to solve the local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields in arbitrary geometry. The method avoids by construction the numerical pollution issues of grid-based algorithms. The potential of the approach is demonstrated with nontrivial applications to integrable (magnetic island), weakly chaotic (Devil's staircase), and fully chaotic magnetic field configurations. For the latter, numerical solutions of the parallel heat transport equation show that the effective radial transport, with local and non-local parallel closures, is non-diffusive, thus casting doubts on the applicability of quasilinear diffusion descriptions. General conditions for the existence of non-diffusive, multivalued flux-gradient relations in the temperature evolution are derived.

Studies on Microwave Heated Drying-rate Equations of Foods

OpenAIRE

呂, 聯通; 久保田, 清; 鈴木, 寛一; 岡崎, 尚; 山下, 洋右

1990-01-01

In order to design various microwave heated drying apparatuses, we must take drying-rate equations which are based on simple drying-rate models. In a previous paper (KUBOTA, et al., 1990), we have studied a convenient microwave heated drying instrument, and studied the simple drying-rate equations of potato and so on by using the simple empirical rate equations that have been reported in previous papers (KUBOTA, 1979-1, 1979-2). In this paper, we studied the microwave drying rate of the const...

Unconditionally stable diffusion-acceleration of the transport equation

International Nuclear Information System (INIS)

Larsen, E.W.

1982-01-01

The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically large regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results

Unconditionally stable diffusion-acceleration of the transport equation

International Nuclear Information System (INIS)

Larson, E.W.

1982-01-01

The standard iterative procedure for solving fixed-source discrete-ordinates problems converges very slowly for problems in optically thick regions with scattering ratios c near unity. The diffusion-synthetic acceleration method has been proposed to make use of the fact that for this class of problems, the diffusion equation is often an accurate approximation to the transport equation. However, stability difficulties have historically hampered the implementation of this method for general transport differencing schemes. In this article we discuss a recently developed procedure for obtaining unconditionally stable diffusion-synthetic acceleration methods for various transport differencing schemes. We motivate the analysis by first discussing the exact transport equation; then we illustrate the procedure by deriving a new stable acceleration method for the linear discontinuous transport differencing scheme. We also provide some numerical results

Simulation of transport equations with Monte Carlo

International Nuclear Information System (INIS)

Matthes, W.

1975-09-01

The main purpose of the report is to explain the relation between the transport equation and the Monte Carlo game used for its solution. The introduction of artificial particles carrying a weight provides one with high flexibility in constructing many different games for the solution of the same equation. This flexibility opens a way to construct a Monte Carlo game for the solution of the adjoint transport equation. Emphasis is laid mostly on giving a clear understanding of what to do and not on the details of how to do a specific game

Exact solution of the neutron transport equation in spherical geometry

Energy Technology Data Exchange (ETDEWEB)

Anli, Fikret; Akkurt, Abdullah; Yildirim, Hueseyin; Ates, Kemal [Kahramanmaras Suetcue Imam Univ. (Turkey). Faculty of Sciences and Letters

2017-03-15

Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using P{sub N} approximation which is widely used in neutron transport theory.

Diffusion equation and spin drag in spin-polarized transport

DEFF Research Database (Denmark)

Flensberg, Karsten; Jensen, Thomas Stibius; Mortensen, Asger

2001-01-01

We study the role of electron-electron interactions for spin-polarized transport using the Boltzmann equation, and derive a set of coupled transport equations. For spin-polarized transport the electron-electron interactions are important, because they tend to equilibrate the momentum of the two-s...

Analytical and numerical treatment of the heat conduction equation obtained via time-fractional distributed-order heat conduction law

Science.gov (United States)

Želi, Velibor; Zorica, Dušan

2018-02-01

Generalization of the heat conduction equation is obtained by considering the system of equations consisting of the energy balance equation and fractional-order constitutive heat conduction law, assumed in the form of the distributed-order Cattaneo type. The Cauchy problem for system of energy balance equation and constitutive heat conduction law is treated analytically through Fourier and Laplace integral transform methods, as well as numerically by the method of finite differences through Adams-Bashforth and Grünwald-Letnikov schemes for approximation derivatives in temporal domain and leap frog scheme for spatial derivatives. Numerical examples, showing time evolution of temperature and heat flux spatial profiles, demonstrate applicability and good agreement of both methods in cases of multi-term and power-type distributed-order heat conduction laws.

Thermophoresis of a spherical particle: Modeling through moment-based, macroscopic transport equations

Science.gov (United States)

Padrino, Juan C.; Sprittles, James; Lockerby, Duncan

2017-11-01

Thermophoresis refers to the forces on and motions of objects caused by temperature gradients when these objects are exposed to rarefied gases. This phenomenon can occur when the ratio of the gas mean free path to the characteristic physical length scale (Knudsen number) is not negligible. In this work, we obtain the thermophoretic force on a rigid, heat-conducting spherical particle immersed in a rarefied gas resulting from a uniform temperature gradient imposed far from the sphere. To this end, we model the gas dynamics using the steady, linearized version of the so-called regularized 13-moment equations (R13). This set of equations, derived from the Boltzmann equation using the moment method, provides closures to the mass, momentum, and energy conservation laws in the form of constitutive, transport equations for the stress and heat flux that extends the Navier-Stokes-Fourier model to include rarefaction effects. Integration of the pressure and stress on the surface of the sphere leads to the net force as a function of the Knudsen number, dimensionless temperature gradient, and particle-to-gas thermal conductivity ratio. Results from this expression are compared with predictions from other moment-based models as well as from kinetic models. Supported in the UK by the Engineering and Physical Sciences Research Council (EP/N016602/1).

Heat transport and storage

International Nuclear Information System (INIS)

Despois, J.

1977-01-01

Recalling the close connections existing between heat transport and storage, some general considerations on the problem of heat distribution and transport are presented 'in order to set out the problem' of storage in concrete form. This problem is considered in its overall plane, then studied under the angle of the different technical choices it involves. The two alternatives currently in consideration are described i.e.: storage in a mined cavity and underground storage as captive sheet [fr

Dynamic modeling of interfacial structures via interfacial area transport equation

International Nuclear Information System (INIS)

Seungjin, Kim; Mamoru, Ishii

2005-01-01

The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. In the present paper, the interfacial area transport equations currently available are reviewed to address the feasibility and reliability of the model along with extensive experimental results. These include the data from adiabatic upward air-water two-phase flow in round tubes of various sizes, from a rectangular duct, and from adiabatic co-current downward air-water two-phase flow in round pipes of two sizes. (authors)

Transport methods: general. 8. Formulation of Transport Equation in a Split Form

International Nuclear Information System (INIS)

Stancic, V.

2001-01-01

The singular eigenfunction expansion method has enabled the application of functional analysis methods in transport theory. However, when applying it, the users were discouraged, since in most problems, including slab problems, an extra problem has occurred. It appears necessary to solve the Fredholm integral equation in order to determine the expansion coefficients. There are several reasons for this difficulty. One reason might be the use of the full-range expansion techniques even in the regions where the function is singular. Such an example is the free boundary condition that requires the distribution to be equal to zero. Moreover, at μ = 0, the transport equation becomes an integral one. Both reasons motivated us to redefine the transport equation in a more natural way. Similar to scattering theory, here we define the flux distribution as a direct sum of forward- and backward-directed neutrons, e.g., μ ≥ 0 and μ < 0, respectively. As a result, the plane geometry transport equation is being split into coupled-pair equations. Further, using an appropriate transformation, this pair of equations reduces to a self-adjoint one having the same form as the known full-range single flux. It is interesting that all the methods of full-range theory are applicable here provided the flux as well as the transformed transport operator are two-dimensional matrices. Applying this to the slab problem, we find explicit expressions for reflected and transmitted particles caused by an arbitrary plane source. That is the news in this paper. Because of space constraints, only fundamentals of this approach will be presented here. We assume that the reader is familiar with this field; therefore, the applications are noted only at the end. (author)

almaBTE : A solver of the space-time dependent Boltzmann transport equation for phonons in structured materials

Science.gov (United States)

Carrete, Jesús; Vermeersch, Bjorn; Katre, Ankita; van Roekeghem, Ambroise; Wang, Tao; Madsen, Georg K. H.; Mingo, Natalio

2017-11-01

almaBTE is a software package that solves the space- and time-dependent Boltzmann transport equation for phonons, using only ab-initio calculated quantities as inputs. The program can predictively tackle phonon transport in bulk crystals and alloys, thin films, superlattices, and multiscale structures with size features in the nm- μm range. Among many other quantities, the program can output thermal conductances and effective thermal conductivities, space-resolved average temperature profiles, and heat-current distributions resolved in frequency and space. Its first-principles character makes almaBTE especially well suited to investigate novel materials and structures. This article gives an overview of the program structure and presents illustrative examples for some of its uses. PROGRAM SUMMARY Program Title:almaBTE Program Files doi:http://dx.doi.org/10.17632/8tfzwgtp73.1 Licensing provisions: Apache License, version 2.0 Programming language: C++ External routines/libraries: BOOST, MPI, Eigen, HDF5, spglib Nature of problem: Calculation of temperature profiles, thermal flux distributions and effective thermal conductivities in structured systems where heat is carried by phonons Solution method: Solution of linearized phonon Boltzmann transport equation, Variance-reduced Monte Carlo

Hot electrons in superlattices: quantum transport versus Boltzmann equation

DEFF Research Database (Denmark)

Wacker, Andreas; Jauho, Antti-Pekka; Rott, S.

1999-01-01

A self-consistent solution of the transport equation is presented for semiconductor superlattices within different approaches: (i) a full quantum transport model based on nonequilibrium Green functions, (ii) the semiclassical Boltzmann equation for electrons in a miniband, and (iii) Boltzmann...

The plasma transport equations derived by multiple time-scale expansions and turbulent transport. I. General theory

International Nuclear Information System (INIS)

Edenstrasser, J.W.

1995-01-01

A multiple time-scale derivative expansion scheme is applied to the dimensionless Fokker--Planck equation and to Maxwell's equations, where the parameter range of a typical fusion plasma was assumed. Within kinetic theory, the four time scales considered are those of Larmor gyration, particle transit, collisions, and classical transport. The corresponding magnetohydrodynamic (MHD) time scales are those of ion Larmor gyration, Alfven, MHD collision, and resistive diffusion. The solution of the zeroth-order equations results in the force-free equilibria and ideal Ohm's law. The solution of the first-order equations leads under the assumption of a weak collisional plasma to the ideal MHD equations. On the MHD-collision time scale, not only the full set of the MHD transport equations is obtained, but also turbulent terms, where the related transport quantities are one order in the expansion parameter larger than those of classical transport. Finally, at the resistive diffusion time scale the known transport equations are arrived at including, however, also turbulent contributions. copyright 1995 American Institute of Physics

Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas

International Nuclear Information System (INIS)

Zawaideh, E.S.

1985-01-01

A new set of two-fluid equations which are valid from collisional to weakly collisional limits are derived. Starting from gyrokinetic equations in flux coordinates with no zeroth order drifts, a set of moment equations describing plasma transport along the field lines of a space and time dependent magnetic field are derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii while in the weakly collisional limit, they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations. The new transport equations are used to study the effects of collisionality, magnetic field structure, and plasma anisotropy on plasma parallel transport. Numerical examples comparing these equations with conventional transport equations show that the conventional equations may contain large errors near the sound speed (M approx. = 1). It is also found that plasma anisotropy, which is not included in the conventional equations, is a critical parameter in determining plasma transport in varying magnetic field. The new transport equations are also used to study axial confinement in multiple mirror devices from the strongly to weakly collisional regime. A new ion conduction model was worked out to extend the regime of validity of the transport equations to the low density multiple mirror regime

Approximate solution of the transport equation by methods of Galerkin type

International Nuclear Information System (INIS)

Pitkaranta, J.

1977-01-01

Questions of the existence, uniqueness, and convergence of approximate solutions of transport equations by methods of the Galerkin type (where trial and weighting functions are the same) are discussed. The results presented do not exclude the infinite-dimensional case. Two strategies can be followed in the variational approximation of the transport operator: one proceeds from the original form of the transport equation, while the other is based on the partially symmetrized equation. Both principles are discussed in this paper. The transport equation is assumed in a discretized multigroup form

Three-dimensional model of heat transport during In Situ Vitrification with melting and cool down

International Nuclear Information System (INIS)

Hawkes, G.L.

1993-01-01

A potential technology for permanent remediation of buried wastes is the In Situ Vitrification (ISV) process. This process uses electrical resistance heating to melt waste and contaminated soil in place to produce a durable, glasslike material that encapsulates and immobilizes buried wastes. The magnitude of the resulting electrical resistance heating is sufficient to cause soil melting. As the molten region grows, surface heat losses cause the soil near the surface to re solidify. This paper presents numerical results obtained by considering heat transport and melting when solving the conservation of mass and energy equations using finite element methods. A local heat source is calculated by solving the electric field equation and calculating a Joule Heat source term. The model considered is a three-dimensional model of the electrodes and surrounding soil. Also included in the model is subsidence; where the surface of the melted soil subsides due to the change in density when the soil melts. A power vs. time profile is implemented for typical ISV experiments. The model agrees well with experimental data for melt volume and melt shape

Heat transfer analysis of porous media receiver with different transport and thermophysical models using mixture as feeding gas

International Nuclear Information System (INIS)

Wang, Fuqiang; Tan, Jianyu; Wang, Zhiqiang

2014-01-01

Highlights: • Using local thermal non-equilibrium model to solve heat transfer of porous media. • CH 4 /H 2 O mixture is adopted as feeding gas of porous media receiver. • Radiative transfer equation between porous strut is solved by Rosseland approximation. • Transport and thermophysical models not included in Fluent are programmed by UDFs. • Variations of model on thermal performance of porous media receiver are studied. - Abstract: The local thermal non-equilibrium model is adopted to solve the steady state heat and mass transfer problems of porous media solar receiver. The fluid entrance surface is subjected to concentrated solar radiation, and CH 4 /H 2 O mixture is adopted as feeding gas. The radiative heat transfer equation between porous strut is solved by Rosseland approximation. The impacts of variation in transport and thermophysical characteristics model of gas mixture on thermal performance of porous media receiver are investigated. The transport and thermophysical characteristics models which are not included in software Fluent are programmed by user defined functions (UDFs). The numerical results indicate that models of momentum source term for porous media receiver have significant impact on pressure drop and static pressure distribution, and the radiative heat transfer cannot be omitted during the thermal performance analysis of porous media receiver

Analytical solution to the hybrid diffusion-transport equation

International Nuclear Information System (INIS)

Nanneh, M.M.; Williams, M.M.R.

1986-01-01

A special integral equation was derived in previous work using a hybrid diffusion-transport theory method for calculating the flux distribution in slab lattices. In this paper an analytical solution of this equation has been carried out on a finite reactor lattice. The analytical results of disadvantage factors are shown to be accurate in comparison with the numerical results and accurate transport theory calculations. (author)

Swarm analysis by using transport equations, 1

International Nuclear Information System (INIS)

Dote, Toshihiko; Shimada, Masatoshi

1980-01-01

By evolving Maxwell-Boltzmann transport equations, various quantities on swarm of charged particles have been analyzed. Although this treatment is properly general, and common transport equations for charged particles ought to be given, in particular, equations only for electrons were presented here. The relation between the random energy and the drift energy was first derived and the general expression of the electron velocity was deduced too. For a simple example, one dimensional steady-state electron swarm in a uniform medium was treated. Electron swarm characteristics numerically calculated in He, Ne or Ar exhibited some interesting properties, which were physically clearly elucidated. These results were also compared with several data already published. Agreements between them were qualitatively rather well in detailed structures. (author)

Application of two-equation turbulence models to turbulent gas flow heated by a high heat flux

International Nuclear Information System (INIS)

Kawamura, Hiroshi

1978-01-01

Heat transfer in heated turbulent gas flow is analyzed using two-equation turbulence models. Four kinds of two-equation models are examined; that is, k-epsilon model by Jones-Launder, k-w model by Wilcox-Traci, k-kL model by Rotta, k-ω model by Saffman-Wilcox. The results are compared with more than ten experiments by seven authors. The k-kL model proposed originally by Rotta and modified by the present author is found to give relatively the best results. It well predicts the decrease in the heat transfer coefficient found in the heated turbulent gas flow; however, it fails to predict the laminarization due to a strong heating. (author)

Fundaments of transport equation splitting and the eigenvalue problem

International Nuclear Information System (INIS)

Stancic, V.

2000-01-01

In order to remove some singularities concerning the boundary conditions of one dimensional transport equation, a split form of transport equation describing the forward i.e. μ≥0, and a backward μ<0 directed neutrons is being proposed here. The eigenvalue problem has also been considered here (author)

Stochastic modeling of stock price process induced from the conjugate heat equation

Science.gov (United States)

Paeng, Seong-Hun

2015-02-01

Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.

Dynamic modeling of interfacial structures via interfacial area transport equation

International Nuclear Information System (INIS)

Seungjin, Kim; Mamoru, Ishii

2004-01-01

Full text of publication follows:In the current thermal-hydraulic system analysis codes using the two-fluid model, the empirical correlations that are based on the two-phase flow regimes and regime transition criteria are being employed as closure relations for the interfacial transfer terms. Due to its inherent shortcomings, however, such static correlations are inaccurate and present serious problems in the numerical analysis. In view of this, a new dynamic approach employing the interfacial area transport equation has been studied. The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Therefore, the interfacial area transport equation can make a leapfrog improvement in the current capability of the two-fluid model from both scientific and practical point of view. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right hand-side of the transport equations have been established by mechanistically modeling the creation and destruction of bubbles due to major bubble interaction mechanisms. The coalescence mechanisms include the random collision driven by turbulence, and the entrainment of trailing bubbles in the wake region of the preceding bubble. The disintegration mechanisms include the break-up by turbulence impact, shearing-off at the rim of large cap bubbles and the break-up of large cap

Large-Eddy Simulation of Flow and Pollutant Transport in Urban Street Canyons with Ground Heating

Science.gov (United States)

Li, Xian-Xiang; Britter, Rex E.; Koh, Tieh Yong; Norford, Leslie K.; Liu, Chun-Ho; Entekhabi, Dara; Leung, Dennis Y. C.

2010-11-01

Our study employed large-eddy simulation (LES) based on a one-equation subgrid-scale model to investigate the flow field and pollutant dispersion characteristics inside urban street canyons. Unstable thermal stratification was produced by heating the ground of the street canyon. Using the Boussinesq approximation, thermal buoyancy forces were taken into account in both the Navier-Stokes equations and the transport equation for subgrid-scale turbulent kinetic energy (TKE). The LESs were validated against experimental data obtained in wind-tunnel studies before the model was applied to study the detailed turbulence, temperature, and pollutant dispersion characteristics in the street canyon of aspect ratio 1. The effects of different Richardson numbers ( Ri) were investigated. The ground heating significantly enhanced mean flow, turbulence, and pollutant flux inside the street canyon, but weakened the shear at the roof level. The mean flow was observed to be no longer isolated from the free stream and fresh air could be entrained into the street canyon at the roof-level leeward corner. Weighed against higher temperature, the ground heating facilitated pollutant removal from the street canyon.

Diffusive limits for linear transport equations

International Nuclear Information System (INIS)

Pomraning, G.C.

1992-01-01

The authors show that the Hibert and Chapman-Enskog asymptotic treatments that reduce the nonlinear Boltzmann equation to the Euler and Navier-Stokes fluid equations have analogs in linear transport theory. In this linear setting, these fluid limits are described by diffusion equations, involving familiar and less familiar diffusion coefficients. Because of the linearity extant, one can carry out explicitly the initial and boundary layer analyses required to obtain asymptotically consistent initial and boundary conditions for the diffusion equations. In particular, the effects of boundary curvature and boundary condition variation along the surface can be included in the boundary layer analysis. A brief review of heuristic (nonasymptotic) diffusion description derivations is also included in our discussion

Geometry, Heat Equation and Path Integrals on the Poincare Upper Half-Plane

OpenAIRE

Reijiro, KUBO; Research Institute for Theoretical Physics Hiroshima University

1988-01-01

Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation ∂f/∂t=Δ_Hf is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's statement that Feynman's path integral satisfies the Schrodinger equation is also valid for our case.

A modular spherical harmonics approach to the neutron transport equation

International Nuclear Information System (INIS)

Inanc, F.; Rohach, A.F.

1989-01-01

A modular nodal method was developed for solving the neutron transport equation in 2-D xy coordinates. The spherical harmonic expansion was used for approximating the second-order even-parity form of the neutron transport equation. The boundary conditions of the spherical harmonics approximation were derived in a form to have forms analogous to the partial currents in the neutron diffusion equation. Relations were developed for generating both the second-order spherical harmonic equations and the boundary conditions in an automated computational algorithm. Nodes using different orders of the spherical harmonics approximation to the transport equation were interfaced through mixed-type boundary conditions. The determination of spherical harmonic orders implemented in the nodes were determined by the scheme in an automated manner. Results of the method compared favorably to benchmark problems. (author)

Heat and momentum transport scalings in vertical convection

Science.gov (United States)

Shishkina, Olga

2016-11-01

For vertical convection, where a fluid is confined between two differently heated isothermal vertical walls, we investigate the heat and momentum transport, which are measured, respectively, by the Nusselt number Nu and the Reynolds number Re . For laminar vertical convection we derive analytically the dependence of Re and Nu on the Rayleigh number Ra and the Prandtl number Pr from our boundary layer equations and find two different scaling regimes: Nu Pr 1 / 4 Ra 1 / 4 , Re Pr - 1 / 2 Ra 1 / 2 for Pr > 1 . Direct numerical simulations for Ra from 105 to 1010 and Pr from 0.01 to 30 are in excellent ageement with our theoretical findings and show that the transition between the regimes takes place for Pr around 0.1. We summarize the results from and present new theoretical and numerical results for transitional and turbulent vertical convection. The work is supported by the Deutsche Forschungsgemeinschaft (DFG) under the Grant Sh 405/4 - Heisenberg fellowship.

Heat-flow equation motivated by the ideal-gas shock wave.

Science.gov (United States)

Holian, Brad Lee; Mareschal, Michel

2010-08-01

We present an equation for the heat-flux vector that goes beyond Fourier's Law of heat conduction, in order to model shockwave propagation in gases. Our approach is motivated by the observation of a disequilibrium among the three components of temperature, namely, the difference between the temperature component in the direction of a planar shock wave, versus those in the transverse directions. This difference is most prominent near the shock front. We test our heat-flow equation for the case of strong shock waves in the ideal gas, which has been studied in the past and compared to Navier-Stokes solutions. The new heat-flow treatment improves the agreement with nonequilibrium molecular-dynamics simulations of hard spheres under strong shockwave conditions.

Geometry, heat equation and path integrals on the Poincare upper half-plane

International Nuclear Information System (INIS)

Kubo, Reijiro.

1987-08-01

Geometry, heat equation and Feynman's path integrals are studied on the Poincare upper half-plane. The fundamental solution to the heat equation δf/δt = Δ H f is expressed in terms of a path integral defined on the upper half-plane. It is shown that Kac's proof that Feynman's path integral satisfies the Schroedinger equation is also valid for our case. (author)

Currents and fluctuations of quantum heat transport in harmonic chains

International Nuclear Information System (INIS)

Motz, T; Ankerhold, J; Stockburger, J T

2017-01-01

Heat transport in open quantum systems is particularly susceptible to the modeling of system–reservoir interactions. It thus requires us to consistently treat the coupling between a quantum system and its environment. While perturbative approaches are successfully used in fields like quantum optics and quantum information, they reveal deficiencies—typically in the context of thermodynamics, when it is essential to respect additional criteria such as fluctuation-dissipation theorems. We use a non-perturbative approach for quantum dissipative dynamics based on a stochastic Liouville–von Neumann equation to provide a very general and extremely efficient formalism for heat currents and their correlations in open harmonic chains. Specific results are derived not only for first- but also for second-order moments, which requires us to account for both real and imaginary parts of bath–bath correlation functions. Spatiotemporal patterns are compared with weak coupling calculations. The regime of stronger system–reservoir couplings gives rise to an intimate interplay between reservoir fluctuations and heat transfer far from equilibrium. (paper)

Homogenization of the critically spectral equation in neutron transport

International Nuclear Information System (INIS)

Allaire, G.; Paris-6 Univ., 75; Bal, G.

1998-01-01

We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. On terms is the first eigenvector of the transport equation in the periodicity cell. The other term is the first eigenvector of a diffusion equation in the homogenized domain. Furthermore, the corresponding eigenvalue gives a second order corrector for the eigenvalue of the heterogeneous transport problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations. (author)

Homogenization of the critically spectral equation in neutron transport

Energy Technology Data Exchange (ETDEWEB)

Allaire, G. [CEA Saclay, 91 - Gif-sur-Yvette (France). Dept. de Mecanique et de Technologie]|[Paris-6 Univ., 75 (France). Lab. d' Analyse Numerique; Bal, G. [Electricite de France (EDF), 92 - Clamart (France). Direction des Etudes et Recherches

1998-07-01

We address the homogenization of an eigenvalue problem for the neutron transport equation in a periodic heterogeneous domain, modeling the criticality study of nuclear reactor cores. We prove that the neutron flux, corresponding to the first and unique positive eigenvector, can be factorized in the product of two terms, up to a remainder which goes strongly to zero with the period. On terms is the first eigenvector of the transport equation in the periodicity cell. The other term is the first eigenvector of a diffusion equation in the homogenized domain. Furthermore, the corresponding eigenvalue gives a second order corrector for the eigenvalue of the heterogeneous transport problem. This result justifies and improves the engineering procedure used in practice for nuclear reactor cores computations. (author)

From statistic mechanic outside equilibrium to transport equations

International Nuclear Information System (INIS)

Balian, R.

1995-01-01

This lecture notes give a synthetic view on the foundations of non-equilibrium statistical mechanics. The purpose is to establish the transport equations satisfied by the relevant variables, starting from the microscopic dynamics. The Liouville representation is introduced, and a projection associates with any density operator , for given choice of relevant observables, a reduced density operator. An exact integral-differential equation for the relevant variables is thereby derived. A short-memory approximation then yields the transport equations. A relevant entropy which characterizes the coarseness of the description is associated with each level of description. As an illustration, the classical gas, with its three levels of description and with the Chapman-Enskog method, is discussed. (author). 3 figs., 5 refs

One-Loop Operation of Primary Heat Transport System in MONJU During Heat Transport System Modifications

International Nuclear Information System (INIS)

Goto, T.; Tsushima, H.; Sakurai, N.; Jo, T.

2006-01-01

MONJU is a prototype fast breeder reactor (FBR). Modification work commenced in March 2005. Since June 2004, MONJU has changed to one-loop operation of the primary heat transport system (PHTS) with all of the secondary heat transport systems (SHTS) drained of sodium. The purposes of this change are to shorten the modification period and to reduce the cost incurred for circuit trace heating electrical consumption. Before changing condition, the following issues were investigated to show that this mode of operation was possible. The heat loss from the reactor vessel and the single primary loop must exceed the decay heat by an acceptable margin but the capacity of pre-heaters to keep the sodium within the primary vessel at about 200 deg. C must be maintained. With regard to the heat loss and the decay heat, the estimated heat loss in the primary system was in the range of 90-170 kW in one-loop operation, and the calculated decay heat was 21.2 kW. Although the heat input of the primary pump was considered, it was clear that circuit heat loss greatly exceeded the decay heat. As for pre-heaters, effective capacity was less than the heat loss. Therefore, the temperature of the reactor vessel room was raised to reduce the heat loss. One-loop operation of the PHTS was able to be executed by means of these measures. The cost of electrical consumption in the power plant has been reduced by one-loop operation of the PHTS and the modification period was shortened. (authors)

Particle and heat transport in Tokamaks

International Nuclear Information System (INIS)

Chatelier, M.

1984-01-01

A limitation to performances of tokamaks is heat transport through magnetic surfaces. Principles of ''classical'' or ''neoclassical'' transport -i.e. transport due to particle and heat fluxes due to Coulomb scattering of charged particle in a magnetic field- are exposed. It is shown that beside this classical effect, ''anomalous'' transport occurs; it is associated to the existence of fluctuating electric or magnetic fields which can appear in the plasma as a result of charge and current perturbations. Tearing modes and drift wave instabilities are taken as typical examples. Experimental features are presented which show that ions behave approximately in a classical way whereas electrons are strongly anomalous [fr

Non-equilibrium thermodynamics, heat transport and thermal waves in laminar and turbulent superfluid helium

Science.gov (United States)

Mongiovì, Maria Stella; Jou, David; Sciacca, Michele

2018-01-01

This review paper puts together some results concerning non equilibrium thermodynamics and heat transport properties of superfluid He II. A one-fluid extended model of superfluid helium, which considers heat flux as an additional independent variable, is presented, its microscopic bases are analyzed, and compared with the well known two-fluid model. In laminar situations, the fundamental fields are density, velocity, absolute temperature, and heat flux. Such a theory is able to describe the thermomechanical phenomena, the propagation of two sounds in liquid helium, and of fourth sound in superleak. It also leads in a natural way to a two-fluid model on purely macroscopical grounds and allows a small amount of entropy associated with the superfluid component. Other important features of liquid He II arise in rotating situations and in superfluid turbulence, both characterized by the presence of quantized vortices (thin vortex lines whose circulation is restricted by a quantum condition). Such vortices have a deep influence on the transport properties of superfluid helium, as they increase very much its thermal resistance. Thus, heat flux influences the vortices which, in turn, modify the heat flux. The dynamics of vortex lines is the central topic in turbulent superfluid helium. The model is generalized to take into account the vortices in different cases of physical interest: rotating superfluids, counterflow superfluid turbulence, combined counterflow and rotation, and mass flow in addition to heat flow. To do this, the averaged vortex line density per unit volume L, is introduced and its dynamical equations are considered. Linear and non-linear evolution equations for L are written for homogeneous and inhomogeneous, isotropic and anisotropic situations. Several physical experiments are analyzed and the influence of vortices on the effective thermal conductivity of turbulent superfluid helium is found. Transitions from laminar to turbulent flows, from diffusive to

Basic equations of interfacial area transport in gas-liquid two-phase flow

International Nuclear Information System (INIS)

Kataoka, I.; Yoshida, K.; Naitoh, M.; Okada, H.; Morii, T.

2011-01-01

The rigorous and consistent formulations of basic equations of interfacial area transport were derived using correlation functions of characteristic function of each phase and velocities of each phase. Turbulent transport term of interfacial area concentration was consistently derived and related to the difference between interfacial velocity and averaged velocity of each phase. Constitutive equations of turbulent transport terms of interfacial area concentration were proposed for bubbly flow. New transport model and constitutive equations were developed for churn flow. These models and constitutive equations are validated by experimental data of radial distributions of interfacial area concentration in bubbly and churn flow. (author)

General particle transport equation. Final report

International Nuclear Information System (INIS)

Lafi, A.Y.; Reyes, J.N. Jr.

1994-12-01

The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

Heat in the Barents Sea: transport, storage, and surface fluxes

Directory of Open Access Journals (Sweden)

L. H. Smedsrud

2010-02-01

Full Text Available A column model is set up for the Barents Sea to explore sensitivity of surface fluxes and heat storage from varying ocean heat transport. Mean monthly ocean transport and atmospheric forcing are synthesised and force the simulations. Results show that by using updated ocean transports of heat and freshwater the vertical mean hydrographic seasonal cycle can be reproduced fairly well.

Our results indicate that the ~70 TW of heat transported to the Barents Sea by ocean currents is lost in the southern Barents Sea as latent, sensible, and long wave radiation, each contributing 23–39 TW to the total heat loss. Solar radiation adds 26 TW in the south, as there is no significant ice production.

The northern Barents Sea receives little ocean heat transport. This leads to a mixed layer at the freezing point during winter and significant ice production. There is little net surface heat loss annually in the north. The balance is achieved by a heat loss through long wave radiation all year, removing most of the summer solar heating.

During the last decade the Barents Sea has experienced an atmospheric warming and an increased ocean heat transport. The Barents Sea responds to such large changes by adjusting temperature and heat loss. Decreasing the ocean heat transport below 50 TW starts a transition towards Arctic conditions. The heat loss in the Barents Sea depend on the effective area for cooling, and an increased heat transport leads to a spreading of warm water further north.

Numerical Simulation of Density-Driven Flow and Heat Transport Processes in Porous Media Using the Network Method

Directory of Open Access Journals (Sweden)

Manuel Cánovas

2017-09-01

Full Text Available Density-driven flow and heat transport processes in 2-D porous media scenarios are governed by coupled, non-linear, partial differential equations that normally have to be solved numerically. In the present work, a model based on the network method simulation is designed and applied to simulate these processes, providing steady state patterns that demonstrate its computational power and reliability. The design is relatively simple and needs very few rules. Two applications in which heat is transported by natural convection in confined and saturated media are studied: slender boxes heated from below (a kind of Bénard problem and partially heated horizontal plates in rectangular domains (the Elder problem. The streamfunction and temperature patterns show that the results are coherent with those of other authors: steady state patterns and heat transfer depend both on the Rayleigh number and on the characteristic Darcy velocity derived from the values of the hydrological, thermal and geometrical parameters of the problems.

Extension of ANISN and DOT 3.5 transport computer codes to calculate heat generation by radiation and temperature distribution in nuclear reactors

International Nuclear Information System (INIS)

Torres, L.M.R.; Gomes, I.C.; Maiorino, J.R.

1986-01-01

The ANISN and DOT 3.5 codes solve the transport equation using the discrete ordinate method, in one and two-dimensions, respectively. The objectives of the study were to modify these two codes, frequently used in reactor shielding problems, to include nuclear heating calculations due to the interaction of neutrons and gamma-rays with matter. In order to etermine the temperature distribution, a numerical algorithm was developed using the finite difference method to solve the heat conduction equation, in one and two-dimensions, considering the nuclear heating from neutron and gamma-rays, as the source term. (Author) [pt

Transport methods: general. 7. Formulation of a Fourier-Boltzmann Transformation to Solve the Three-Dimensional Transport Equation

International Nuclear Information System (INIS)

Stancic, V.

2001-01-01

This paper presents some elements of a new approach to solve analytically the linearized three-dimensional (3-D) transport equation of neutral particles. Since this task is of such special importance, we present some results of a paper that is still in progress. The most important is that using this transformation, an integro-differential equation with an analytical solution is obtained. For this purpose, a simplest 3-D equation is being considered which describes the transport process in an infinite medium. Until now, this equation has been analytically considered either using the Laplace transform with respect to time parameter t or applying the Fourier transform over the space coordinate. Both of them reduce the number of differential terms in the equation; however, evaluation of the inverse transformation is complicated. In this paper, we introduce for the first time a Fourier transform induced by the Boltzmann operator. For this, we use a complete set of 3-D eigenfunctions of the Boltzmann transport operator defined in a similar way as those that have been already used in 3-D transport theory as a basic set to transform the transport equation. This set consists of a continuous part and a discrete one with spectral measure. The density distribution equation shows the known form asymptotic behavior. Several applications are to be performed using this equation and compared to the benchmark one. Such an analysis certainly would be out of the available space

LLE-LLNL progress report on studies in nonlocal heat transport in spherical plasmas using the Fokker-Planck code SPARK

International Nuclear Information System (INIS)

Epperlein, E.M.

1992-01-01

Preliminary 1-D studies of nonlocal heat transport in spherical plasmas based on the Fokker-Planck code SPARK indicate significant levels of electron preheat and radial heat flux across a spherical heat sink surface kept at fixed temperature. However, the diffusive approximation to the Fokker-Planck equation is shown to be particularly sensitive to the nature of the inner surface boundary condition chosen. A suggested remedy is the inclusion of a target capsule in future simulations studies with SPARK

Heat transport and surface heat transfer with helium in rotating channels

International Nuclear Information System (INIS)

Schnapper, C.

1978-06-01

Heat transport and surface heat transfer with helium in rotating radially arranged channels were experimentally studied with regard to cooling of large turbogenerators with superconducting windings. Measurements with thermosiphon and thermosiphon loops of different channel diameters were performed, and results are presented. The thermodynamic state of the helium in a rotating thermosiphon and the mass flow rate in a thermosiphon loop is characterized by formulas. Heat transport by directed convection in thermosiphon loops is found to be more efficient 12 cm internal convection in thermosiphons. Steady state is reached sooner in thermosiphon loops than in thermosiphons, when heat load suddenly changes. In a very large centrifugal field single-phase heat transfer with natural and forced convection is described by similar formulas which are also applicable 10 thermosiphons in gravitation field or to heat transfer to non-rotating helium. (orig.) [de

Some results on the neutron transport and the coupling of equations; Quelques resultats sur le transport neutronique et le couplage d`equations

Energy Technology Data Exchange (ETDEWEB)

Bal, G. [Electricite de France (EDF), Direction des Etudes et Recherches, 92 - Clamart (France)

1997-12-31

Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author). 34 refs.

Radio-frequency heating and neutral atom transport in a fluid-magnetohydrodynamic treatment of burning tokamak plasmas

International Nuclear Information System (INIS)

Conn, R.W.; Mau, T.K.; Prinja, A.K.

1983-01-01

A physical model for the space and time evolution of the primary parameters of ordinary and burning tokamak plasmas is described by employing a fluid plasma treatment coupled to a magnetohydrodynamic equilibrium description, the solution to the appropriate Maxwell equations, and the solution of the linear transport equation describing neutral atom transport in plasmas. The specific problems of plasma heating by ion cyclotron radiofrequency (ICRF) waves and neutral atom transport in the plasma edge and in complicated geometrical components such as divertor channels or pumped limiter structures are analyzed. A theoretical, onedimensional slab model of ICRF heating at ω = 2ω/SUB cD/ is developed and applied to determine the space-time response of tokamak plasmas. Generally, strong single-pass absorption is found for high-density, high (β) plasmas using a low k 11 spectrum (0.05 to 0.1 cm -1 ) although for (β > 1%, electron Landau damping becomes important. Deterministic and Monte Carlo methods to solve the neutral atom transport problem are described. Specific application to determine the spectrum of neutral atoms emerging from the duct of a pump limiter shows it to be hard (mean energy > 20 eV), indicating very incomplete energy thermalization. Uncertainties are identified in the overall problem of dynamic burning plasma analysis caused by the complexity of the problem itself and by uncertainties in fundamental areas such as plasma transport coefficients, stability, and plasma edge physics

Heat and fission product transport in molten core material pool with crust

International Nuclear Information System (INIS)

Yun, J.I.; Suh, K.Y.; Kang, C.S.

2005-01-01

Heat transfer and fluid flow in a molten pool are influenced by internal volumetric heat generated from the radioactive decay of fission product species retained in the reactor vessel during a severe accident. The pool superheat is determined based on the overall energy balance that equates the heat production rate to the heat loss rate. Decay heat of fission products in the pool is estimated by product of the mass concentration and energy conversion factor of each fission product. Twenty-nine elements are chosen and classified by their chemical properties to calculate heat generation rate in the pool. The mass concentration of a fission product is obtained from released fraction and the tabular output of the ORIGEN 2 code. The initial core and pool inventories at each time can also be estimated using ORIGEN 2. The released fraction of each fission product is calculated based on the bubble dynamics and mass transport. Numerical analysis is performed for heat and fission product transport in a molten core material pool during the Three Mile Island Unit 2 (TMI-2) accident. The pool is assumed to be a partially filled hemisphere, whose change in geometry is neglected during the numerical calculation. Calculated results indicate that the peak temperature in the molten pool is significantly lowered, since a substantial amount of the volatile fission products is released from the molten pool during progression of the accident. The results may directly be applied to the existing severe accident analysis codes to more mechanistically determine the thermal load to the reactor vessel lower head during the in-vessel retention

Adaptive integral equation methods in transport theory

International Nuclear Information System (INIS)

Kelley, C.T.

1992-01-01

In this paper, an adaptive multilevel algorithm for integral equations is described that has been developed with the Chandrasekhar H equation and its generalizations in mind. The algorithm maintains good performance when the Frechet derivative of the nonlinear map is singular at the solution, as happens in radiative transfer with conservative scattering and in critical neutron transport. Numerical examples that demonstrate the algorithm's effectiveness are presented

Thermal transport properties of helium, helium--air mixtures, water, and tubing steel used in the CACHE program to compute HTGR auxiliary heat exchanger performance

International Nuclear Information System (INIS)

Tallackson, J.R.

1976-02-01

A description is presented of the thermal transport properties of the materials involved in digital computer calculations of heat transfer rates by the core auxiliary heat exchangers in large HTGR nuclear steam supply systems. These materials are pure helium, mixtures of helium with common gases having molecular weights in the range of 28 to 32, alloy steel tubing, and water. For use in programmed computations the viscosity, thermal conductivity, and specific heat are represented primarily by equations augmented by curves and tabulations. Materials supporting the development and selection of the property equations are included

Understanding of flux-limited behaviors of heat transport in nonlinear regime

Energy Technology Data Exchange (ETDEWEB)

Guo, Yangyu, E-mail: yangyuhguo@gmail.com [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China); Jou, David, E-mail: david.jou@uab.es [Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia (Spain); Wang, Moran, E-mail: mrwang@tsinghua.edu [Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics and CNMM, Tsinghua University, Beijing 100084 (China)

2016-01-28

The classical Fourier's law of heat transport breaks down in highly nonequilibrium situations as in nanoscale heat transport, where nonlinear effects become important. The present work is aimed at exploring the flux-limited behaviors based on a categorization of existing nonlinear heat transport models in terms of their theoretical foundations. Different saturation heat fluxes are obtained, whereas the same qualitative variation trend of heat flux versus exerted temperature gradient is got in diverse nonlinear models. The phonon hydrodynamic model is proposed to act as a standard to evaluate other heat flux limiters because of its more rigorous physical foundation. A deeper knowledge is thus achieved about the phenomenological generalized heat transport models. The present work provides deeper understanding and accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit. - Highlights: • Exploring flux-limited behaviors based on a categorization of existing nonlinear heat transport models. • Proposing phonon hydrodynamic model as a standard to evaluate heat flux limiters. • Providing accurate modeling of nonlocal and nonlinear heat transport beyond the diffusive limit.

Interpretation of heat and density pulse measurements in JET in terms of coupled transport

International Nuclear Information System (INIS)

Haas, J.C.M. de; O'Rourke, J.; Sips, A.C.C.; Lopes Cardozo, N.J.

1990-01-01

The perturbations of electron density and temperature profiles in a tokamak following a sawtooth collapse are considered. An analytic model for the interpretation of such perturbations is presented. It is shown that the perturbation can be decomposed into two contributions, which are eigenmodes of the linearised coupled diffusion equations for particle and energy. The approximations made in the analytical treatment are checked using computer simulations. Measurements of heat and density pulses in Joint European Torus are used to illustrate the power of the new approach. It is shown that using the coupled equations, an improved description of the heat and density pulses is obtained. The analysis yields the four diffusion coefficients in the linearised transport matrix. The non-zero off-diagonal elements explain certain salient features of the measurements, notably a marked decrease of the local density which occurs during the maximum of the temperature pulse. (author)

Theory of ion heat transport in tokamaks

International Nuclear Information System (INIS)

Gott, Y.V.; Yurchenko, E.I.

1987-01-01

Experiments which have been carried out in several tokamaks to determine the ion thermal conductivity show that it is several times the value predicted by the neoclassical theory. A possible explanation for this discrepancy is proposed. When the finite width of a banana is taken into account, there are substantial increases in the heat fluxes which stem from the important contribution of superthermal ions to the transport. If the electron diffusive flux is zero, a systematic account of the ions with E>T leads to an ion heat flux with a finite banana width which is two to four times the neoclassical prediction. The effect of the anomalous nature of the electron flux on the ion heat transport is analyzed. An expression is derived for calculating the ion heat transport over the entire range of collision rates

Moment equation approach to neoclassical transport theory

International Nuclear Information System (INIS)

Hirshman, S.P.

1978-01-01

The neoclassical cross-field fluxes for a toroidally confined, axisymmetric plasma are calculated in terms of the thermodynamic forces from the fluid continuity and momentum balance equations. This macroscopic formulation of neoclassical transport theory unifies the numerous complex expressions for the transport coefficients, previously obtained by solving the Fokker--Planck equation, and elucidates their physical basis. In the large aspect ratio limit, the continuous transition in the scaling of the diffusion coefficient throughout various collisionality regimes is shown to depend on the ratio of parallel viscosity coefficients of the plasma species. Comparison of the present results with the kinetic theory expressions for the neoclassical fluxes determines the parallel viscosity coefficients for a multispecies plasma in the long-mean-free-path regime

Variational formulation and projectional methods for the second order transport equation

International Nuclear Information System (INIS)

Borysiewicz, M.; Stankiewicz, R.

1979-01-01

Herein the variational problem for a second-order boundary value problem for the neutron transport equation is formulated. The projectional methods solving the problem are examined. The approach is compared with that based on the original untransformed form of the neutron transport equation

On the Operator ⨁Bk Related to Bessel Heat Equation

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Wanchak Satsanit

2010-01-01

Full Text Available We study the equation (∂/∂tu(x,t=c2⊕Bku(x,t with the initial condition u(x,0=f(x for x∈Rn+. The operator ⊕Bk is the operator iterated k-times and is defined by ⊕Bk=((∑i=1pBxi4-(∑j=p+1p+qBxi4k, where p+q=n is the dimension of the Rn+, Bxi=∂2/∂xi2+(2vi/xi(∂/∂xi, 2vi=2αi+1, αi>-1/2, i=1,2,3,…,n, and k is a nonnegative integer, u(x,t is an unknown function for (x,t=(x1,x2,…,xn,t∈Rn+×(0,∞, f(x is a given generalized function, and c is a positive constant. We obtain the solution of such equation, which is related to the spectrum and the kernel, which is so called Bessel heat kernel. Moreover, such Bessel heat kernel has interesting properties and also related to the kernel of an extension of the heat equation.

Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

Science.gov (United States)

Ullah, Azmat; Malik, Suheel Abdullah; Alimgeer, Khurram Saleem

2018-01-01

In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations.

Directory of Open Access Journals (Sweden)

Azmat Ullah

Full Text Available In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA with Interior Point Algorithm (IPA is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

Progress in understanding heat transport at JET

International Nuclear Information System (INIS)

Mantica, P.; Garbet, X.; Angioni, C.

2005-01-01

This paper reports recent progress in understanding heat transport mechanisms either in conventional or advanced tokamak scenarios in JET. A key experimental tool has been the use of perturbative transport techniques, both by ICH power modulation and by edge cold pulses. The availability of such results has allowed careful comparison with theoretical modelling using 1D empirical or physics based transport models, 3D fluid turbulence simulations or gyrokinetic stability analysis. In conventional L- and H-mode plasmas the issue of temperature profile stiffness has been addressed. JET results are consistent with the concept of a critical inverse temperature gradient length above which transport is enhanced by the onset of turbulence. A threshold value R/L Te ∼5 has been found for the onset of stiff electron transport, while the level of electron stiffness appears to vary strongly with plasma parameters, in particular with the ratio of electron and ion heating: electrons become stiffer when ions are strongly heated, resulting in larger R/L Ti values. This behaviour has also been found theoretically, although quantitatively weaker than in experiments. In plasmas characterized by Internal Transport Barriers (ITB), the properties of heat transport inside the ITB layer and the ITB formation mechanisms have been investigated. The plasma current profile is found to play a major role in ITB formation. The effect of negative magnetic shear on electron and ion stabilization is demonstrated both experimentally and theoretically using turbulence codes. The role of rational magnetic surfaces in ITB triggering is well assessed experimentally, but still lacks a convincing theoretical explanation. Attempts to trigger an ITB by externally induced magnetic reconnection using saddle coils have shown that MHD islands in general do not produce a sufficient variation of ExB flow shear to lead to ITB formation. First results of perturbative transport in ITBs show that the ITB is a narrow

Assessment of Haar Wavelet-Quasilinearization Technique in Heat Convection-Radiation Equations

Directory of Open Access Journals (Sweden)

Umer Saeed

2014-01-01

Full Text Available We showed that solutions by the Haar wavelet-quasilinearization technique for the two problems, namely, (i temperature distribution equation in lumped system of combined convection-radiation in a slab made of materials with variable thermal conductivity and (ii cooling of a lumped system by combined convection and radiation are strongly reliable and also more accurate than the other numerical methods and are in good agreement with exact solution. According to the Haar wavelet-quasilinearization technique, we convert the nonlinear heat transfer equation to linear discretized equation with the help of quasilinearization technique and apply the Haar wavelet method at each iteration of quasilinearization technique to get the solution. The main aim of present work is to show the reliability of the Haar wavelet-quasilinearization technique for heat transfer equations.

Numerical solution of the transport equation describing the radon transport from subsurface soil to buildings

International Nuclear Information System (INIS)

Savovic, S.; Djordjevich, A.; Ristic, G.

2012-01-01

A theoretical evaluation of the properties and processes affecting the radon transport from subsurface soil into buildings is presented in this work. The solution of the relevant transport equation is obtained using the explicit finite difference method (EFDM). Results are compared with analytical steady-state solution reported in the literature. Good agreement is found. It is shown that EFDM is effective and accurate for solving the equation that describes radon diffusion, advection and decay during its transport from subsurface to buildings, which is especially important when arbitrary initial and boundary conditions are required. (authors)

Active transport and heat.

Science.gov (United States)

Tait, Peter W

2011-07-01

Increasing heat may impede peoples' ability to be active outdoors thus limiting active transport options. Co-benefits from mitigation of and adaptation to global warming should not be assumed but need to be actively designed into strategies.

Numerical simulation of heat and mass transport during hydration of Portland cement mortar in semi-adiabatic and steam curing conditions

OpenAIRE

Hernandez-Bautista, E.; Bentz, D. P.; Sandoval-Torres, S.; de Cano-Barrita, P. F. J.

2016-01-01

A model that describes hydration and heat-mass transport in Portland cement mortar during steam curing was developed. The hydration reactions are described by a maturity function that uses the equivalent age concept, coupled to a heat and mass balance. The thermal conductivity and specific heat of mortar with water-to-cement mass ratio of 0.30 was measured during hydration, using the Transient Plane Source method. The parameters for the maturity equation and the activation energy were obtaine...

Possible role of oceanic heat transport in early Eocene climate

Science.gov (United States)

Sloan, L. C.; Walker, J. C.; Moore, T. C. Jr

1995-01-01

Increased oceanic heat transport has often been cited as a means of maintaining warm high-latitude surface temperatures in many intervals of the geologic past, including the early Eocene. Although the excess amount of oceanic heat transport required by warm high latitude sea surface temperatures can be calculated empirically, determining how additional oceanic heat transport would take place has yet to be accomplished. That the mechanisms of enhanced poleward oceanic heat transport remain undefined in paleoclimate reconstructions is an important point that is often overlooked. Using early Eocene climate as an example, we consider various ways to produce enhanced poleward heat transport and latitudinal energy redistribution of the sign and magnitude required by interpreted early Eocene conditions. Our interpolation of early Eocene paleotemperature data indicate that an approximately 30% increase in poleward heat transport would be required to maintain Eocene high-latitude temperatures. This increased heat transport appears difficult to accomplish by any means of ocean circulation if we use present ocean circulation characteristics to evaluate early Eocene rates. Either oceanic processes were very different from those of the present to produce the early Eocene climate conditions or oceanic heat transport was not the primary cause of that climate. We believe that atmospheric processes, with contributions from other factors, such as clouds, were the most likely primary cause of early Eocene climate.

An Implementation of Interfacial Transport Equation into the CUPID code

Energy Technology Data Exchange (ETDEWEB)

Park, Ik Kyu; Cho, Heong Kyu; Yoon, Han Young; Jeong, Jae Jun

2009-11-15

A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components for a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted a three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAS, semi-implicit ICE, SIMPLE. The governing equations for a 2-phase flow are composed of mass, momentum, and energy conservation equations for each phase. These equation sets are closed by the interfacial transfer rate of mass, momentum, and energy. The interfacial transfer of mass, momentum, and energy occurs through the interfacial area, and this area plays an important role in the transfer rate. The flow regime based correlations are used for calculating the interracial area in the traditional style 2-phase flow model. This is dependent upon the flow regime and is limited to the fully developed 2-phase flow region. Its application to the multi-dimensional 2-phase flow has some limitation because it adopts the measured results of 2-phase flow in the 1-dimensional tube. The interfacial area concentration transport equation had been suggested in order to calculate the interfacial area without the interfacial area correlations. The source terms to close the interfacial area transport equation should be further developed for a wide ranger usage of it. In this study, the one group interfacial area concentration transport equation has been implemented into the CUPID code. This interfacial area concentration transport equation can be used instead of the interfacial area concentration correlations for the bubbly flow region.

An Implementation of Interfacial Transport Equation into the CUPID code

International Nuclear Information System (INIS)

Park, Ik Kyu; Cho, Heong Kyu; Yoon, Han Young; Jeong, Jae Jun

2009-11-01

A component scale thermal hydraulic analysis code, CUPID (Component Unstructured Program for Interfacial Dynamics), is being developed for the analysis of components for a nuclear reactor, such as reactor vessel, steam generator, containment, etc. It adopted a three-dimensional, transient, two phase and three-field model. In order to develop the numerical schemes for the three-field model, various numerical schemes have been examined including the SMAS, semi-implicit ICE, SIMPLE. The governing equations for a 2-phase flow are composed of mass, momentum, and energy conservation equations for each phase. These equation sets are closed by the interfacial transfer rate of mass, momentum, and energy. The interfacial transfer of mass, momentum, and energy occurs through the interfacial area, and this area plays an important role in the transfer rate. The flow regime based correlations are used for calculating the interracial area in the traditional style 2-phase flow model. This is dependent upon the flow regime and is limited to the fully developed 2-phase flow region. Its application to the multi-dimensional 2-phase flow has some limitation because it adopts the measured results of 2-phase flow in the 1-dimensional tube. The interfacial area concentration transport equation had been suggested in order to calculate the interfacial area without the interfacial area correlations. The source terms to close the interfacial area transport equation should be further developed for a wide ranger usage of it. In this study, the one group interfacial area concentration transport equation has been implemented into the CUPID code. This interfacial area concentration transport equation can be used instead of the interfacial area concentration correlations for the bubbly flow region

Heating of leads casks. An analytical solution to the heat equation made up of a series of Laguerre functions; Echauffement des chateaux de plomb. Une solution analytique a l'equation de la chaleur constituee par une serie de fonctions de Laguerre

Energy Technology Data Exchange (ETDEWEB)

Formery, Ph; Gilles, A [Commissariat a l' Energie Atomique, Dir. des Productions, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

1968-07-01

The packing used for the transport of highly radioactive materials such as in-pile irradiated rods; have to comply to fairly strict safety standards. They should in particular resist to fire without the radioactive protection being seriously affected. The heating of a transport cask placed in a fire has been calculated by normal automatic computation methods assuming that only thermal radiation is responsible for the heating and that this obeys STEFAN'S law. Simultaneously, a purely analytical treatment has been attempted as follows. The existence of a simple solution, of the Laguerre function type, to the heat equation has been demonstrated. By superposing an infinite number of simple solutions, it is possible to produce a fairly general solution, depending on parameters, which satisfies the initial state and the limiting conditions. The parameters can be adjusted so that the temperature and the flux produced on the shell by this solution satisfy approximately STEFAN'S relationship. (authors) [French] Les emballages qui servent au transport de produits fortement radioactifs, tels que des barreaux irradies dans les piles, doivent satisfaire a des normes de securite assez strictes. Ils doivent, en particulier, resister au feu sans que la protection contre le rayonnement soit sensiblement entamee. L'echauffement, par seul rayonnement thermique suppose obeir a la loi de STEFAN, d'un chateau de transport plonge dans un feu a ete calcule par les methodes habituelles du calcul automatique. Parallelement a ete tentee l'approche purement analytique que voici: Une solution simple, du type fonction de LAGUERRE, a l'equation de la chaleur est mise en evidence. La superposition, en nombre infini, de solutions simples, permet de fabriquer une solution assez generale dependant de parametres, satisfaisant a l'etat initial et aux conditions aux limites. Les parametres peuvent etre ajustes de facon que la temperature et le flux engendres sur la coque par cette solution

Modified two-fluid model for the two-group interfacial area transport equation

International Nuclear Information System (INIS)

Sun Xiaodong; Ishii, Mamoru; Kelly, Joseph M.

2003-01-01

This paper presents a modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not practical to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model

Nodal collocation approximation for the multidimensional PL equations applied to transport source problems

Energy Technology Data Exchange (ETDEWEB)

Verdu, G. [Departamento de Ingenieria Quimica Y Nuclear, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain); Capilla, M.; Talavera, C. F.; Ginestar, D. [Dept. of Nuclear Engineering, Departamento de Matematica Aplicada, Universitat Politecnica de Valencia, Cami de Vera, 14, 46022. Valencia (Spain)

2012-07-01

PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)

Nodal collocation approximation for the multidimensional PL equations applied to transport source problems

International Nuclear Information System (INIS)

Verdu, G.; Capilla, M.; Talavera, C. F.; Ginestar, D.

2012-01-01

PL equations are classical high order approximations to the transport equations which are based on the expansion of the angular dependence of the angular neutron flux and the nuclear cross sections in terms of spherical harmonics. A nodal collocation method is used to discretize the PL equations associated with a neutron source transport problem. The performance of the method is tested solving two 1D problems with analytical solution for the transport equation and a classical 2D problem. (authors)

Dynamics of charged bulk viscous collapsing cylindrical source with heat flux

Energy Technology Data Exchange (ETDEWEB)

Shah, S.M.; Abbas, G. [The Islamia University of Bahawalpur, Department of Mathematics, Bahawalpur (Pakistan)

2017-04-15

In this paper, we have explored the effects of dissipation on the dynamics of charged bulk viscous collapsing cylindrical source which allows the out-flow of heat flux in the form of radiations. The Misner-Sharp formalism has been implemented to drive the dynamical equation in terms of proper time and radial derivatives. We have investigated the effects of charge and bulk viscosity on the dynamics of collapsing cylinder. To determine the effects of radial heat flux, we have formulated the heat transport equations in the context of Mueller-Israel-Stewart theory by assuming that thermodynamics viscous/heat coupling coefficients can be neglected within some approximations. In our discussion, we have introduced the viscosity by the standard (non-causal) thermodynamics approach. The dynamical equations have been coupled with the heat transport equation; the consequences of the resulting coupled heat equation have been analyzed in detail. (orig.)

A multilevel method for conductive-radiative heat transfer

Energy Technology Data Exchange (ETDEWEB)

Banoczi, J.M.; Kelley, C.T. [North Carolina State Univ., Raleigh, NC (United States)

1996-12-31

We present a fast multilevel algorithm for the solution of a system of nonlinear integro-differential equations that model steady-state combined radiative-conductive heat transfer. The equations can be formulated as a compact fixed point problem with a fixed point map that requires both a solution of the linear transport equation and the linear heat equation for its evaluation. We use fast transport solvers developed by the second author, to construct an efficient evaluation of the fixed point map and then apply the Atkinson-Brakhage, method, with Newton-GMRES as the coarse mesh solver, to the full nonlinear system.

About Navier-Stokes Equation in the Theory of Convective Heat Transfer

Science.gov (United States)

Davidzon, M. Y.

2017-10-01

A system of differential equations (Navier-Stokes, continuity, heat conductivity) is used to solve convective heat transfer problems. While solving Navier-Stokes equation, it is usually assumed that tangent stress is proportional to the velocity gradient. This assumption is valid with a small velocity gradient, for example, near an axis of the channel, but velocity gradient can be very large near the channel wall. Our paper shows that if we accept power law instead of linear law for tangential stress, then the velocity profile for creeping, laminar, and turbulent flow in the channel can be calculated without using Navier-Stokes equation. Also, in this case Navier-Stokes equation itself changes: the coefficient of dynamic viscosity changes its value from normal (in case of the creeping flow) to tending to infinity (in case of the well-developed turbulent flow).

Nonlinear heat conduction equations with memory: Physical meaning and analytical results

Science.gov (United States)

Artale Harris, Pietro; Garra, Roberto

2017-06-01

We study nonlinear heat conduction equations with memory effects within the framework of the fractional calculus approach to the generalized Maxwell-Cattaneo law. Our main aim is to derive the governing equations of heat propagation, considering both the empirical temperature-dependence of the thermal conductivity coefficient (which introduces nonlinearity) and memory effects, according to the general theory of Gurtin and Pipkin of finite velocity thermal propagation with memory. In this framework, we consider in detail two different approaches to the generalized Maxwell-Cattaneo law, based on the application of long-tail Mittag-Leffler memory function and power law relaxation functions, leading to nonlinear time-fractional telegraph and wave-type equations. We also discuss some explicit analytical results to the model equations based on the generalized separating variable method and discuss their meaning in relation to some well-known results of the ordinary case.

Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems

International Nuclear Information System (INIS)

Cartier, J.

2006-04-01

This thesis focuses on mathematical analysis, numerical resolution and modelling of the transport equations. First of all, we deal with numerical approximation of the solution of the transport equations by using a mixed-hybrid scheme. We derive and study a mixed formulation of the transport equation, then we analyse the related variational problem and present the discretization and the main properties of the scheme. We particularly pay attention to the behavior of the scheme and we show its efficiency in the diffusion limit (when the mean free path is small in comparison with the characteristic length of the physical domain). We present academical benchmarks in order to compare our scheme with other methods in many physical configurations and validate our method on analytical test cases. Unstructured and very distorted meshes are used to validate our scheme. The second part of this thesis deals with two transport problems. The first one is devoted to the study of diffusion due to boundary conditions in a transport problem between two plane plates. The second one consists in modelling and simulating radiative transfer phenomenon in case of the industrial context of inertial confinement fusion. (author)

Heat Transfer in Directional Water Transport Fabrics

Directory of Open Access Journals (Sweden)

Chao Zeng

2016-10-01

Full Text Available Directional water transport fabrics can proactively transfer moisture from the body. They show great potential in making sportswear and summer clothing. While moisture transfer has been previously reported, heat transfer in directional water transport fabrics has been little reported in research literature. In this study, a directional water transport fabric was prepared using an electrospraying technique and its heat transfer properties under dry and wet states were evaluated, and compared with untreated control fabric and the one pre-treated with NaOH. All the fabric samples showed similar heat transfer features in the dry state, and the equilibrium temperature in the dry state was higher than for the wet state. Wetting considerably enhanced the thermal conductivity of the fabrics. Our studies indicate that directional water transport treatment assists in moving water toward one side of the fabric, but has little effect on thermal transfer performance. This study may be useful for development of “smart” textiles for various applications.

Analysis of discrete reaction-diffusion equations for autocatalysis and continuum diffusion equations for transport

Energy Technology Data Exchange (ETDEWEB)

Wang, Chi-Jen [Iowa State Univ., Ames, IA (United States)

2013-01-01

In this thesis, we analyze both the spatiotemporal behavior of: (A) non-linear “reaction” models utilizing (discrete) reaction-diffusion equations; and (B) spatial transport problems on surfaces and in nanopores utilizing the relevant (continuum) diffusion or Fokker-Planck equations. Thus, there are some common themes in these studies, as they all involve partial differential equations or their discrete analogues which incorporate a description of diffusion-type processes. However, there are also some qualitative differences, as shall be discussed below.

The transport equation in general geometry

International Nuclear Information System (INIS)

Pomraning, G.C.

1990-01-01

As stated in the introduction to the paper, the motivation for this work was to obtain an explicit form for the streaming operator in the transport equation, which could be used to compute curvature effects in an asymptotic analysis leading to diffusion theory. This sign error was discovered while performing this analysis

Differential equation of exospheric lateral transport and its application to terrestrial hydrogen

Science.gov (United States)

Hodges, R. R., Jr.

1973-01-01

The differential equation description of exospheric lateral transport of Hodges and Johnson is reformulated to extend its utility to light gases. Accuracy of the revised equation is established by applying it to terrestrial hydrogen. The resulting global distributions for several static exobase models are shown to be essentially the same as those that have been computed by Quessette using an integral equation approach. The present theory is subsequently used to elucidate the effects of nonzero lateral flow, exobase rotation, and diurnal tidal winds on the hydrogen distribution. Finally it is shown that the differential equation of exospheric transport is analogous to a diffusion equation. Hence it is practical to consider exospheric transport as a continuation of thermospheric diffusion, a concept that alleviates the need for an artificial exobase dividing thermosphere and exosphere.

Exactly averaged equations for flow and transport in random media

International Nuclear Information System (INIS)

Shvidler, Mark; Karasaki, Kenzi

2001-01-01

It is well known that exact averaging of the equations of flow and transport in random porous media can be realized only for a small number of special, occasionally exotic, fields. On the other hand, the properties of approximate averaging methods are not yet fully understood. For example, the convergence behavior and the accuracy of truncated perturbation series. Furthermore, the calculation of the high-order perturbations is very complicated. These problems for a long time have stimulated attempts to find the answer for the question: Are there in existence some exact general and sufficiently universal forms of averaged equations? If the answer is positive, there arises the problem of the construction of these equations and analyzing them. There exist many publications related to these problems and oriented on different applications: hydrodynamics, flow and transport in porous media, theory of elasticity, acoustic and electromagnetic waves in random fields, etc. We present a method of finding the general form of exactly averaged equations for flow and transport in random fields by using (1) an assumption of the existence of Green's functions for appropriate stochastic problems, (2) some general properties of the Green's functions, and (3) the some basic information about the random fields of the conductivity, porosity and flow velocity. We present a general form of the exactly averaged non-local equations for the following cases. 1. Steady-state flow with sources in porous media with random conductivity. 2. Transient flow with sources in compressible media with random conductivity and porosity. 3. Non-reactive solute transport in random porous media. We discuss the problem of uniqueness and the properties of the non-local averaged equations, for the cases with some types of symmetry (isotropic, transversal isotropic, orthotropic) and we analyze the hypothesis of the structure non-local equations in general case of stochastically homogeneous fields. (author)

A Laplace transform certified reduced basis method; application to the heat equation and wave equation

OpenAIRE

Knezevic, David; Patera, Anthony T.; Huynh, Dinh Bao Phuong

2010-01-01

We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accura...

Ion heat transport studies in JET

DEFF Research Database (Denmark)

Mantica, P; Angioni, C; Baiocchi, B

2011-01-01

Detailed experimental studies of ion heat transport have been carried out in JET exploiting the upgrade of active charge exchange spectroscopy and the availability of multi-frequency ion cyclotron resonance heating with 3He minority. The determination of ion temperature gradient (ITG) threshold a...

Self-Adjoint Angular Flux Equation for Coupled Electron-Photon Transport

International Nuclear Information System (INIS)

Liscum-Powell, J.L.; Lorence, L.J. Jr.; Morel, J.E.; Prinja, A.K.

1999-01-01

Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere and, like the even- and odd- parity form, S n source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here we apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross-sections from the CEPXS code and S n discretization

Self-adjoint angular flux equation for coupled electron-photon transport

International Nuclear Information System (INIS)

Liscum-Powell, J.L.; Prinja, A.K.; Morel, J.E.; Lorence, L.J. Jr.

1999-01-01

Recently, Morel and McGhee described an alternate second-order form of the transport equation called the self-adjoint angular flux (SAAF) equation that has the angular flux as its unknown. The SAAF formulation has all the advantages of the traditional even- and odd-parity self-adjoint equations, with the added advantages that it yields the full angular flux when it is numerically solved, it is significantly easier to implement reflective and reflective-like boundary conditions, and in the appropriate form it can be solved in void regions. The SAAF equation has the disadvantage that the angular domain is the full unit sphere, and, like the even- and odd-parity form, S n source iteration cannot be implemented using the standard sweeping algorithm. Also, problems arise in pure scattering media. Morel and McGhee demonstrated the efficacy of the SAAF formulation for neutral particle transport. Here, the authors apply the SAAF formulation to coupled electron-photon transport problems using multigroup cross sections from the CEPXS code and S n discretization

Electron and ion heat transport with lower hybrid current drive and neutral beam injection heating in ASDEX

International Nuclear Information System (INIS)

Soeldner, F.X.; Pereverzev, G.V.; Bartiromo, R.; Fahrbach, H.U.; Leuterer, F.; Murmann, H.D.; Staebler, A.; Steuer, K.H.

1993-01-01

Transport code calculations were made for experiments with the combined operation of lower hybrid current drive and heating and of neutral beam injection heating on ASDEX. Peaking or flattening of the electron temperature profile are mainly explained by modifications of the MHD induced electron heat transport. They originate from current profile changes due to lower hybrid and neutral beam current drive and to contributions from the bootstrap current. Ion heat transport cannot be described by one single model for all heating scenarios. The ion heat conductivity is reduced during lower hybrid heated phases with respect to Ohmic and neutral beam heating. (author). 13 refs, 5 figs

On standard forms for transport equations and fluxes: Part 2

International Nuclear Information System (INIS)

Ross, D.W.

1990-03-01

Quasilinear expressions for anomalous particle and energy fluxes arising from electrostatic plasma turbulence in a tokamak are reviewed yet again. Further clarifications are made, and the position taken in a previous report is modified. There, the total energy flux, Q j , and the conductive heat flux, q j , were correctly defined, and the anomalous Q j was correctly calculated. It was shown that the anomalous energy transport can be correctly described by ∇·Q* j , where Q* j = 3/5 Q j , with all remaining source terms such as left-angle p j ∇·Vj} cancelling. Here, a revised discussion is given of the identification of the anomalous conductive flux, q j , in which the distinction between Q j and Q* j is reconsidered. It is shown that there is more than one consistent way to define q j . Transport calculations involving only theoretical electrostatic turbulent fluxes are unaffected by these distinctions since Q j or Q* j , rather than q j , is the quantity naturally calculated in the theory. However, an ambiguity remains in experimental transport analysis if the measured particle flux Γ j = n j V j is to be used in the energy equation. This is because we cannot be sure how properly to treat the source terms p j ∇·V j or { p j ∇·V j }. 17 refs

An Overview of Liquid Fluoride Salt Heat Transport Systems

Energy Technology Data Exchange (ETDEWEB)

Holcomb, David Eugene [ORNL; Cetiner, Sacit M [ORNL

2010-09-01

Heat transport is central to all thermal-based forms of electricity generation. The ever increasing demand for higher thermal efficiency necessitates power generation cycles transitioning to progressively higher temperatures. Similarly, the desire to provide direct thermal coupling between heat sources and higher temperature chemical processes provides the underlying incentive to move toward higher temperature heat transfer loops. As the system temperature rises, the available materials and technology choices become progressively more limited. Superficially, fluoride salts at {approx}700 C resemble water at room temperature being optically transparent and having similar heat capacity, roughly three times the viscosity, and about twice the density. Fluoride salts are a leading candidate heat-transport material at high temperatures. Fluoride salts have been extensively used in specialized industrial processes for decades, yet they have not entered widespread deployment for general heat transport purposes. This report does not provide an exhaustive screening of potential heat transfer media and other high temperature liquids such as alkali metal carbonate eutectics or chloride salts may have economic or technological advantages. A particular advantage of fluoride salts is that the technology for their use is relatively mature as they were extensively studied during the 1940s-1970s as part of the U.S. Atomic Energy Commission's program to develop molten salt reactors (MSRs). However, the instrumentation, components, and practices for use of fluoride salts are not yet developed sufficiently for commercial implementation. This report provides an overview of the current understanding of the technologies involved in liquid salt heat transport (LSHT) along with providing references to the more detailed primary information resources. Much of the information presented here derives from the earlier MSR program. However, technology has evolved over the intervening years

Coupling of neutron transport equations. First results; Couplage d`equations en transport neutronique. premiere approche 1D monocinetique

Energy Technology Data Exchange (ETDEWEB)

Bal, G.

1995-07-01

To achieve whole core calculations of the neutron transport equation, we have to follow this 2 step method: space and energy homogenization of the assemblies; resolution of the homogenized equation on the whole core. However, this is no more valid when accidents occur (for instance depressurization causing locally strong heterogeneous media). One solution consists then in coupling two kinds of resolutions: a fine computation on the damaged cell (fine mesh, high number of energy groups) coupled with a coarse one everywhere else. We only deal here with steady state solutions (which already live in 6D spaces). We present here two such methods: The coupling by transmission of homogenized sections and the coupling by transmission of boundary conditions. To understand what this coupling is, we first restrict ourselves to 1D with respect to space in one energy group. The first two chapters deal with a recall of basic properties of the neutron transport equation. We give at chapter 3 some indications of the behaviour of the flux with respect to the cross sections. We present at chapter 4 some couplings and give some properties. Chapter 5 is devoted to a presentation of some numerical applications. (author). 9 refs., 7 figs.

Some factors affecting radiative heat transport in PWR cores

International Nuclear Information System (INIS)

Hall, A.N.

1989-04-01

This report discusses radiative heat transport in Pressurized Water Reactor cores, using simple models to illustrate basic features of the transport process. Heat transport by conduction and convection is ignored in order to focus attention on the restrictions on radiative heat transport imposed by the geometry of the heat emitting and absorbing structures. The importance of the spacing of the emitting and absorbing structures is emphasised. Steady state temperature distributions are found for models of cores which are uniformly heated by fission product decay. In all of the models, a steady state temperature distribution can only be obtained if the central core temperature is in excess of the melting point of UO 2 . It has recently been reported that the MIMAS computer code, which takes into account radiative heat transport, has been used to model the heat-up of the Three Mile Island-2 reactor core, and the computations indicate that the core could not have reached the melting point of UO 2 at any time or any place. We discuss this result in the light of the calculations presented in this paper. It appears that the predicted stabilisation of the core temperatures at ∼ 2200 0 C may be a consequence of the artificially large spacing between the radial rings employed in the MIMAS code, rather than a result of physical significance. (author)

A computational procedure for finding multiple solutions of convective heat transfer equations

International Nuclear Information System (INIS)

Mishra, S; DebRoy, T

2005-01-01

In recent years numerical solutions of the convective heat transfer equations have provided significant insight into the complex materials processing operations. However, these computational methods suffer from two major shortcomings. First, these procedures are designed to calculate temperature fields and cooling rates as output and the unidirectional structure of these solutions preclude specification of these variables as input even when their desired values are known. Second, and more important, these procedures cannot determine multiple pathways or multiple sets of input variables to achieve a particular output from the convective heat transfer equations. Here we propose a new method that overcomes the aforementioned shortcomings of the commonly used solutions of the convective heat transfer equations. The procedure combines the conventional numerical solution methods with a real number based genetic algorithm (GA) to achieve bi-directionality, i.e. the ability to calculate the required input variables to achieve a specific output such as temperature field or cooling rate. More important, the ability of the GA to find a population of solutions enables this procedure to search for and find multiple sets of input variables, all of which can lead to the desired specific output. The proposed computational procedure has been applied to convective heat transfer in a liquid layer locally heated on its free surface by an electric arc, where various sets of input variables are computed to achieve a specific fusion zone geometry defined by an equilibrium temperature. Good agreement is achieved between the model predictions and the independent experimental results, indicating significant promise for the application of this procedure in finding multiple solutions of convective heat transfer equations

Transition to ballistic regime for heat transport in helium II

Energy Technology Data Exchange (ETDEWEB)

Sciacca, Michele, E-mail: michele.sciacca@unipa.it [Dipartimento Scienze Agrarie e Forestali, Università degli studi di Palermo, Viale delle Scienze, 90128 Palermo (Italy); Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia (Spain); Sellitto, Antonio, E-mail: ant.sellitto@gmail.com [Dipartimento di Matematica, Informatica ed Economia, Università della Basilicata, Campus Macchia Romana, 85100 Potenza (Italy); Jou, David, E-mail: david.jou@uab.cat [Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Catalonia (Spain); Institut d' Estudis Catalans, Carme 47, 08001 Barcelona, Catalonia (Spain)

2014-07-04

The size-dependent and flux-dependent effective thermal conductivity of narrow capillaries filled with superfluid helium is analyzed from a thermodynamic continuum perspective. The classical Landau evaluation of the effective thermal conductivity of quiescent superfluid, or the Gorter–Mellinck regime of turbulent superfluids, is extended to describe the transition to ballistic regime in narrow channels wherein the radius R is comparable to (or smaller than) the phonon mean-free path ℓ in superfluid helium. To do so, we start from an extended equation for the heat flux incorporating non-local terms, and take into consideration a heat slip flow along the walls of the tube. This leads from an effective thermal conductivity proportional to R{sup 2} (Landau regime) to another one proportional to Rℓ (ballistic regime). We consider two kinds of flows: along cylindrical pipes and along two infinite parallel plates. - Highlights: • Heat transport in counterflow helium in the ballistic regime. • The one-fluid model based on the Extended Thermodynamics is used. • The transition from the Landau regime to the ballistic regime. • The transition from quantum turbulence to ballistic regime.

One-dimensional heat conduction equation of the polar bear hair

Directory of Open Access Journals (Sweden)

Zhu Wei-Hong

2015-01-01

Full Text Available Hairs of a polar bear (Ursus maritimus possess special membrane-pore structure. The structure enables the polar bear to survive in the harsh Arctic regions. In this paper, the membrane-pore structure be approximately considered as fractal space, 1-D heat conduction equation of the polar bear hair is established and the solution of the equation is obtained.

Solution of heat equation with variable coefficient using derive

CSIR Research Space (South Africa)

Lebelo, RS

2008-09-01

Full Text Available In this paper, the method of approximating solutions of partial differential equations with variable coefficients is studied. This is done by considering heat flow through a one-dimensional model with variable cross-sections. Two cases...

Coupled light transport-heat diffusion model for laser dosimetry with dynamic optical properties

International Nuclear Information System (INIS)

London, R.A.; Glinsky, M.E.; Zimmerman, G.B.; Eder, D.C.; Jacques, S.L.

1995-01-01

The effect of dynamic optical properties on the spatial distribution of light in laser therapy is studied via numerical simulations. A two-dimensional, time dependent computer program called LATIS is used. Laser light transport is simulated with a Monte Carlo technique including anisotropic scattering and absorption. Thermal heat transport is calculated with a finite difference algorithm. Material properties are specified on a 2-D mesh and can be arbitrary functions of space and time. Arrhenius rate equations are solved for tissue damage caused by elevated temperatures. Optical properties are functions of tissue damage, as determined by previous measurements. Results are presented for the time variation of the light distribution and damage within the tissue as the optical properties of the tissue are altered

Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source

Directory of Open Access Journals (Sweden)

B.S. Bhadauria

2014-12-01

Full Text Available In this paper, a theoretical investigation has been carried out to study the combined effect of rotation speed modulation and internal heating on thermal instability in a temperature dependent viscous horizontal fluid layer. Rayleigh–Bénard momentum equation with Coriolis term has been considered to describe the convective flow. The system is rotating about it is own axis with non-uniform rotational speed. In particular, a time-periodic and sinusoidally varying rotational speed has been considered. A weak nonlinear stability analysis is performed to find the effect of modulation on heat transport. Nusselt number is obtained in terms of amplitude of convection and internal Rayleigh number, and depicted graphically for showing the effects of various parameters of the system. The effect of modulated rotation speed is found to have a stabilizing effect for different values of modulation frequency. Further, internal heating and thermo-rheological parameters are found to destabilize the system.

Modification of the finite element heat and mass transfer code (FEHMN) to model multicomponent reactive transport

International Nuclear Information System (INIS)

Viswanathan, H.S.

1995-01-01

The finite element code FEHMN is a three-dimensional finite element heat and mass transport simulator that can handle complex stratigraphy and nonlinear processes such as vadose zone flow, heat flow and solute transport. Scientists at LANL have been developed hydrologic flow and transport models of the Yucca Mountain site using FEHMN. Previous FEHMN simulations have used an equivalent K d model to model solute transport. In this thesis, FEHMN is modified making it possible to simulate the transport of a species with a rigorous chemical model. Including the rigorous chemical equations into FEHMN simulations should provide for more representative transport models for highly reactive chemical species. A fully kinetic formulation is chosen for the FEHMN reactive transport model. Several methods are available to computationally implement a fully kinetic formulation. Different numerical algorithms are investigated in order to optimize computational efficiency and memory requirements of the reactive transport model. The best algorithm of those investigated is then incorporated into FEHMN. The algorithm chosen requires for the user to place strongly coupled species into groups which are then solved for simultaneously using FEHMN. The complete reactive transport model is verified over a wide variety of problems and is shown to be working properly. The simulations demonstrate that gas flow and carbonate chemistry can significantly affect 14 C transport at Yucca Mountain. The simulations also provide that the new capabilities of FEHMN can be used to refine and buttress already existing Yucca Mountain radionuclide transport studies

Variance estimates for transport in stochastic media by means of the master equation

International Nuclear Information System (INIS)

Pautz, S. D.; Franke, B. C.; Prinja, A. K.

2013-01-01

The master equation has been used to examine properties of transport in stochastic media. It has been shown previously that not only may the Levermore-Pomraning (LP) model be derived from the master equation for a description of ensemble-averaged transport quantities, but also that equations describing higher-order statistical moments may be obtained. We examine in greater detail the equations governing the second moments of the distribution of the angular fluxes, from which variances may be computed. We introduce a simple closure for these equations, as well as several models for estimating the variances of derived transport quantities. We revisit previous benchmarks for transport in stochastic media in order to examine the error of these new variance models. We find, not surprisingly, that the errors in these variance estimates are at least as large as the corresponding estimates of the average, and sometimes much larger. We also identify patterns in these variance estimates that may help guide the construction of more accurate models. (authors)

Symmetrized neutron transport equation and the fast Fourier transform method

International Nuclear Information System (INIS)

Sinh, N.Q.; Kisynski, J.; Mika, J.

1978-01-01

The differential equation obtained from the neutron transport equation by the application of the source iteration method in two-dimensional rectangular geometry is transformed into a symmetrized form with respect to one of the angular variables. The discretization of the symmetrized equation leads to finite difference equations based on the five-point scheme and solved by use of the fast Fourier transform method. Possible advantages of the approach are shown on test calculations

Advances in the solution of three-dimensional nodal neutron transport equation

International Nuclear Information System (INIS)

Pazos, Ruben Panta; Hauser, Eliete Biasotto; Vilhena, Marco Tullio de

2003-01-01

In this paper we study the three-dimensional nodal discrete-ordinates approximations of neutron transport equation in a convex domain with piecewise smooth boundaries. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtaining the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. We give numerical results obtained with an algebraic computer system (for N up to 8) and with a code for higher values of N. We compare our results for the geometry of a box with a source in a vertex and a leakage zone in the opposite with others techniques used in this problem. (author)

Source effects on impurity and heat transport in a tokamak

International Nuclear Information System (INIS)

Bennett, R.B.

1980-12-01

A recently developed generalization of neoclassical theory is extended here to study heat flux contributions to impurity transport, as well as the heat fluxes themselves. The theory accounts for the first four source moments, with external drags, which has been studied previously with either fewer moments or restricted to a collisional plasma. Conditions are established for which a momentum source may be used to modify the particle and heat transport. In the course of this work, the particle and heat transport is evaluated for a two species plasma with arbitrary plasma geometry, beta, and collisionality

Validation of CFD-methods to predict heat transfer and temperatures during the transport and storage of casks under a cover

International Nuclear Information System (INIS)

Leber, A.; Graf, W.; Hueggenberg, R.

2004-01-01

With respect to the transport of casks for radioactive material, the proof of the safe heat removal can be accomplished by validated calculation methods. The boundary conditions for thermal tests for type B packages are specified in the ADR based on the regulations defined by the International Atomic Energy Agency. The varying boundary conditions under transport or storage conditions are based on the varying thermal conditions true for different cask types. In most cases the cask will be transported in lying position under a cover (e.g. canopy or tarpaulin) and stored in standing position in an array with other casks. The main heat transport mechanisms are natural convection and thermal radiation. The cover or the storage building are furnished with vents that create an air flow, which will improve the natural convection. Depending on the thermal boundary conditions, the cask design and the heat power, about 50 - 95% of the heat power will be removed from the finned cask surface by natural convection. Consequently the convection by air flow is the main heat transport mechanism. The air flow can be approximated with analytical methods by solving the integral heat and flow balances for the domain. In a stationary state the overpressure due the buoyancy and the pressure loss in the flow resistances are equal. Based on the air flow, the relevant temperatures of the cask can be calculated in an iterative process. Due to the fast development of numerical calculation methods and computer hardware, the use of Computational- Fluid-Dynamics(CFD) calculations plays an important role. CFD-calculations are based on solving the equations of conservation (Navier-Stokes equations) using a finite element mesh or a finite volume mesh of the model. For a finned cask lying under a cover, where the main contributing element for heat removal is natural convection in combination with the thermal radiation, a CFD-calculation can be the most appropriate method. Common CFD-Codes are FLUENT

Solving the equation of neutron transport

International Nuclear Information System (INIS)

Nasfi, Rim

2009-01-01

This work is devoted to the study of some numerical methods of resolution of the problem of transport of the neutrons. We started by introducing the equation integro-differential transport of the neutrons. Then we applied the finite element method traditional for stationary and nonstationary linear problems in 2D. A great part is reserved for the presentation of the mixed numerical diagram and mixed hybrid with two types of uniform grids: triangular and rectangular. Thereafter we treated some numerical examples by implementations in Matlab in order to test the convergence of each method. To finish, we had results of simulation by the Monte Carlo method on a problem of two-dimensional transport with an aim of comparing them with the results resulting from the finite element method mixed hybrids. Some remarks and prospects conclude this work.

Regularization algorithm within two-parameters for identification heat-coefficient in the parabolic equation

International Nuclear Information System (INIS)

Hinestroza Gutierrez, D.

2006-08-01

In this work a new and promising algorithm based on the minimization of especial functional that depends on two regularization parameters is considered for the identification of the heat conduction coefficient in the parabolic equation. This algorithm uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient (as in conventional Tikhonov algorithms) but the other is associated with the calculated solution. (author)

Regularization algorithm within two-parameters for identification heat-coefficient in the parabolic equation

International Nuclear Information System (INIS)

Hinestroza Gutierrez, D.

2006-12-01

In this work a new and promising algorithm based in the minimization of especial functional that depends on two regularization parameters is considered for identification of the heat conduction coefficient in the parabolic equation. This algorithm uses the adjoint and sensibility equations. One of the regularization parameters is associated with the heat-coefficient (as in conventional Tikhonov algorithms) but the other is associated with the calculated solution. (author)

An integral equation arising in two group neutron transport theory

International Nuclear Information System (INIS)

Cassell, J S; Williams, M M R

2003-01-01

An integral equation describing the fuel distribution necessary to maintain a flat flux in a nuclear reactor in two group transport theory is reduced to the solution of a singular integral equation. The formalism developed enables the physical aspects of the problem to be better understood and its relationship with the corresponding diffusion theory model is highlighted. The integral equation is solved by reducing it to a non-singular Fredholm equation which is then evaluated numerically

Aspheric surface testing by irradiance transport equation

Science.gov (United States)

Shomali, Ramin; Darudi, Ahmad; Nasiri, Sadollah; Asgharsharghi Bonab, Armir

2010-10-01

In this paper a method for aspheric surface testing is presented. The method is based on solving the Irradiance Transport Equation (ITE).The accuracy of ITE normally depends on the amount of the pick to valley of the phase distribution. This subject is investigated by a simulation procedure.

Intense radiative heat transport across a nano-scale gap

International Nuclear Information System (INIS)

Budaev, Bair V.; Ghafari, Amin; Bogy, David B.

2016-01-01

In this paper, we analyze the radiative heat transport in layered structures. The analysis is based on our prior description of the spectrum of thermally excited waves in systems with a heat flux. The developed method correctly predicts results for all known special cases for both large and closing gaps. Numerical examples demonstrate the applicability of our approach to the calculation of the radiative heat transport coefficient across various layered structures.

Radiative transport equation for the Mittag-Leffler path length distribution

Science.gov (United States)

Liemert, André; Kienle, Alwin

2017-05-01

In this paper, we consider the radiative transport equation for infinitely extended scattering media that are characterized by the Mittag-Leffler path length distribution p (ℓ ) =-∂ℓEα(-σtℓα ) , which is a generalization of the usually assumed Lambert-Beer law p (ℓ ) =σtexp(-σtℓ ) . In this context, we derive the infinite-space Green's function of the underlying fractional transport equation for the spherically symmetric medium as well as for the one-dimensional string. Moreover, simple analytical solutions are presented for the prediction of the radiation field in the single-scattering approximation. The resulting equations are compared with Monte Carlo simulations in the steady-state and time domain showing, within the stochastic nature of the simulations, an excellent agreement.

Solution of the two- dimensional heat equation for a rectangular plate

Directory of Open Access Journals (Sweden)

Nurcan BAYKUŞ SAVAŞANERİL

2015-11-01

Full Text Available Laplace equation is a fundamental equation of applied mathematics. Important phenomena in engineering and physics, such as steady-state temperature distribution, electrostatic potential and fluid flow, are modeled by means of this equation. The Laplace equation which satisfies boundary values is known as the Dirichlet problem. The solutions to the Dirichlet problem form one of the most celebrated topics in the area of applied mathematics. In this study, a novel method is presented for the solution of two-dimensional heat equation for a rectangular plate. In this alternative method, the solution function of the problem is based on the Green function, and therefore on elliptic functions.

Effects of system-bath coupling on a photosynthetic heat engine: A polaron master-equation approach

Science.gov (United States)

Qin, M.; Shen, H. Z.; Zhao, X. L.; Yi, X. X.

2017-07-01

Stimulated by suggestions of quantum effects in energy transport in photosynthesis, the fundamental principles responsible for the near-unit efficiency of the conversion of solar to chemical energy became active again in recent years. Under natural conditions, the formation of stable charge-separation states in bacteria and plant reaction centers is strongly affected by the coupling of electronic degrees of freedom to a wide range of vibrational motions. These inspire and motivate us to explore the effects of the environment on the operation of such complexes. In this paper, we apply the polaron master equation, which offers the possibilities to interpolate between weak and strong system-bath coupling, to study how system-bath couplings affect the exciton-transfer processes in the Photosystem II reaction center described by a quantum heat engine (QHE) model over a wide parameter range. The effects of bath correlation and temperature, together with the combined effects of these factors are also discussed in detail. We interpret these results in terms of noise-assisted transport effect and dynamical localization, which correspond to two mechanisms underpinning the transfer process in photosynthetic complexes: One is resonance energy transfer and the other is the dynamical localization effect captured by the polaron master equation. The effects of system-bath coupling and bath correlation are incorporated in the effective system-bath coupling strength determining whether noise-assisted transport effect or dynamical localization dominates the dynamics and temperature modulates the balance of the two mechanisms. Furthermore, these two mechanisms can be attributed to one physical origin: bath-induced fluctuations. The two mechanisms are manifestations of the dual role played by bath-induced fluctuations depending on the range of parameters. The origin and role of coherence are also discussed. It is the constructive interplay between noise and coherent dynamics, rather

Modelling of Temperature Profiles and Transport Scaling in Auxiliary Heated Tokamaks

DEFF Research Database (Denmark)

Callen, J.D.; Christiansen, J.P.; Cordey, J.G.

1987-01-01

time , the heating effectiveness η, and the energy offset W(0). Considering both the temperature profile responses and the global transport scaling, the constant heat pinch or excess temperature gradient model is found to best characterize the present JET data. Finally, new methods are proposed......The temperature profiles produced by various heating profiles are calculated from local heat transport models. The models take the heat flux to be the sum of heat diffusion and a non-diffusive heat flow, consistent with local measurements of heat transport. Two models are developed analytically...... in detail: (i) a heat pinch or excess temperature gradient model with constant coefficients; and (ii) a non-linear heat diffusion coefficient (χ) model. Both models predict weak (lesssim20%) temperature profile responses to physically relevant changes in the heat deposition profile – primarily because...

Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems; Resolution de l'equation du transport par une methode d'elements finis mixtes-hybrides et approximation par la diffusion de problemes de transport

Energy Technology Data Exchange (ETDEWEB)

Cartier, J

2006-04-15

This thesis focuses on mathematical analysis, numerical resolution and modelling of the transport equations. First of all, we deal with numerical approximation of the solution of the transport equations by using a mixed-hybrid scheme. We derive and study a mixed formulation of the transport equation, then we analyse the related variational problem and present the discretization and the main properties of the scheme. We particularly pay attention to the behavior of the scheme and we show its efficiency in the diffusion limit (when the mean free path is small in comparison with the characteristic length of the physical domain). We present academical benchmarks in order to compare our scheme with other methods in many physical configurations and validate our method on analytical test cases. Unstructured and very distorted meshes are used to validate our scheme. The second part of this thesis deals with two transport problems. The first one is devoted to the study of diffusion due to boundary conditions in a transport problem between two plane plates. The second one consists in modelling and simulating radiative transfer phenomenon in case of the industrial context of inertial confinement fusion. (author)

Non-local model analysis of heat pulse propagation

International Nuclear Information System (INIS)

Iwasaki, Takuya; Itoh, Sanae-I.; Yagi, Masatoshi

1998-01-01

A new theoretical model equation which includes the non-local effect in the heat flux is proposed to study the transient transport phenomena. A non-local heat flux, which is expressed in terms of the integral equation, is superimposed on the conventional form of the heat flux. This model is applied to describe the experimental results from the power switching [Stroth U, et al 1996 Plasma Phys. Control. Fusion 38 1087] and the power modulation experiments [Giannone L, et al 1992 Nucl. Fusion 32 1985] in the W7-AS stellarator. A small fraction of non-local component in the heat flux is found to be very effective in modifying the response against an external modulation. The transient feature of the transport property, which are observed in the response of heat pulse propagation, are qualitatively reproduced by the transport simulations based on this model. A possibility is discussed to determine the correlation length of the non-local effect experimentally by use of the results of transport simulations. (author)

Solution of the transport equation with account for inelastic collisions

International Nuclear Information System (INIS)

Kalashnikov, N.P.; Remizovich, V.S.; Ryazanov, M.I.

1980-01-01

The theory of charged particle scattering in a matter with account for inelastic collisions is considered. In ''directly-forward'' approximation the transport equation at the absence of elastic collisions is obtained. The solution of the transport equation is made without and with account for fluctuation of energy losses. Formulas for path-energy relation are given. Energy spectrum and distribution of fast charged particles with respect to paths are studied. The problem of quantum mechanical approach to the theory of multiple scattering of fast charged particles in a matter is discussed briefly

Generalized fluid equations for parallel transport in collisional to weakly collisional plasmas

International Nuclear Information System (INIS)

Zawaideh, E.; Najmabadi, F.; Conn, R.W.

1986-01-01

A new set of two-fluid equations that are valid from collisional to weakly collisional limits is derived. Starting from gyrokinetic equations in flux coordinates with no zero-order drifts, a set of moment equations describing plasma transport along the field lines of a space- and time-dependent magnetic field is derived. No restriction on the anisotropy of the ion distribution function is imposed. In the highly collisional limit, these equations reduce to those of Braginskii, while in the weakly collisional limit they are similar to the double adiabatic or Chew, Goldberger, and Low (CGL) equations [Proc. R. Soc. London, Ser. A 236, 112 (1956)]. The new set of equations also exhibits a physical singularity at the sound speed. This singularity is used to derive and compute the sound speed. Numerical examples comparing these equations with conventional transport equations show that in the limit where the ratio of the mean free path lambda to the scale length of the magnetic field gradient L/sub B/ approaches zero, there is no significant difference between the solution of the new and conventional transport equations. However, conventional fluid equations, ordinarily expected to be correct to the order (lambda/L/sub B/) 2 , are found to have errors of order (lambda/L/sub u/) 2 = (lambda/L/sub B/) 2 /(1-M 2 ) 2 , where L/sub u/ is the scale length of the flow velocity gradient and M is the Mach number. As such, the conventional equations may contain large errors near the sound speed (Mroughly-equal1)

Normal and adjoint integral and integrodifferential neutron transport equations. Pt. 2

International Nuclear Information System (INIS)

Velarde, G.

1976-01-01

Using the simplifying hypotheses of the integrodifferential Boltzmann equations of neutron transport, given in JEN 334 report, several integral equations, and theirs adjoint ones, are obtained. Relations between the different normal and adjoint eigenfunctions are established and, in particular, proceeding from the integrodifferential Boltzmann equation it's found out the relation between the solutions of the adjoint equation of its integral one, and the solutions of the integral equation of its adjoint one (author)

The non-differentiable solution for local fractional Laplace equation in steady heat-conduction problem

Directory of Open Access Journals (Sweden)

Chen Jie-Dong

2016-01-01

Full Text Available In this paper, we investigate the local fractional Laplace equation in the steady heat-conduction problem. The solutions involving the non-differentiable graph are obtained by using the characteristic equation method (CEM via local fractional derivative. The obtained results are given to present the accuracy of the technology to solve the steady heat-conduction in fractal media.

Simulation of the fusion materials irradiation test facility lithium and heat transport systems for abnormal events study

International Nuclear Information System (INIS)

Carlson, W.F.; Elyashar, N.N.

1981-01-01

A digital computer model of Fusion Materials Irradiation Test Facility's heat transport system has been developed. The model utilizes a set of coupled differential equations to simulate the dynamic behavior of the primary and secondary heat transport loop systems. The model has been used to investigate the stability of the proposed control schemes for lithium temperature and flow rate and for an extensive study of equipment failures and malfunction analysis. It was determined that certain equipment failures and malfunctions in the primary loop require a response from the control system within less than one second of the occurrence of the failure. The effects of equipment failures in the secondary loop were found to be less dramatic than the equivalent failures in the primary loop. The failures in the secondary loop generally required control action in time frames of the order of minutes

A method for solving neutron transport equation

International Nuclear Information System (INIS)

Dimitrijevic, Z.

1993-01-01

The procedure for solving the transport equation by directly integrating for case one-dimensional uniform multigroup medium is shown. The solution is expressed in terms of linear combination of function H n (x,μ), and the coefficient is determined from given conditions. The solution is applied for homogeneous slab of critical thickness. (author)

Least-squares finite element discretizations of neutron transport equations in 3 dimensions

Energy Technology Data Exchange (ETDEWEB)

Manteuffel, T.A [Univ. of Colorado, Boulder, CO (United States); Ressel, K.J. [Interdisciplinary Project Center for Supercomputing, Zurich (Switzerland); Starkes, G. [Universtaet Karlsruhe (Germany)

1996-12-31

The least-squares finite element framework to the neutron transport equation introduced in is based on the minimization of a least-squares functional applied to the properly scaled neutron transport equation. Here we report on some practical aspects of this approach for neutron transport calculations in three space dimensions. The systems of partial differential equations resulting from a P{sub 1} and P{sub 2} approximation of the angular dependence are derived. In the diffusive limit, the system is essentially a Poisson equation for zeroth moment and has a divergence structure for the set of moments of order 1. One of the key features of the least-squares approach is that it produces a posteriori error bounds. We report on the numerical results obtained for the minimum of the least-squares functional augmented by an additional boundary term using trilinear finite elements on a uniform tesselation into cubes.

Miniature Heat Transport System for Spacecraft Thermal Control

Science.gov (United States)

Ochterbeck, Jay M.; Ku, Jentung (Technical Monitor)

2002-01-01

Loop heat pipes (LHP) are efficient devices for heat transfer and use the basic principle of a closed evaporation-condensation cycle. The advantage of using a loop heat pipe over other conventional methods is that large quantities of heat can be transported through a small cross-sectional area over a considerable distance with no additional power input to the system. By using LHPs, it seems possible to meet the growing demand for high-power cooling devices. Although they are somewhat similar to conventional heat pipes, LHPs have a whole set of unique properties, such as low pressure drops and flexible lines between condenser and evaporator, that make them rather promising. LHPs are capable of providing a means of transporting heat over long distances with no input power other than the heat being transported because of the specially designed evaporator and the separation of liquid and vapor lines. For LHP design and fabrication, preliminary analysis on the basis of dimensionless criteria is necessary because of certain complicated phenomena that take place in the heat pipe. Modeling the performance of the LHP and miniaturizing its size are tasks and objectives of current research. In the course of h s work, the LHP and its components, including the evaporator (the most critical and complex part of the LHP), were modeled with the corresponding dimensionless groups also being investigated. Next, analysis of heat and mass transfer processes in the LHP, selection of the most weighted criteria from known dimensionless groups (thermal-fluid sciences), heat transfer rate limits, (heat pipe theory), and experimental ratios which are unique to a given heat pipe class are discussed. In the third part of the report, two-phase flow heat and mass transfer performances inside the LHP condenser are analyzed and calculated for Earth-normal gravity and microgravity conditions. On the basis of recent models and experimental databanks, an analysis for condensing two-phase flow regimes

Policies and initiatives for carbon neutrality in nordic heating and transport systems

DEFF Research Database (Denmark)

Muller, Jakob Glarbo; Wu, Qiuwei; Ostergaard, Jacob

2012-01-01

Policies and initiatives promoting carbon neutrality in the Nordic heating and transport systems are presented. The focus within heating systems is the propagation of heat pumps while the focus within transport systems is initiatives regarding electric vehicles (EVs). It is found that conversion...... to heat pumps in the Nordic region rely on both private economic and national economic incentives. Initiatives toward carbon neutrality in the transport system are mostly concentrated on research, development and demonstration for deployment of a large number of EVs. All Nordic countries have plans...... for the future heating and transport systems with the ambition of realizing carbon neutrality....

Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

International Nuclear Information System (INIS)

FAN, WESLEY C.; DRUMM, CLIFTON R.; POWELL, JENNIFER L. email wcfan@sandia.gov

2002-01-01

The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations

Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

CERN Document Server

Fan, W C; Powell, J L

2002-01-01

The conventional discrete ordinates approximation to the Boltzmann transport equation can be described in a matrix form. Specifically, the within-group scattering integral can be represented by three components: a moment-to-discrete matrix, a scattering cross-section matrix and a discrete-to-moment matrix. Using and extending these entities, we derive and summarize the matrix representations of the second-order transport equations.

Some results on the neutron transport and the coupling of equations

International Nuclear Information System (INIS)

Bal, G.

1997-01-01

Neutron transport in nuclear reactors is well modeled by the linear Boltzmann transport equation. Its resolution is relatively easy but very expensive. To achieve whole core calculations, one has to consider simpler models, such as diffusion or homogeneous transport equations. However, the solutions may become inaccurate in particular situations (as accidents for instance). That is the reason why we wish to solve the equations on small area accurately and more coarsely on the remaining part of the core. It is than necessary to introduce some links between different discretizations or modelizations. In this note, we give some results on the coupling of different discretizations of all degrees of freedom of the integral-differential neutron transport equation (two degrees for the angular variable, on for the energy component, and two or three degrees for spatial position respectively in 2D (cylindrical symmetry) and 3D). Two chapters are devoted to the coupling of discrete ordinates methods (for angular discretization). The first one is theoretical and shows the well posing of the coupled problem, whereas the second one deals with numerical applications of practical interest (the results have been obtained from the neutron transport code developed at the R and D, which has been modified for introducing the coupling). Next, we present the nodal scheme RTN0, used for the spatial discretization. We show well posing results for the non-coupled and the coupled problems. At the end, we deal with the coupling of energy discretizations for the multigroup equations obtained by homogenization. Some theoretical results of the discretization of the velocity variable (well-posing of problems), which do not deal directly with the purposes of coupling, are presented in the annexes. (author)

Transport in Auxiliary Heated NSTX Discharges

International Nuclear Information System (INIS)

LeBlanc, B.P.; Bell, M.G.; Bell, R.E.; Bitte, M.L.; Bourdelle, C.; Gates, D.A.; Kaye, S.M.; Maingi, R.; Menard, J.E.; Mueller, D.; Ono, M.; Paul, S.F.; Redi, M.H.; Roquemore, A.L.; Rosenberg, A.; Sabbagh, S.A.; Stutman, D.; Synakowski, E.J.; Soukhanovskii, V.A.; Wilson, J.R.

2003-01-01

The NSTX spherical torus (ST) provides a unique platform to investigate magnetic confinement in auxiliary-heated plasmas at low aspect ratio. Auxiliary power is routinely coupled to ohmically heated plasmas by deuterium neutral-beam injection (NBI) and by high-harmonic fast waves (HHFW) launch. While theory predicts both techniques to preferentially heat electrons, experiment reveals the electron temperature is greater than the ion temperature during HHFW, but the electron temperature is less than the ion temperature during NBI. In the following we present the experimental data and the results of transport analyses

Electron heat transport analysis of low-collisionality plasmas in the neoclassical-transport-optimized configuration of LHD

International Nuclear Information System (INIS)

Murakami, Sadayoshi; Yamada, Hiroshi; Wakasa, Arimitsu

2002-01-01

Electron heat transport in low-collisionality LHD plasma is investigated in order to study the neoclassical transport optimization effect on thermal plasma transport with an optimization level typical of so-called ''advanced stellarators''. In the central region, a higher electron temperature is obtained in the optimized configuration, and transport analysis suggests the considerable effect of neoclassical transport on the electron heat transport assuming the ion-root level of radial electric field. The obtained experimental results support future reactor design in which the neoclassical and/or anomalous transports are reduced by magnetic field optimization in a non-axisymmetric configuration. (author)

Development and validation of a new solver based on the interfacial area transport equation for the numerical simulation of sub-cooled boiling with OpenFOAM CFD code for nuclear safety applications

Energy Technology Data Exchange (ETDEWEB)

Alali, Abdullah

2014-02-21

The one-group interfacial area transport equation has been coupled to a wall heat flux partitioning model in the framework of two-phase Eulerian approach using the OpenFOAM CFD code for better prediction of subcooled boiling phenomena which is essential for safety analysis of nuclear reactors. The interfacial area transport equation has been modified to include the effect of bubble nucleation at the wall and condensation by subcooled liquid in the bulk that governs the non-uniform bubble size distribution.

Development and validation of a new solver based on the interfacial area transport equation for the numerical simulation of sub-cooled boiling with OpenFOAM CFD code for nuclear safety applications

International Nuclear Information System (INIS)

Alali, Abdullah

2014-01-01

The one-group interfacial area transport equation has been coupled to a wall heat flux partitioning model in the framework of two-phase Eulerian approach using the OpenFOAM CFD code for better prediction of subcooled boiling phenomena which is essential for safety analysis of nuclear reactors. The interfacial area transport equation has been modified to include the effect of bubble nucleation at the wall and condensation by subcooled liquid in the bulk that governs the non-uniform bubble size distribution.

STELLTRANS: A Transport Analysis Suite for Stellarators

Science.gov (United States)

Mittelstaedt, Joseph; Lazerson, Samuel; Pablant, Novimir; Weir, Gavin; W7-X Team

2016-10-01

The stellarator transport code STELLTRANS allows us to better analyze the power balance in W7-X. Although profiles of temperature and density are measured experimentally, geometrical factors are needed in conjunction with these measurements to properly analyze heat flux densities in stellarators. The STELLTRANS code interfaces with VMEC to find an equilibrium flux surface configuration and with TRAVIS to determine the RF heating and current drive in the plasma. Stationary transport equations are then considered which are solved using a boundary value differential equation solver. The equations and quantities considered are averaged over flux surfaces to reduce the system to an essentially one dimensional problem. We have applied this code to data from W-7X and were able to calculate the heat flux coefficients. We will also present extensions of the code to a predictive capacity which would utilize DKES to find neoclassical transport coefficients to update the temperature and density profiles.

A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold

Directory of Open Access Journals (Sweden)

Abimbola Abolarinwa

2014-08-01

Full Text Available In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwise differential inequality for heat kernel. The consequences of which are various gradient and Harnack estimates for all positive solutions to the heat equation on compact manifold.

Application of the finite element method to the neutron transport equation

International Nuclear Information System (INIS)

Martin, W.R.

1976-01-01

This paper examines the theoretical and practical application of the finite element method to the neutron transport equation. It is shown that in principle the system of equations obtained by application of the finite element method can be solved with certain physical restrictions concerning the criticality of the medium. The convergence of this approximate solution to the exact solution with mesh refinement is examined, and a non-optical estimate of the convergence rate is obtained analytically. It is noted that the numerical results indicate a faster convergence rate and several approaches to obtain this result analytically are outlined. The practical application of the finite element method involved the development of a computer code capable of solving the neutron transport equation in 1-D plane geometry. Vacuum, reflecting, or specified incoming boundary conditions may be analyzed, and all are treated as natural boundary conditions. The time-dependent transport equation is also examined and it is shown that the application of the finite element method in conjunction with the Crank-Nicholson time discretization method results in a system of algebraic equations which is readily solved. Numerical results are given for several critical slab eigenvalue problems, including anisotropic scattering, and the results compare extremely well with benchmark results. It is seen that the finite element code is more efficient than a standard discrete ordinates code for certain problems. A problem with severe heterogeneities is considered and it is shown that the use of discontinuous spatial and angular elements results in a marked improvement in the results. Finally, time-dependent problems are examined and it is seen that the phenomenon of angular mode separation makes the numerical treatment of the transport equation in slab geometry a considerable challenge, with the result that the angular mesh has a dominant effect on obtaining acceptable solutions

Two-scale approach to oscillatory singularly perturbed transport equations

CERN Document Server

Frénod, Emmanuel

2017-01-01

This book presents the classical results of the two-scale convergence theory and explains – using several figures – why it works. It then shows how to use this theory to homogenize ordinary differential equations with oscillating coefficients as well as oscillatory singularly perturbed ordinary differential equations. In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations. Further, it introduces readers to the two-scale numerical methods that can be built from the previous approaches to solve oscillatory singularly perturbed transport equations (ODE and hyperbolic PDE) and demonstrates how they can be used efficiently. This book appeals to master’s and PhD students interested in homogenization and numerics, as well as to the Iter community.

Transport equations in an enzymatic glucose fuel cell

Science.gov (United States)

Jariwala, Soham; Krishnamurthy, Balaji

2018-01-01

A mathematical model is developed to study the effects of convective flux and operating temperature on the performance of an enzymatic glucose fuel cell with a membrane. The model assumes isothermal operating conditions and constant feed rate of glucose. The glucose fuel cell domain is divided into five sections, with governing equations describing transport characteristics in each region, namely - anode diffusion layer, anode catalyst layer (enzyme layer), membrane, cathode catalyst layer and cathode diffusion layer. The mass transport is assumed to be one-dimensional and the governing equations are solved numerically. The effects flow rate of glucose feed on the performance of the fuel cell are studied as it contributes significantly to the convective flux. The effects of operating temperature on the performance of a glucose fuel cell are also modeled. The cell performances are compared using cell polarization curves, which were found compliant with experimental observations.

Two analytic transport equation solutions for particular cases of particle history

International Nuclear Information System (INIS)

Simovic, R.

1997-01-01

For anisotropic scattering and plane geometry, the linear transport equation of particles generated by a monodirectional unit source A(x,μ) = δ(x-0)δ(μ - μ 0 ) > 0, can be stated in the form of an integral equation

A stochastic solution of the advective transport equation with uncertainty

International Nuclear Information System (INIS)

Williams, M.M.R.

1991-01-01

A model has been developed for calculating the transport of water-borne radionuclides through layers of porous materials, such as rock or clay. The model is based upon a purely advective transport equation, in which the fluid velocity is a random variable, thereby simulating dispersion in a more realistic manner than the ad hoc introduction of a dispersivity. In addition to a random velocity field, which is an observable physical phenomenon, allowance is made for uncertainty in our knowledge of the parameters which enter the equation, e.g. the retardation coefficient. This too, is assumed to be a random variable and contributes to the stochasticity of the resulting partial differential equation of transport. The stochastic differential equation can be solved analytically and then ensemble averages taken over the associated probability distribution of velocity and retardation coefficient. A method based upon a novel form of the central limit theorem of statistics is employed to obtain tractable solutions of a system consisting of many serial legs of varying properties. One interesting conclusion is that the total flux out of a medium is significantly underestimated by using the deterministic solution with an average transit time compared with that from the stochastically averaged solution. The theory is illustrated numerically for a number of physically relevant cases. (author) 8 figs., 4 tabs., 7 refs

Results from transient transport experiments in Rijnhuizen tokamak project: Heat convection, transport barriers and 'non-local' effects

International Nuclear Information System (INIS)

Mantica, P.; Gorini, G.; Hogeweij, G.M.D.; Kloe, J. de; Lopez Cardozo, N.J.; Schilham, A.M.R.

2001-01-01

An overview of experimental transport studies performed on the Rijnhuizen Tokamak Project (RTP) using transient transport techniques in both Ohmic and ECH dominated plasmas is presented. Modulated Electron Cyclotron Heating (ECH) and oblique pellet injection (OPI) have been used to induce electron temperature (T e ) perturbations at different radial locations. These were used to probe the electron transport barriers observed near low order rational magnetic surfaces in ECH dominated steady-state RTP plasmas. Layers of inward electron heat convection in off-axis ECH plasmas were detected with modulated ECH. This suggests that RTP electron transport barriers consist of heat pinch layers rather than layers of low thermal diffusivity. In a different set of experiments, OPI triggered a transient rise of the core T e due to an increase of the T e gradient in the 1< q<2 region. These transient transport barriers were probed with modulated ECH and found to be due to a transient drop of the electron heat diffusivity, except for off-axis ECH plasmas, where a transient inward pinch is also observed. Transient transport studies in RTP could not solve this puzzling interplay between heat diffusion and convection in determining an electron transport barrier. They nevertheless provided challenging experimental evidence both for theoretical modelling and for future experiments. (author)

Mixed-hybrid finite element method for the transport equation and diffusion approximation of transport problems; Resolution de l'equation du transport par une methode d'elements finis mixtes-hybrides et approximation par la diffusion de problemes de transport

Energy Technology Data Exchange (ETDEWEB)

Cartier, J

2006-04-15

This thesis focuses on mathematical analysis, numerical resolution and modelling of the transport equations. First of all, we deal with numerical approximation of the solution of the transport equations by using a mixed-hybrid scheme. We derive and study a mixed formulation of the transport equation, then we analyse the related variational problem and present the discretization and the main properties of the scheme. We particularly pay attention to the behavior of the scheme and we show its efficiency in the diffusion limit (when the mean free path is small in comparison with the characteristic length of the physical domain). We present academical benchmarks in order to compare our scheme with other methods in many physical configurations and validate our method on analytical test cases. Unstructured and very distorted meshes are used to validate our scheme. The second part of this thesis deals with two transport problems. The first one is devoted to the study of diffusion due to boundary conditions in a transport problem between two plane plates. The second one consists in modelling and simulating radiative transfer phenomenon in case of the industrial context of inertial confinement fusion. (author)

Current & Heat Transport in Graphene Nanoribbons: Role of Non-Equilibrium Phonons

Science.gov (United States)

Pennington, Gary; Finkenstadt, Daniel

2010-03-01

The conducting channel of a graphitic nanoscale device is expected to experience a larger degree of thermal isolation when compared to traditional inversion channels of electronic devices. This leads to enhanced non-equilibrium phonon populations which are likely to adversely affect the mobility of graphene-based nanoribbons due to enhanced phonon scattering. Recent reports indicating the importance of carrier scattering with substrate surface polar optical phonons in carbon nanotubes^1 and graphene^2,3 show that this mechanism may allow enhanced heat removal from the nanoribbon channel. To investigate the effects of hot phonon populations on current and heat conduction, we solve the graphene nanoribbon multiband Boltzmann transport equation. Monte Carlo transport techniques are used since phonon populations may be tracked and updated temporally.^4 The electronic structure is solved using the NRL Tight-Binding method,^5 where carriers are scattered by confined acoustic, optical, edge and substrate polar optical phonons. [1] S. V. Rotkin et al., Nano Lett. 9, 1850 (2009). [2] J. H. Chen, C. Jang, S. Xiao, M. Ishigami and M. S. Fuhrer, Nature Nanotech. 3, 206 (2008). [3] V. Perebeinos and P. Avouris, arXiv:0910.4665v1 [cond-mat.mes-hall] (2009). [4] P. Lugli et al., Appl. Phys. Lett. 50, 1251 (1987). [5] D. Finkenstadt, G. Pennington & M.J. Mehl, Phys. Rev. B 76, 121405(R) (2007).

Transport equations, Level Set and Eulerian mechanics. Application to fluid-structure coupling

International Nuclear Information System (INIS)

Maitre, E.

2008-11-01

My works were devoted to numerical analysis of non-linear elliptic-parabolic equations, to neutron transport equation and to the simulation of fabrics draping. More recently I developed an Eulerian method based on a level set formulation of the immersed boundary method to deal with fluid-structure coupling problems arising in bio-mechanics. Some of the more efficient algorithms to solve the neutron transport equation make use of the splitting of the transport operator taking into account its characteristics. In the present work we introduced a new algorithm based on this splitting and an adaptation of minimal residual methods to infinite dimensional case. We present the case where the velocity space is of dimension 1 (slab geometry) and 2 (plane geometry) because the splitting is simpler in the former

Monte Carlo simulation of neutron transport phenomena

International Nuclear Information System (INIS)

Srinivasan, P.

2009-01-01

Neutron transport is one of the central problems in nuclear reactor related studies and other applied sciences. Some of the major applications of neutron transport include nuclear reactor design and safety, criticality safety of fissile material handling, neutron detector design and development, nuclear medicine, assessment of radiation damage to materials, nuclear well logging, forensic analysis etc. Most reactor and dosimetry studies assume that neutrons diffuse from regions of high to low density just like gaseous molecules diffuse to regions of low concentration or heat flow from high to low temperature regions. However while treatment of gaseous or heat diffusion is quite accurately modeled, treatment of neutron transport as simple diffusion is quite limited. In simple diffusion, the neutron trajectories are irregular, random and zigzag - where as in neutron transport low reaction cross sections (1 barn- 10 -24 cm 2 ) lead to long mean free paths which again depend on the nature and irregularities of the medium. Hence a more accurate representation of the neutron transport evolved based on the Boltzmann equation of kinetic gas theory. In fact the neutron transport equation is a linearized version of the Boltzmann gas equation based on neutron conservation with seven independent variables. The transport equation is difficult to solve except in simple cases amenable to numerical methods. The diffusion (equation) approximation follows from removing the angular dependence of the neutron flux

Numerical investigation into the highly nonlinear heat transfer equation with bremsstrahlung emission in the inertial confinement fusion plasmas

Energy Technology Data Exchange (ETDEWEB)

Habibi, M.; Oloumi, M.; Hosseinkhani, H.; Magidi, S. [Plasma and Fusion Research School, Nuclear Science and Technology Research Institute, Tehran (Iran, Islamic Republic of)

2015-10-15

A highly nonlinear parabolic partial differential equation that models the electron heat transfer process in laser inertial fusion has been solved numerically. The strong temperature dependence of the electron thermal conductivity and heat loss term (Bremsstrahlung emission) makes this a highly nonlinear process. In this case, an efficient numerical method is developed for the energy transport mechanism from the region of energy deposition into the ablation surface by a combination of the Crank-Nicolson scheme and the Newton-Raphson method. The quantitative behavior of the electron temperature and the comparison between analytic and numerical solutions are also investigated. For more clarification, the accuracy and conservation of energy in the computations are tested. The numerical results can be used to evaluate the nonlinear electron heat conduction, considering the released energy of the laser pulse at the Deuterium-Tritium (DT) targets and preheating by heat conduction ahead of a compression shock in the inertial confinement fusion (ICF) approach. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

Tokamak electron heat transport by direct numerical simulation of small scale turbulence

International Nuclear Information System (INIS)

Labit, B.

2002-10-01

In a fusion machine, understanding plasma turbulence, which causes a degradation of the measured energy confinement time, would constitute a major progress in this field. In tokamaks, the measured ion and electron thermal conductivities are of comparable magnitude. The possible sources of turbulence are the temperature and density gradients occurring in a fusion plasma. Whereas the heat losses in the ion channel are reasonably well understood, the origin of the electron losses is more uncertain. In addition to the radial velocity associated to the fluctuations of the electric field, electrons are more affected than ions by the magnetic field fluctuations. In experiments, the confinement time can be conveniently expressed in terms of dimensionless parameters. Although still somewhat too imprecise, these scaling laws exhibit strong dependencies on the normalized pressure β or the normalized Larmor radius, ρ * . The present thesis assesses whether a tridimensional, electromagnetic, nonlinear fluid model of plasma turbulence driven by a specific instability can reproduce the dependence of the experimental electron heat losses on the dimensionless parameters β and ρ * . The investigated interchange instability is the Electron Temperature Gradient driven one (ETG). The model is built by using the set of Braginskii equations. The developed simulation code is global in the sense that a fixed heat flux is imposed at the inner boundary, leaving the gradients free to evolve. From the nonlinear simulations, we have put in light three characteristics for the ETG turbulence: the turbulent transport is essentially electrostatic; the potential and pressure fluctuations form radially elongated cells called streamers; the transport level is very low compared to the experimental values. The thermal transport dependence study has shown a very small role of the normalized pressure, which is in contradiction with the Ohkama's formula. On the other hand, the crucial role of the

Heat transport system

International Nuclear Information System (INIS)

Pierce, B.L.

1978-01-01

A heat transport system of small size which can be operated in any orientation consists of a coolant loop containing a vaporizable liquid as working fluid and includes in series a vaporizer, a condenser and two one-way valves and a pressurizer connected to the loop between the two valves. The pressurizer may be divided into two chambers by a flexible diaphragm, an inert gas in one chamber acts as a pneumatic spring for the system. This system is suitable for use in a nuclear-powered artificial heart

A non-local model analysis of heat pulse propagation

International Nuclear Information System (INIS)

Iwasaki, T.; Itoh, S.I.; Yagi, M.; Stroth, U.

1998-01-01

The anomalous transport in high temperature plasma has been studied for a long time, from the beginning of the fusion research. Since the electron channel in stellarators and tokamaks is clearly anomalous, it is of fundamental importance to investigate the electron heat diffusivity coefficient, χ e and to understand the physical mechanism. Recently, the experimental data for the transient transport of the heat pulse propagation in fusion plasma has been accumulated. An observation was reported on W7-AS which the heat flux changes faster than the change of the temperature profile, responding to the switching on off of the central heating power. The observation on the transient response has simulated the transport modeling, e.g., the critical marginality which implies the existence of a finite threshold in ∇T for the excitation of the turbulence, or the model in which the thermal conductivity is assumed to depend on the heating power. Extensive study is made by use of these models, and the critical marginally model seems to be insufficient to explain various transient transport. The rapid change of the plasma state and its hysteresis nature were successfully modeled by a heating-power-dependent model. The foundation of this model, however, is left for future work. The development of the transport modeling remains to be an urgent problem. In this paper, we investigate the role of the non-locality of the plasma transport in the study of the heat pulse propagation. For this purpose, a model equation is proposed, in which the non-local effect is taken into account in the heat flux. The properties of this model are investigated by performing a transport simulation. The organization of this paper is as follows: In Sec. II, the model equation is proposed and the properties of the model are explained. Using the model equation, the switching on off experiment is simulated in Sec. III. Summary and discussion are given in Sec. IV. (author)

Ballistic near-field heat transport in dense many-body systems

Science.gov (United States)

Latella, Ivan; Biehs, Svend-Age; Messina, Riccardo; Rodriguez, Alejandro W.; Ben-Abdallah, Philippe

2018-01-01

Radiative heat transport mediated by near-field interactions is known to be superdiffusive in dilute, many-body systems. Here we use a generalized Landauer theory of radiative heat transfer in many-body planar systems to demonstrate a nonmonotonic transition from superdiffusive to ballistic transport in dense systems. We show that such a transition is associated to a change of the polarization of dominant modes. Our findings are complemented by a quantitative study of the relaxation dynamics of the system in the different regimes of heat transport. This result could have important consequences on thermal management at nanoscale of many-body systems.

Alternative formulation of the monokinetic transport equation

International Nuclear Information System (INIS)

Coppa, G.; Ravetto, P.; Sumini, M.

1985-01-01

After recalling a technique already exploited in stationary neutron transport, the dynamic linear monokinetic equation for general geometry is cast into an integro-differential form where a second order space Laplace operator and both a second and first time derivatives appear. The introduced unknowns are given a physical interpretation for plane geometry and their relations with the total flux and current are derived

The accuracy of time dependent transport equation ergodic approximation

International Nuclear Information System (INIS)

Stancic, V.

1995-01-01

In order to predict the accuracy of the ergodic approximation for solving the time dependent transport equation, a comparison with respect to multiple collision and time finite difference methods, has been considered. (author)

Cable Connected Spinning Spacecraft, 1. the Canonical Equations, 2. Urban Mass Transportation, 3

Science.gov (United States)

Sitchin, A.

1972-01-01

Work on the dynamics of cable-connected spinning spacecraft was completed by formulating the equations of motion by both the canonical equations and Lagrange's equations and programming them for numerical solution on a digital computer. These energy-based formulations will permit future addition of the effect of cable mass. Comparative runs indicate that the canonical formulation requires less computer time. Available literature on urban mass transportation was surveyed. Areas of the private rapid transit concept of urban transportation are also studied.

Enhanced heat transport in environmental systems using microencapsulated phase change materials

Science.gov (United States)

Colvin, D. P.; Mulligan, J. C.; Bryant, Y. G.

1992-01-01

A methodology for enhanced heat transport and storage that uses a new two-component fluid mixture consisting of a microencapsulated phase change material (microPCM) for enhanced latent heat transport is outlined. SBIR investigations for NASA, USAF, SDIO, and NSF since 1983 have demonstrated the ability of the two-component microPCM coolants to provide enhancements in heat transport up to 40 times over that of the carrier fluid alone, enhancements of 50 to 100 percent in the heat transfer coefficient, practically isothermal operation when the coolant flow is circulated in an optimal manner, and significant reductions in pump work.

Solution and study of nodal neutron transport equation applying the LTSN-DiagExp method

International Nuclear Information System (INIS)

Hauser, Eliete Biasotto; Pazos, Ruben Panta; Vilhena, Marco Tullio de; Barros, Ricardo Carvalho de

2003-01-01

In this paper we report advances about the three-dimensional nodal discrete-ordinates approximations of neutron transport equation for Cartesian geometry. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S N equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS N method, first applying the Laplace transform to the set of the nodal S N equations and then obtained the solution by symbolic computation. We include the LTS N method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS N approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. (author)

Integral transform method for solving time fractional systems and fractional heat equation

Directory of Open Access Journals (Sweden)

Arman Aghili

2014-01-01

Full Text Available In the present paper, time fractional partial differential equation is considered, where the fractional derivative is defined in the Caputo sense. Laplace transform method has been applied to obtain an exact solution. The authors solved certain homogeneous and nonhomogeneous time fractional heat equations using integral transform. Transform method is a powerful tool for solving fractional singular Integro - differential equations and PDEs. The result reveals that the transform method is very convenient and effective.

Experimental study on the supercritical startup and heat transport capability of a neon-charged cryogenic loop heat pipe

International Nuclear Information System (INIS)

Guo, Yuandong; Lin, Guiping; He, Jiang; Bai, Lizhan; Zhang, Hongxing; Miao, Jianyin

2017-01-01

Highlights: • A neon-charged CLHP integrated with a G-M cryocooler was designed and investigated. • The CLHP can realize the supercritical startup with an auxiliary heat load of 1.5 W. • Maximum heat transport capability of the CLHP was 4.5 W over a distance of 0.6 m. • There existed an optimum auxiliary heat load to expedite the supercritical startup. • There existed an optimum charged pressure to reach the largest heat transfer limit. - Abstract: Neon-charged cryogenic loop heat pipe (CLHP) can realize efficient cryogenic heat transport in the temperature range of 30–40 K, and promises great application potential in the thermal control of future space infrared exploration system. In this work, extensive experimental studies on the supercritical startup and heat transport capability of a neon-charged CLHP integrated with a G-M cryocooler were carried out, where the effects of the auxiliary heat load applied to the secondary evaporator and charged pressure of the working fluid were investigated. Experimental results showed that the CLHP could successfully realize the supercritical startup with an auxiliary heat load of 1.5 W, and there existed an optimum auxiliary heat load and charged pressure of the working fluid respectively, to achieve the maximum temperature drop rate of the primary evaporator during the supercritical startup. The CLHP could reach a maximum heat transport capability of 4.5 W over a distance of 0.6 m corresponding to the optimum charged pressure of the working fluid; however, the heat transport capability decreased with the increase of the auxiliary heat load. Furthermore, the inherent mechanisms responsible for the phenomena observed in the experiments were analyzed and discussed, to provide a better understanding from the theoretical view.

Solving the transport equation with quadratic finite elements: Theory and applications

International Nuclear Information System (INIS)

Ferguson, J.M.

1997-01-01

At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids

Heat and Fission Product Transport in a Molten U-Zr-O Pool With Crust

International Nuclear Information System (INIS)

Yun, J.I.; Suh, K.Y.; Kang, C.S.

2002-01-01

Heat transfer and fluid flow in a molten pool are influenced by internal volumetric heat generated from the radioactive decay of fission product species retained in the pool. The pool superheat is determined based on the overall energy balance that equates the heat production rate to the heat loss rate. Decay heat of fission products in the pool was estimated by product of the mass concentration and energy conversion factor of each fission product. For the calculation of heat generation rate in the pool, twenty-nine elements were chosen and classified by their chemical properties. The mass concentration of a fission product is obtained from released fraction and the tabular output of the ORIGEN 2 code. The initial core and pool inventories at each time can also be estimated using ORIGEN 2. The released fraction of each fission product is calculated based on the bubble dynamics and mass transport. Numerical analysis was performed for the TMI-2 accident. The pool is assumed to be a partially filled hemispherical geometry and the change of pool geometry during the numerical calculation was neglected. Results of the numerical calculation revealed that the peak temperature of the molten pool significantly decreased and most of the volatile fission products were released from the molten pool during the accident. (authors)

New diffusion-like solutions of one-speed transport equations in spherical geometry

International Nuclear Information System (INIS)

Sahni, D.C.

1988-01-01

Stationary, one-speed, spherically symmetric transport equations are considered in a conservative medium. Closed-form expressions are obtained for the angular flux ψ(r, μ) that yield a total flux varying as 1/r by using Sonine transforms. Properties of this solution are studied and it is shown that the solution can not be identified as a diffusion mode solution of the transport equation. Limitations of the Sonine transform technique are noted. (author)

Bayesian recovery of the initial condition for the heat equation

NARCIS (Netherlands)

Knapik, B.T.; Vaart, van der A.W.; Zanten, van J.H.

2011-01-01

We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying "smoothness" and show that the corresponding posterior distributions contract

The relationship between the local temperature and the local heat flux within a one-dimensional semi-infinite domain of heat wave propagation

Directory of Open Access Journals (Sweden)

Kulish Vladimir V.

2003-01-01

Full Text Available The relationship between the local temperature and the local heat flux has been established for the homogeneous hyperbolic heat equation. This relationship has been written in the form of a convolution integral involving the modified Bessel functions. The scale analysis of the hyperbolic energy equation has been performed and the dimensionless criterion for the mode of energy transport, similar to the Reynolds criterion for the flow regimes, has been proposed. Finally, the integral equation, relating the local temperature and the local heat flux, has been solved numerically for those processes of surface heating whose time scale is of the order of picoseconds.

A modified two-fluid model for the application of two-group interfacial area transport equation

International Nuclear Information System (INIS)

Sun, X.; Ishii, M.; Kelly, J.

2003-01-01

This paper presents the modified two-fluid model that is ready to be applied in the approach of the two-group interfacial area transport equation. The two-group interfacial area transport equation was developed to provide a mechanistic constitutive relation for the interfacial area concentration in the two-fluid model. In the two-group transport equation, bubbles are categorized into two groups: spherical/distorted bubbles as Group 1 while cap/slug/churn-turbulent bubbles as Group 2. Therefore, this transport equation can be employed in the flow regimes spanning from bubbly, cap bubbly, slug to churn-turbulent flows. However, the introduction of the two groups of bubbles requires two gas velocity fields. Yet it is not desirable to solve two momentum equations for the gas phase alone. In the current modified two-fluid model, a simplified approach is proposed. The momentum equation for the averaged velocity of both Group-1 and Group-2 bubbles is retained. By doing so, the velocity difference between Group-1 and Group-2 bubbles needs to be determined. This may be made either based on simplified momentum equations for both Group-1 and Group-2 bubbles or by a modified drift-flux model

Elliptic random-walk equation for suspension and tracer transport in porous media

DEFF Research Database (Denmark)

Shapiro, Alexander; Bedrikovetsky, P. G.

2008-01-01

. The new theory predicts delay of the maximum of the tracer, compared to the velocity of the flow, while its forward "tail" contains much more particles than in the solution of the classical parabolic (advection-dispersion) equation. This is in agreement with the experimental observations and predictions......We propose a new approach to transport of the suspensions and tracers in porous media. The approach is based on a modified version of the continuous time random walk (CTRW) theory. In the framework of this theory we derive an elliptic transport equation. The new equation contains the time...... of the CTRW theory. (C) 2008 Elsevier B.V. All rights reserved....

Electron heat transport studies using transient phenomena in ASDEX Upgrade

International Nuclear Information System (INIS)

Jacchia, A.; Angioni, C.; Manini, A.; Ryter, F.; Apostoliceanu, M.; Conway, G.; Fahrbach, H.-U.; Kirov, K.K.; Leuterer, F.; Reich, M.; Sutttrop, W.; Cirant, S.; Mantica, P.; De Luca, F.; Weiland, J.

2005-01-01

Experiments in tokamaks suggest that a critical gradient length may cause the resilient behavior of T e profiles, in the absence of ITBs. This agrees in general with ITG/TEM turbulence physics. Experiments in ASDEX Upgrade using modulation techniques with ECH and/or cold pulses demonstrate the existence of a threshold in R/L Te when T e >T i and T e ≤T i . For T e >T i linear stability analyses indicate that electron heat transport is dominated by TEM modes. They agree in the value of the threshold (both T e and n e ) and for the electron heat transport increase above the threshold. The stabilization of TEM modes by collisions yielded by gyro-kinetic calculations, which suggests a transition from TEM to ITG dominated transport at high collisionality, is experimentally demonstrated by comparing heat pulse and steady-state diffusivities. For the T e ∼T i discharges above the threshold the resilience, normalized by T e 3/2 , is similar to that of the TEM dominated cases, despite very different conditions. The heat pinch predicted by fluid modeling of ITG/TEM turbulence is investigated by perturbative transport in off-axis ECH-heated discharges. (author)

Long-distance heat transport by hot water

International Nuclear Information System (INIS)

Munser, H.; Reetz, B.

1990-01-01

From the analysis of the centralized heat supply in the GDR energy-economical and ecological indispensable developments of long-distance heat systems in conurbation are derived. The heat extraction from a nuclear power plant combined with long- distance hot-water transport over about 110 kilometres is investigated and presented as a possibility to perspective base load heat demands for the district around Dresden. By help of industrial-economic, hydraulic and thermic evaluations of first design variants of the transit system the acceptance of this ecologic and energetic preferred solution is proved and requirements for its realization are shown

A Green function of neutron transport equation

International Nuclear Information System (INIS)

Simovic, R.

1993-01-01

In this paper the angularly dependent Green function of the neutron transport equation is derived analytically and approximately. By applying the analytical FDPN approximation up to eighth order, numerical values of the Green functions are obtained with the accuracy of six significant figures in the whole range of parameter c, angle cosine μ and distances x up to the ten optical lengths from the neutron source. (author)

Analytical solution for the transport equation for neutral particles in cylindrical and Cartesian geometry

International Nuclear Information System (INIS)

Goncalves, Glenio Aguiar

2003-01-01

In this work, we are reported analytical solutions for the transport equation for neutral particles in cylindrical and cartesian geometry. For the cylindrical geometry, it is applied the Hankel transform of order zero in the S N approximation of the one-dimensional cylindrical transport equation, assuming azimuthal symmetry and isotropic scattering. This procedure is coined HTSN method. The anisotropic problem is handled using the decomposition method, generating a recursive approach, which the HTSN solution is used as initial condition. For cartesian geometry, the one and two dimensional transport equation is derived in the angular variable as many time as the degree of the anisotropic scattering. This procedure leads to set of integro-differential plus one differential equation that can be really solved by the variable separation method. Following this procedure, it was possible to come out with the Case solution for the one-dimensional problem. Numerical simulations are reported for the cylindrical transport problem both isotropic and anisotropic case of quadratic degree. (author)

Modification of the finite element heat and mass transfer code (FEHM) to model multicomponent reactive transport

International Nuclear Information System (INIS)

Viswanathan, H.S.

1996-08-01

The finite element code FEHMN, developed by scientists at Los Alamos National Laboratory (LANL), is a three-dimensional finite element heat and mass transport simulator that can handle complex stratigraphy and nonlinear processes such as vadose zone flow, heat flow and solute transport. Scientists at LANL have been developing hydrologic flow and transport models of the Yucca Mountain site using FEHMN. Previous FEHMN simulations have used an equivalent Kd model to model solute transport. In this thesis, FEHMN is modified making it possible to simulate the transport of a species with a rigorous chemical model. Including the rigorous chemical equations into FEHMN simulations should provide for more representative transport models for highly reactive chemical species. A fully kinetic formulation is chosen for the FEHMN reactive transport model. Several methods are available to computationally implement a fully kinetic formulation. Different numerical algorithms are investigated in order to optimize computational efficiency and memory requirements of the reactive transport model. The best algorithm of those investigated is then incorporated into FEHMN. The algorithm chosen requires for the user to place strongly coupled species into groups which are then solved for simultaneously using FEHMN. The complete reactive transport model is verified over a wide variety of problems and is shown to be working properly. The new chemical capabilities of FEHMN are illustrated by using Los Alamos National Laboratory's site scale model of Yucca Mountain to model two-dimensional, vadose zone 14 C transport. The simulations demonstrate that gas flow and carbonate chemistry can significantly affect 14 C transport at Yucca Mountain. The simulations also prove that the new capabilities of FEHMN can be used to refine and buttress already existing Yucca Mountain radionuclide transport studies

Integration of the time-dependent heat equation in the fuel rod performance program IAMBUS

International Nuclear Information System (INIS)

West, G.

1982-01-01

An iterative numerical method for integration of the time-dependent heat equation is described. No presuppositions are made for the dependency of the thermal conductivity and heat capacity on space, time and temperature. (orig.) [de

Sn approach applied to the solution of transport equation

International Nuclear Information System (INIS)

Lopes, J.P.

1973-09-01

In this work the origin of the Transport Theory is considered and the Transport Equation for the movement of the neutron in a system is established in its more general form, using the laws of nuclear physics. This equation is used as the starting point for development, under adequate assumptions, of simpler models that render the problem suitable for numerical solution. Representation of this model in different geometries is presented. The different processes of nuclear physics are introduced briefly and discussed. In addition, the boundary conditions for the different cases and a general procedure for the application of the Conservation Law are stated. The last chapter deals specifically with the S n method, its development, definitions and generalities. Computational schemes for obtaining the S n solution in spherical and cylindrical geometry, and convergence acceleration methods are also developed. (author)

On the derivation of vector radiative transfer equation for polarized radiative transport in graded index media

International Nuclear Information System (INIS)

Zhao, J.M.; Tan, J.Y.; Liu, L.H.

2012-01-01

Light transport in graded index media follows a curved trajectory determined by Fermat's principle. Besides the effect of variation of the refractive index on the transport of radiative intensity, the curved ray trajectory will induce geometrical effects on the transport of polarization ellipse. This paper presents a complete derivation of vector radiative transfer equation for polarized radiation transport in absorption, emission and scattering graded index media. The derivation is based on the analysis of the conserved quantities for polarized light transport along curved trajectory and a novel approach. The obtained transfer equation can be considered as a generalization of the classic vector radiative transfer equation that is only valid for uniform refractive index media. Several variant forms of the transport equation are also presented, which include the form for Stokes parameters defined with a fixed reference and the Eulerian forms in the ray coordinate and in several common orthogonal coordinate systems.

Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation

International Nuclear Information System (INIS)

Panta Pazos, Ruben; Biasotto Hauser, Eliete; Tullio de Vilhena, Marco

2002-01-01

In the last decade Vilhena and coworkers reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional S N equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTS N method, which consists in the application of the Laplace transform to the set of nodal S N equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of S N up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal S N equations for N up to 16 and we begin the convergence of the S N nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation. (authors)

High efficiency heat transport and power conversion system for cascade

International Nuclear Information System (INIS)

Maya, I.; Bourque, R.F.; Creedon, R.L.; Schultz, K.R.

1985-02-01

The Cascade ICF reactor features a flowing blanket of solid BeO and LiAlO 2 granules with very high temperature capability (up to approx. 2300 K). The authors present here the design of a high temperature granule transport and heat exchange system, and two options for high efficiency power conversion. The centrifugal-throw transport system uses the peripheral speed imparted to the granules by the rotating chamber to effect granule transport and requires no additional equipment. The heat exchanger design is a vacuum heat transfer concept utilizing gravity-induced flow of the granules over ceramic heat exchange surfaces. A reference Brayton power cycle is presented which achieves 55% net efficiency with 1300 K peak helium temperature. A modified Field steam cycle (a hybrid Rankine/Brayton cycle) is presented as an alternate which achieves 56% net efficiency

On the Boltzmann Equation of Thermal Transport for Interacting Phonons and Electrons

Directory of Open Access Journals (Sweden)

Amelia Carolina Sparavigna

2016-05-01

Full Text Available The thermal transport in a solid can be determined by means of the Boltzmann equations regarding its distributions of phonons and electrons, when the solid is subjected to a thermal gradient. After solving the coupled equations, the related thermal conductivities can be obtained. Here we show how to determine the coupled equations for phonons and electrons.

Blow-Up Time for Nonlinear Heat Equations with Transcendental Nonlinearity

Directory of Open Access Journals (Sweden)

Hee Chul Pak

2012-01-01

Full Text Available A blow-up time for nonlinear heat equations with transcendental nonlinearity is investigated. An upper bound of the first blow-up time is presented. It is pointed out that the upper bound of the first blow-up time depends on the support of the initial datum.

A review on transportation of heat energy over long distance. Exploratory development

Energy Technology Data Exchange (ETDEWEB)

Ma, Q.; Wang, R.Z. [Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240 (China); Luo, L.; Sauce, G. [LOCIE, Polytech' Savoie, Campus Scientifique, Savoie Technolac, 73376 Le Bourget-Du-Lac cedex (France)

2009-08-15

This paper presents a review on transportation of heat energy over long distance. For the transportation of high-temperature heat energy, the chemical catalytic reversible reaction is almost the only way available, and there are several reactions have been studied. For the relatively low-temperature heat energy, which exists widely as waste heat, there are mainly five researching aspects at present: chemical reversible reactions, phase change thermal energy storage and transportation, hydrogen-absorbing alloys, solid-gas adsorption and liquid-gas absorption. The basic principles and the characteristics of these methods are discussed. (author)

Fluctuation theory for transport properties in multicomponent mixtures: thermodiffusion and heat conductivity

DEFF Research Database (Denmark)

Shapiro, Alexander

2004-01-01

The theory of transport properties in multicomponent gas and liquid mixtures, which was previously developed for diffusion coefficients, is extended onto thermodiffusion coefficients and heat conductivities. The derivation of the expressions for transport properties is based on the general statis...... of the heat conductivity coefficient for ideal gas. (C) 2003 Elsevier B.V. All rights reserved.......The theory of transport properties in multicomponent gas and liquid mixtures, which was previously developed for diffusion coefficients, is extended onto thermodiffusion coefficients and heat conductivities. The derivation of the expressions for transport properties is based on the general...

Solution of the transient Fourier heat conduction equation in r,phi geometry

International Nuclear Information System (INIS)

Kowa, E.; Ehnis, L.

1978-11-01

The two-dimensional transient Fourier heat conduction equation is solved in r,phi geometry for anisotropic materials with the computer program TERFI. The Alternating-Direction-Implicit method is used for the solution of this equation with specified start- and boundary conditions, temperature dependent material properties and space dependent heat sources. The solution area is devided in a mesh grid by the finite difference method. Slidely non-orthogonaly geometry (displacement of mesh grid) can be regarded. There were some difficulties in the treatment of the boundary conditions for the circularly-closed solution area because of the continuity of temperature and heat flux on the 0 0 /360 0 -line. This problem can be solved by an iterativ method with different starting points for the solution scheme. Emphasis was put on reaching reasonable computer time for the iteration. The computer code TERFI, programed in FORTRAN IV, is a modul of the program system RSYST. As an example the temperature distribution of a PWR fuel rod is calculated. (orig.) [de

Statistically derived conservation equations for fluid particle flows

International Nuclear Information System (INIS)

Reyes, J.N. Jr.

1989-01-01

The behavior of water droplets in a heated nuclear fuel channel is of significant interest to nuclear reactor safety studies pertaining to loss-of-coolant accidents. This paper presents the derivation of the mass, momentum, and energy conservation equations for a distribution of fluid particles (bubbles or droplets) transported by a continuous fluid medium. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior

Fem Formulation of Heat Transfer in Cylindrical Porous Medium

Science.gov (United States)

Azeem; Khaleed, H. M. T.; Soudagar, Manzoor Elahi M.

2017-08-01

Heat transfer in porous medium can be derived from the fundamental laws of flow in porous region ass given by Henry Darcy. The fluid flow and energy transport inside the porous medium can be described with the help of momentum and energy equations. The heat transfer in cylindrical porous medium differs from its counterpart in radial and axial coordinates. The present work is focused to discuss the finite element formulation of heat transfer in cylindrical porous medium. The basic partial differential equations are derived using Darcy law which is the converted into a set of algebraic equations with the help of finite element method. The resulting equations are solved by matrix method for two solution variables involved in the coupled equations.

PORFLO - a continuum model for fluid flow, heat transfer, and mass transport in porous media. Model theory, numerical methods, and computational tests

International Nuclear Information System (INIS)

Runchal, A.K.; Sagar, B.; Baca, R.G.; Kline, N.W.

1985-09-01

Postclosure performance assessment of the proposed high-level nuclear waste repository in flood basalts at Hanford requires that the processes of fluid flow, heat transfer, and mass transport be numerically modeled at appropriate space and time scales. A suite of computer models has been developed to meet this objective. The theory of one of these models, named PORFLO, is described in this report. Also presented are a discussion of the numerical techniques in the PORFLO computer code and a few computational test cases. Three two-dimensional equations, one each for fluid flow, heat transfer, and mass transport, are numerically solved in PORFLO. The governing equations are derived from the principle of conservation of mass, momentum, and energy in a stationary control volume that is assumed to contain a heterogeneous, anisotropic porous medium. Broad discrete features can be accommodated by specifying zones with distinct properties, or these can be included by defining an equivalent porous medium. The governing equations are parabolic differential equations that are coupled through time-varying parameters. Computational tests of the model are done by comparisons of simulation results with analytic solutions, with results from other independently developed numerical models, and with available laboratory and/or field data. In this report, in addition to the theory of the model, results from three test cases are discussed. A users' manual for the computer code resulting from this model has been prepared and is available as a separate document. 37 refs., 20 figs., 15 tabs

Heat transport the cold way

International Nuclear Information System (INIS)

Anon.

1981-01-01

A novel system for long-distance heat transport is being born in the 'Kernforschungsanlage Juelich' with the project being called 'Nukleare Fernenergie' (nuclear district energy). The project is also known as 'EVA/ADAM' [EVA = Einzelrohr-Versuchs-Anlage (single tube test facility); ADAM = Anlage mit Drei Adiabaten Methanisierungsreaktoren (plant provided with three adiabate methanising reactors)] and is based in principle on transport of energy in chemical bond within a closed loop. In the 60ies already this development was discussed both in the 'Kernforschungsanlage Juelich' and in the 'Rheinische Braunkohlenwerke' independent of each other. In 1975 these two organizations concluded a co-operation contract. (orig.) [de

Exact traveling wave solutions for a new nonlinear heat transfer equation

Directory of Open Access Journals (Sweden)

Gao Feng

2017-01-01

Full Text Available In this paper, we propose a new non-linear partial differential equation to de-scribe the heat transfer problems at the extreme excess temperatures. Its exact traveling wave solutions are obtained by using Cornejo-Perez and Rosu method.

Projection scheme for a reflected stochastic heat equation with additive noise

Science.gov (United States)

Higa, Arturo Kohatsu; Pettersson, Roger

2005-02-01

We consider a projection scheme as a numerical solution of a reflected stochastic heat equation driven by a space-time white noise. Convergence is obtained via a discrete contraction principle and known convergence results for numerical solutions of parabolic variational inequalities.

Quantum-mechanical transport equation for atomic systems.

Science.gov (United States)

Berman, P. R.

1972-01-01

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Quantum group and symmetry of the heat equation

International Nuclear Information System (INIS)

Jha, P.K.; Tripathy, K.C.

1992-07-01

The symmetry associated with the heat equation is re-examined using Lie's method. Under suitable choice of the arbitrary parameters in the Lie field, it is shown that the system exhibits SL(2,R) symmetry. On inspection of the q-analogue of the principal solution, we find broadening of the Gaussian-flow curve when q is varied from 1 to 0.002. The q-analogue of the general solution predicts the existence of additional degeneracy. (author). 8 refs, 1 fig

CHMTRNS, Non-Equilibrium Chemical Transport Code

International Nuclear Information System (INIS)

Noorishad, J.; Carnahan, C.L.; Benson, L.V.

1998-01-01

1 - Description of program or function: CHMTRNS simulates solute transport for steady one-dimensional fluid flow by convection and diffusion or dispersion in a saturated porous medium based on the assumption of local chemical equilibrium. The chemical interactions included in the model are aqueous-phase complexation, solid-phase ion exchange of bare ions and complexes using the surface complexation model, and precipitation or dissolution of solids. The program can simulate the kinetic dissolution or precipitation for calcite and silica as well as irreversible dissolution of glass. Thermodynamic parameters are temperature dependent and are coupled to a companion heat transport simulator; thus, the effects of transient temperature conditions can be considered. Options for oxidation-reduction (redox) and C-13 fractionation as well as non-isothermal conditions are included. 2 - Method of solution: The governing equations for both reactive chemical and heat transport are discretized in time and space. For heat transport, the Crank-Nicolson approximation is used in conjunction with a LU decomposition and backward substitution solution procedure. To deal with the strong nonlinearity of the chemical transport equations, a generalized Newton-Raphson method is used

Electron heat transport in shaped TCV L-mode plasmas

International Nuclear Information System (INIS)

Camenen, Y; Pochelon, A; Bottino, A; Coda, S; Ryter, F; Sauter, O; Behn, R; Goodman, T P; Henderson, M A; Karpushov, A; Porte, L; Zhuang, G

2005-01-01

Electron heat transport experiments are performed in L-mode discharges at various plasma triangularities, using radially localized electron cyclotron heating to vary independently both the electron temperature T e and the normalized electron temperature gradient R/L T e over a large range. Local gyro-fluid (GLF23) and global collisionless gyro-kinetic (LORB5) linear simulations show that, in the present experiments, trapped electron mode (TEM) is the most unstable mode. Experimentally, the electron heat diffusivity χ e is shown to decrease with increasing collisionality, and no dependence of χ e on R/L T e is observed at high R/L T e values. These two observations are consistent with the predictions of TEM simulations, which supports the fact that TEM plays a crucial role in electron heat transport. In addition, over the broad range of positive and negative triangularities investigated, the electron heat diffusivity is observed to decrease with decreasing plasma triangularity, leading to a strong increase of plasma confinement at negative triangularity

Correction of the wavefront using the irradiance transport equation

Science.gov (United States)

García, M.; Granados, F.; Cornejo, A.

2008-07-01

The correction of the wavefront in optical systems implies the use of wavefront sensors, software, and auxiliary optical systems. We propose evaluated the wavefront using the fact that the wavefront and its intensity are related in the mathematical expression the irradiance transport equation (ITE)

Thaw flow control for liquid heat transport systems

Science.gov (United States)

Kirpich, Aaron S.

1989-01-01

In a liquid metal heat transport system including a source of thaw heat for use in a space reactor power system, the thaw flow throttle or control comprises a fluid passage having forward and reverse flow sections and a partition having a plurality of bleed holes therein to enable fluid flow between the forward and reverse sections. The flow throttle is positioned in the system relatively far from the source of thaw heat.

Perturbative Heat Transport Experiments on TJ-II

International Nuclear Information System (INIS)

Eguilor, S.; Castejon, F.; Luna, E. de la; Cappa, A.; Likin, K.; Fernandez, A.; Tj-II, T.

2002-01-01

Heat wave experiments are performed on TJ-II stellarator plasmas to estimate both heat diffusivity and power deposition profiles. High frequency ECRH modulation experiments are used to obtain the power deposition profiles, which is observed to be wider and duller than estimated by tracing techniques. The causes of this difference are discussed in the paper. Fourier analysis techniques are used to estimate the heat diffusivity in low frequency ECRH modulation experiments. This include the power deposition profile as a new ingredient. ECHR switch on/off experiments are exploited to obtain power deposition and heat diffusivities profile. Those quantities are compared with the obtained by modulation experiments and transport analysis, showing a good agreement. (Author) 18 refs

Perturbative Heat Transport Experiments on TJ-II

Energy Technology Data Exchange (ETDEWEB)

Eguilor, S.; Castejon, F.; Luna, E. de la; Cappa, A.; Likin, K.; Fernandez, A.; Tj-II, T.

2002-07-01

Heat wave experiments are performed on TJ-II stellarator plasmas to estimate both heat diffusivity and power deposition profiles. High frequency ECRH modulation experiments are used to obtain the power deposition profiles, which is observed to be wider and duller than estimated by tracing techniques. The causes of this difference are discussed in the paper. Fourier analysis techniques are used to estimate the heat diffusivity in low frequency ECRH modulation experiments. This include the power deposition profile as a new ingredient. ECHR switch on/off experiments are exploited to obtain power deposition and heat diffusivities profile. Those quantities are compared with the obtained by modulation experiments and transport analysis, showing a good agreement. (Author) 18 refs.

Diffusive and convective transport modelling from analysis of ECRH-stimulated electron heat wave propagation. [ECRH (Electron Cyclotron Resonance Heating)

Energy Technology Data Exchange (ETDEWEB)

Erckmann, V; Gasparino, U; Giannone, L. (Max-Planck-Institut fuer Plasmaphysik, Garching (Germany)) (and others)

1992-01-01

ECRH power modulation experiments in toroidal devices offer the chance to analyze the electron heat transport more conclusively: the electron heat wave propagation can be observed by ECE (or SX) leading to radial profiles of electron temperature modulation amplitude and time delay (phase shift). Taking also the stationary power balance into account, the local electron heat transport can be modelled by a combination of diffusive and convective transport terms. This method is applied to ECRH discharges in the W7-AS stellarator (B=2.5T, R=2m, a[<=]18 cm) where the ECRH power deposition is highly localized. In W7-AS, the T[sub e] modulation profiles measured by a high resolution ECE system are the basis for the local transport analysis. As experimental errors limit the separation of diffusive and convective terms in the electron heat transport for central power deposition, also ECRH power modulation experiments with off-axis deposition and inward heat wave propagation were performed (with 70 GHz o-mode as well as with 140 GHz x-mode for increased absorption). Because collisional electron-ion coupling and radiative losses are only small, low density ECRH discharges are best candidates for estimating the electron heat flux from power balance. (author) 2 refs., 3 figs.

Approximate solutions for the two-dimensional integral transport equation. The critically mixed methods of resolution

International Nuclear Information System (INIS)

Sanchez, Richard.

1980-11-01

This work is divided into two part the first part (note CEA-N-2165) deals with the solution of complex two-dimensional transport problems, the second one treats the critically mixed methods of resolution. These methods are applied for one-dimensional geometries with highly anisotropic scattering. In order to simplify the set of integral equation provided by the integral transport equation, the integro-differential equation is used to obtain relations that allow to lower the number of integral equation to solve; a general mathematical and numerical study is presented [fr

Molecular representation of molar domain (volume), evolution equations, and linear constitutive relations for volume transport.

Science.gov (United States)

Eu, Byung Chan

2008-09-07

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for the statistical mechanical representation of molecular domain (volume or space) by using the Voronoi volume and its mean value that may be regarded as molar domain (volume) and also the statistical mechanical representation of volume flux. By using their statistical mechanical formulas, the evolution equations of volume transport are derived from the generalized Boltzmann equation of fluids. Approximate solutions of the evolution equations of volume transport provides kinetic theory formulas for the molecular domain, the constitutive equations for molar domain (volume) and volume flux, and the dissipation of energy associated with volume transport. Together with the constitutive equation for the mean velocity of the fluid obtained in a previous paper, the evolution equations for volume transport not only shed a fresh light on, and insight into, irreversible phenomena in fluids but also can be applied to study fluid flow problems in a manner hitherto unavailable in fluid dynamics and irreversible thermodynamics. Their roles in the generalized hydrodynamics will be considered in the sequel.

Non-standard model for electron heat transport for multidimensional hydrodynamic codes

Energy Technology Data Exchange (ETDEWEB)

Nicolai, Ph.; Busquet, M.; Schurtz, G. [CEA/DAM-Ile de France, 91 - Bruyeres Le Chatel (France)

2000-07-01

In simulations of laser-produced plasma, modeling of heat transport requires an artificial limitation of standard Spitzer-Haerm fluxes. To improve heat conduction processing, we have developed a multidimensional model which accounts for non-local features of heat transport and effects of self-generated magnetic fields. This consistent treatment of both mechanisms has been implemented in a two-dimensional radiation-hydrodynamic code. First results indicate good agreements between simulations and experimental data. (authors)

Non-standard model for electron heat transport for multidimensional hydrodynamic codes

International Nuclear Information System (INIS)

Nicolai, Ph.; Busquet, M.; Schurtz, G.

2000-01-01

In simulations of laser-produced plasma, modeling of heat transport requires an artificial limitation of standard Spitzer-Haerm fluxes. To improve heat conduction processing, we have developed a multidimensional model which accounts for non-local features of heat transport and effects of self-generated magnetic fields. This consistent treatment of both mechanisms has been implemented in a two-dimensional radiation-hydrodynamic code. First results indicate good agreements between simulations and experimental data. (authors)

A multi scale approximation solution for the time dependent Boltzmann-transport equation

International Nuclear Information System (INIS)

Merk, B.

2004-03-01

The basis of all transient simulations for nuclear reactor cores is the reliable calculation of the power production. The local power distribution is generally calculated by solving the space, time, energy and angle dependent neutron transport equation known as Boltzmann equation. The computation of exact solutions of the Boltzmann equation is very time consuming. For practical numerical simulations approximated solutions are usually unavoidable. The objective of this work is development of an effective multi scale approximation solution for the Boltzmann equation. Most of the existing methods are based on separation of space and time. The new suggested method is performed without space-time separation. This effective approximation solution is developed on the basis of an expansion for the time derivative of different approximations to the Boltzmann equation. The method of multiple scale expansion is used for the expansion of the time derivative, because the problem of the stiff time behaviour can't be expressed by standard expansion methods. This multiple scale expansion is used in this work to develop approximation solutions for different approximations of the Boltzmann equation, starting from the expansion of the point kinetics equations. The resulting analytic functions are used for testing the applicability and accuracy of the multiple scale expansion method for an approximation solution with 2 delayed neutron groups. The results are tested versus the exact analytical results for the point kinetics equations. Very good agreement between both solutions is obtained. The validity of the solution with 2 delayed neutron groups to approximate the behaviour of the system with 6 delayed neutron groups is demonstrated in an additional analysis. A strategy for a solution with 4 delayed neutron groups is described. A multiple scale expansion is performed for the space-time dependent diffusion equation for one homogenized cell with 2 delayed neutron groups. The result is

Analysis of the dual phase lag bio-heat transfer equation with constant and time-dependent heat flux conditions on skin surface

Directory of Open Access Journals (Sweden)

Ziaei Poor Hamed

2016-01-01

Full Text Available This article focuses on temperature response of skin tissue due to time-dependent surface heat fluxes. Analytical solution is constructed for DPL bio-heat transfer equation with constant, periodic and pulse train heat flux conditions on skin surface. Separation of variables and Duhamel’s theorem for a skin tissue as a finite domain are employed. The transient temperature responses for constant and time-dependent boundary conditions are obtained and discussed. The results show that there is major discrepancy between the predicted temperature of parabolic (Pennes bio-heat transfer, hyperbolic (thermal wave and DPL bio-heat transfer models when high heat flux accidents on the skin surface with a short duration or propagation speed of thermal wave is finite. The results illustrate that the DPL model reduces to the hyperbolic model when τT approaches zero and the classic Fourier model when both thermal relaxations approach zero. However for τq = τT the DPL model anticipates different temperature distribution with that predicted by the Pennes model. Such discrepancy is due to the blood perfusion term in energy equation. It is in contrast to results from the literature for pure conduction material, where the DPL model approaches the Fourier heat conduction model when τq = τT . The burn injury is also investigated.

Heat transport analysis in a district heating and snow melting system in Sapporo and Ishikari, Hokkaido applying waste heat from GTHTR300

International Nuclear Information System (INIS)

Kasahara, Seiji; Kamiji, Yu; Terada, Atsuhiko; Yan Xing; Inagaki, Yoshiyuki; Murata, Tetsuya; Mori, Michitsugu

2015-01-01

A district heating and snow melting system utilizing waste heat from Gas Turbine High temperature Gas Reactor of 300 MW_e (GTHTR300), a heat-electricity cogeneration design of high temperature gas-cooled reactor, was analyzed. Application areas are set in Sapporo and Ishikari, the heavy snowfall cities in Northern Japan. The heat transport analyses are carried out by modeling the components in the system; pipelines of the secondary water loops between GTHTR300s and heat demand district and heat exchangers to transport the heat from the secondary water loops to the tertiary loops in the district. Double pipe for the secondary loops are advantageous for less heat loss and smaller excavation area. On the other hand, these pipes has disadvantage of more electricity consumption for pumping. Most of the heat demand in the month of maximum requirement can be supplied by 2 GTHTR300s and delivered by 9 secondary loops and around 5000 heat exchangers. Closer location of GTHTR300 site to the heat demand district is largely advantageous economically. Less decrease of the distance from 40 km to 20 km made the heat loss half and cost of the heat transfer system 22% smaller. (author)

Coupled equations for transient water flow, heat flow, and ...

Indian Academy of Sciences (India)

interacting processes, including flow of fluids, deformation of porous materials, chemical reactions, and transport of ... systems involving the flow of water, heat, and deformation. Such systems are ..... Defined thus, αI is independent of boundary con- ditions in an ... perature change with free deformation at constant total stress ...

Numerical simulation for fractional order stationary neutron transport equation using Haar wavelet collocation method

Energy Technology Data Exchange (ETDEWEB)

Saha Ray, S., E-mail: santanusaharay@yahoo.com; Patra, A.

2014-10-15

Highlights: • A stationary transport equation has been solved using the technique of Haar wavelet collocation method. • This paper intends to provide the great utility of Haar wavelets to nuclear science problem. • In the present paper, two-dimensional Haar wavelets are applied. • The proposed method is mathematically very simple, easy and fast. - Abstract: In this paper the numerical solution for the fractional order stationary neutron transport equation is presented using Haar wavelet Collocation Method (HWCM). Haar wavelet collocation method is efficient and powerful in solving wide class of linear and nonlinear differential equations. This paper intends to provide an application of Haar wavelets to nuclear science problems. This paper describes the application of Haar wavelets for the numerical solution of fractional order stationary neutron transport equation in homogeneous medium with isotropic scattering. The proposed method is mathematically very simple, easy and fast. To demonstrate about the efficiency and applicability of the method, two test problems are discussed.

Numerical Analysis of Microwave Heating on Saponification Reaction

Science.gov (United States)

Huang, Kama; Jia, Kun

2005-01-01

Currently, microwave is widely used in chemical industry to accelerate chemical reactions. Saponification reaction has important applications in industry; some research results have shown that microwave heating can significantly accelerate the reaction [1]. But so far, no efficient method has been reported for the analysis of the heating process and design of an efficient reactor powered by microwave. In this paper, we present a method to study the microwave heating process on saponification reaction, where the reactant in a test tube is considered as a mixture of dilute solution. According to the preliminary measurement results, the effective permittivity of the mixture is approximately the permittivity of water, but the conductivity, which could change with the reaction, is derived from the reaction equation (RE). The electromagnetic field equation and reaction equation are coupled by the conductivity. Following that, the whole heating processes, which is described by Maxwell's equations, the reaction equation and heat transport equation (HTE), is analyzed by finite difference time domain (FDTD) method. The temperature rising in the test tube are measured and compared with the computational results. Good agreement can be seen between the measured and calculated results.

Studies of transport phenomena in tokamaks with nonstationary intervention into the discharge

International Nuclear Information System (INIS)

Kalmykov, S.G.

1993-01-01

Together with detailed plasma parameter measurements, an experimental basis is provided to deduce radial profiles of local transport coefficients, to obtain their temporal evolution in the transient phase of the discharge. The equations of heat and particle balance were used as proper instrument to perform the coefficients calculation. The majority of the experiments deals with heat transport processes in the electron component of plasma. A problem in getting ohmic heat deposit radial distribution arise with use of the electron population heat balance equation. For its solution, numerical simulation of the plasma column loop voltage based on poloidal magnetic field classical diffusion supposition was used. (L.C.J.A.)

Simplified equations for transient heat transfer problems at low Fourier numbers

DEFF Research Database (Denmark)

Christensen, Martin Gram; Adler-Nissen, Jens

2015-01-01

and validated for infinite slabs, infinite cylinders and spheres and by an industrial application example, covering the center temperature and the volume average temperature. The approach takes ground in the residual difference between a 1 term series solution and a 100 term solution to the Fourier equation...... of the thermal response for solids subjected to convective heat transfer. By representing the residual thermal response as a function of the Biot number and the first eigenvalue, the new approach enables the description of the thermal response in the whole Fourier regime. The presented equation is simple...

Finite element approximation to the even-parity transport equation

International Nuclear Information System (INIS)

Lewis, E.E.

1981-01-01

This paper studies the finite element method, a procedure for reducing partial differential equations to sets of algebraic equations suitable for solution on a digital computer. The differential equation is cast into the form of a variational principle, the resulting domain then subdivided into finite elements. The dependent variable is then approximated by a simple polynomial, and these are linked across inter-element boundaries by continuity conditions. The finite element method is tailored to a variety of transport problems. Angular approximations are formulated, and the extent of ray effect mitigation is examined. Complex trial functions are introduced to enable the inclusion of buckling approximations. The ubiquitous curved interfaces of cell calculations, and coarse mesh methods are also treated. A concluding section discusses limitations of the work to date and suggests possible future directions

Heat Transport in Gapped Spin-Chain Systems

International Nuclear Information System (INIS)

Shimshoni, E.

2006-01-01

Full Text: We study the contribution of magnetic excitations to the heat transport in gapped spin-chain systems. These systems are characterized by a substantially enhanced heat conductivity, which can be traced back to the existence of weakly violated conservation laws. We focus particularly on the behavior of clean two-leg spin ladder compounds, where one-dimensional exotic spin excitations are coupled to three-dimensional phonons. We show that the contributions of the two types of heat carriers can not be easily disentangled. Depending on the ratios of spin gaps and the Debye energy, the heat conductivity can be either exponentially increasing or exponentially decreasing as a function of temperature (T). In addition, the magnetic contribution to the total heat conductivity may be either positive or negative. We discuss its T-dependence in various possible regimes, and note that in most regimes it is dominated by spin-phonon drag: the two types of heat carriers have almost the

Comparison of neutronic transport equation resolution nodal methods

International Nuclear Information System (INIS)

Zamonsky, O.M.; Gho, C.J.

1990-01-01

In this work, some transport equation resolution nodal methods are comparatively studied: the constant-constant (CC), linear-nodal (LN) and the constant-quadratic (CQ). A nodal scheme equivalent to finite differences has been used for its programming, permitting its inclusion in existing codes. Some bidimensional problems have been solved, showing that linear-nodal (LN) are, in general, obtained with accuracy in CPU shorter times. (Author) [es

TLC scheme for numerical solution of the transport equation on equilateral triangular meshes

International Nuclear Information System (INIS)

Walters, W.F.

1983-01-01

A new triangular linear characteristic TLC scheme for numerically solving the transport equation on equilateral triangular meshes has been developed. This scheme uses the analytic solution of the transport equation in the triangle as its basis. The data on edges of the triangle are assumed linear as is the source representation. A characteristic approach or nodal approach is used to obtain the analytic solution. Test problems indicate that the new TLC is superior to the widely used DITRI scheme for accuracy

Measurement of Membrane Characteristics Using the Phenomenological Equation and the Overall Mass Transport Equation in Ion-Exchange Membrane Electrodialysis of Saline Water

Directory of Open Access Journals (Sweden)

Yoshinobu Tanaka

2012-01-01

Full Text Available The overall membrane pair characteristics included in the overall mass transport equation are understandable using the phenomenological equations expressed in the irreversible thermodynamics. In this investigation, the overall membrane pair characteristics (overall transport number , overall solute permeability , overall electro-osmotic permeability and overall hydraulic permeability were measured by seawater electrodialysis changing current density, temperature and salt concentration, and it was found that occasionally takes minus value. For understanding the above phenomenon, new concept of the overall concentration reflection coefficient ∗ is introduced from the phenomenological equation. This is the aim of this investigation. ∗ is defined for describing the permselectivity between solutes and water molecules in the electrodialysis system just after an electric current interruption. ∗ is expressed by the function of and . ∗ is generally larger than 1 and is positive, but occasionally ∗ becomes less than 1 and becomes negative. Negative means that ions are transferred with water molecules (solvent from desalting cells toward concentrating cells just after an electric current interruption, indicating up-hill transport or coupled transport between water molecules and solutes.

Solution and study of nodal neutron transport equation applying the LTS{sub N}-DiagExp method

Energy Technology Data Exchange (ETDEWEB)

Hauser, Eliete Biasotto; Pazos, Ruben Panta [Pontificia Univ. Catolica do Rio Grande do Sul, Porto Alegre, RS (Brazil). Faculdade de Matematica]. E-mail: eliete@pucrs.br; rpp@mat.pucrs.br; Vilhena, Marco Tullio de [Pontificia Univ. Catolica do Rio Grande do Sul, Porto Alegre, RS (Brazil). Instituto de Matematica]. E-mail: vilhena@mat.ufrgs.br; Barros, Ricardo Carvalho de [Universidade do Estado, Nova Friburgo, RJ (Brazil). Instituto Politecnico]. E-mail: ricardo@iprj.uerj.br

2003-07-01

In this paper we report advances about the three-dimensional nodal discrete-ordinates approximations of neutron transport equation for Cartesian geometry. We use the combined collocation method of the angular variables and nodal approach for the spatial variables. By nodal approach we mean the iterated transverse integration of the S{sub N} equations. This procedure leads to the set of one-dimensional averages angular fluxes in each spatial variable. The resulting system of equations is solved with the LTS{sub N} method, first applying the Laplace transform to the set of the nodal S{sub N} equations and then obtained the solution by symbolic computation. We include the LTS{sub N} method by diagonalization to solve the nodal neutron transport equation and then we outline the convergence of these nodal-LTS{sub N} approximations with the help of a norm associated to the quadrature formula used to approximate the integral term of the neutron transport equation. (author)

An appraisal of computational techniques for transient heat conduction equation

International Nuclear Information System (INIS)

Kant, T.

1983-01-01

A semi-discretization procedure in which the ''space'' dimension is discretized by the finite element method is emphasized for transient problems. This standard methodology transforms the space-time partial differential equation (PDE) system into a set of ordinary differential equations (ODE) in time. Existing methods for transient heat conduction calculations are then reviewed. Existence of two general classes of time integration schemes- implicit and explicit is noted. Numerical stability characteristics of these two methods are elucidated. Implicit methods are noted to be numerically stable, permitting large time steps, but the cost per step is high. On the otherhand, explicit schemes are noted to be inexpensive per step, but small step size is required. Low computational cost of the explicit schemes make it very attractive for nonlinear problems. However, numerical stability considerations requiring use of very small time steps come in the way of its general adoption. Effectiveness of the fourth-order Runge-Kutta-Gill explicit integrator is then numerically evaluated. Finally we discuss some very recent works on development of computational algorithms which not only achieve unconditional stability, high accuracy and convergence but involve computations on matrix equations of elements only. This development is considered to be very significant in the light of our experience gained for simple heat conduction calculations. We conclude that such algorithms have the potential for further developments leading to development of economical methods for general transient analysis of complex physical systems. (orig.)

Output feedback control of heat transport mechanisms in parabolic distributed solar collectors

KAUST Repository

Elmetennani, Shahrazed

2016-08-05

This paper presents an output feedback control for distributed parabolic solar collectors. The controller aims at forcing the outlet temperature to track a desired reference in order to manage the produced heat despite the external disturbances. The proposed control strategy is derived using the distributed physical model of the system to avoid the loss of information due to model approximation schemes. The system dynamics are driven to follow reference dynamics defined by a transport equation with a constant velocity, which allows to control the transient behavior and the response time of the closed loop. The designed controller depends only on the accessible measured variables which makes it easy for real time implementation and useful for industrial plants. Simulation results show the efficiency of the reference tracking closed loop under different working conditions.

Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index

International Nuclear Information System (INIS)

Lehtikangas, O.; Tarvainen, T.; Kim, A.D.; Arridge, S.R.

2015-01-01

The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena on the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light

Semiquantum molecular dynamics simulation of thermal properties and heat transport in low-dimensional nanostructures

Science.gov (United States)

Savin, Alexander V.; Kosevich, Yuriy A.; Cantarero, Andres

2012-08-01

We present a detailed description of semiquantum molecular dynamics simulation of stochastic dynamics of a system of interacting particles. Within this approach, the dynamics of the system is described with the use of classical Newtonian equations of motion in which the effects of phonon quantum statistics are introduced through random Langevin-like forces with a specific power spectral density (the color noise). The color noise describes the interaction of the molecular system with the thermostat. We apply this technique to the simulation of thermal properties and heat transport in different low-dimensional nanostructures. We describe the determination of temperature in quantum lattice systems, to which the equipartition limit is not applied. We show that one can determine the temperature of such a system from the measured power spectrum and temperature- and relaxation-rate-independent density of vibrational (phonon) states. We simulate the specific heat and heat transport in carbon nanotubes, as well as the heat transport in molecular nanoribbons with perfect (atomically smooth) and rough (porous) edges, and in nanoribbons with strongly anharmonic periodic interatomic potentials. We show that the effects of quantum statistics of phonons are essential for the carbon nanotube in the whole temperature range T<500K, in which the values of the specific heat and thermal conductivity of the nanotube are considerably less than that obtained within the description based on classical statistics of phonons. This conclusion is also applicable to other carbon-based materials and systems with high Debye temperature like graphene, graphene nanoribbons, fullerene, diamond, diamond nanowires, etc. We show that the existence of rough edges and quantum statistics of phonons change drastically the low-temperature thermal conductivity of the nanoribbon in comparison with that of the nanoribbon with perfect edges and classical phonon dynamics and statistics. The semiquantum molecular

Relativistic transport equation for a discontinuity wave of multiplicity one

Energy Technology Data Exchange (ETDEWEB)

Giambo, S; Palumbo, A [Istituto di Matematica, Universita degli Studi, Messina (Italy)

1980-04-14

In the framework of the theory of the singular hypersurfaces, the transport equation for the amplitude of a discontinuity wave, corresponding to a simple characteristic of a quasi-linear hyperbolic system, is established in the context of special relativity.

Two-dimensional heat conducting simulation of plasma armatures

International Nuclear Information System (INIS)

Huerta, M.A.; Boynton, G.

1991-01-01

This paper reports on our development of a two-dimensional MHD code to simulate internal motions in a railgun plasma armature. The authors use the equations of resistive MHD, with Ohmic heating, and radiation heat transport. The authors use a Flux Corrected Transport code to advance all quantities in time. Our runs show the development of complex flows, subsequent shedding of secondary arcs, and a drop in the acceleration of the armature

Comparison of preconditioned generalized conjugate gradient methods to two-dimensional neutron and photon transport equation

International Nuclear Information System (INIS)

Chen, G.S.

1997-01-01

We apply and compare the preconditioned generalized conjugate gradient methods to solve the linear system equation that arises in the two-dimensional neutron and photon transport equation in this paper. Several subroutines are developed on the basis of preconditioned generalized conjugate gradient methods for time-independent, two-dimensional neutron and photon transport equation in the transport theory. These generalized conjugate gradient methods are used. TFQMR (transpose free quasi-minimal residual algorithm), CGS (conjuage gradient square algorithm), Bi-CGSTAB (bi-conjugate gradient stabilized algorithm) and QMRCGSTAB (quasi-minimal residual variant of bi-conjugate gradient stabilized algorithm). These sub-routines are connected to computer program DORT. Several problems are tested on a personal computer with Intel Pentium CPU. (author)

Evaluation of finite difference and FFT-based solutions of the transport of intensity equation.

Science.gov (United States)

Zhang, Hongbo; Zhou, Wen-Jing; Liu, Ying; Leber, Donald; Banerjee, Partha; Basunia, Mahmudunnabi; Poon, Ting-Chung

2018-01-01

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

Probing liquation cracking and solidification through modeling of momentum, heat, and solute transport during welding of aluminum alloys

International Nuclear Information System (INIS)

Mishra, S.; Chakraborty, S.; DebRoy, T.

2005-01-01

A transport phenomena-based mathematical model is developed to understand liquation cracking in weldments during fusion welding. Equations of conservation of mass, momentum, heat, and solute transport are numerically solved considering nonequilibrium solidification and filler metal addition to determine the solid and liquid phase fractions in the solidifying region and the solute distribution in the weld pool. An effective partition coefficient that considers the local interface velocity and the undercooling is used to simulate solidification during welding. The calculations show that convection plays a dominant role in the solute transport inside the weld pool. The predicted weld-metal solute content agreed well with the independent experimental observations. The liquation cracking susceptibility in Al-Cu alloy weldments could be reliably predicted by the model based on the computed solidifying weld-metal composition and solid fraction considering nonequilibrium solidification

Numerical solution of neutron transport equations in discrete ordinates and slab geometry

International Nuclear Information System (INIS)

Serrano Pedraza, F.

1985-01-01

An unified formalism to solve numerically, between other equation, the neutron transport in discrete ordinates, slab geometry, several energy groups and independents of time, has been developed recently. Such a formalism cover some of the conventional schemes as diamond difference, (WDD) characteristic step (SC) lineal characteristic (LC), quadratic characteristic (QC) and lineal discontinuous. Unified formation gives before hand the convergence order of the previously selected scheme. In fact it allows besides to generate a big amount of numerical schemes, with which is also possible to solve numerical equations as soon as neutron transport. The essential purpose of this work was to solve the neutron transport equations in slab geometry and discrete ordinates considering several energy groups without to take under advisement time dependence based in the above mentioned unified formalism. To reach this purpose it was necesary to design a computer code with the name TNOD1 (Neutron transport in discrete ordinates and 1 dimension) which includes each one of the schemes already pointed out. there exist two numerical schemes, also recently developed, quadratic continuous (QC) and cubic continuous (CN), although covered by unified formalism, it has been possible to include them inside this computer code without make substantial changes in its structure. In chapter I, derivative of neutron transport equation independent of time is taken, for angular flux, including boundary conditions and discontinuity. In chapter II the neutron transport equations are obtained in multigroups, independents of time, for approximation of discrete ordinates. Description of theory related with unified formalism and its relationship with mentioned discretization schemes is presented in chapter III. Chapter IV describes the computer code developed and finally, in chapter V different numerical results obtained with TNOD1 program are shown. In Appendix A theorems and mathematical arguments used

Local Equation of State for Protons, and Implications for Proton Heating in the Solar Wind.

Science.gov (United States)

Zaslavsky, A.; Maksimovic, M.; Kasper, J. C.

2017-12-01

The solar wind protons temperature is observed to decrease with distance to the Sun at a slower rate than expected from an adiabatic expansion law: the protons are therefore said to be heated. This observation raises the question of the evaluation of the heating rate, and the question of the heat source.These questions have been investigated by previous authors by gathering proton data on various distances to the Sun, using spacecraft as Helios or Ulysses, and then computing the radial derivative of the proton temperature in order to obtain a heating rate from the internal energy equation. The problem of such an approach is the computation of the radial derivative of the temperature profile, for which uncertainties are very large, given the dispersion of the temperatures measured at a given distance.An alternative approach, that we develop in this paper, consists in looking for an equation of state that links locally the pressure (or temperature) to the mass density. If such a relation exists then one can evaluate the proton heating rate on a local basis, without having any space derivative to compute.Here we use several years of STEREO and WIND proton data to search for polytropic equation of state. We show that such relationships are indeed a good approximation in given solar wind's velocity intervals and deduce the associated protons heating rates as a function of solar wind's speed. The obtained heating rates are shown to scale from around 1 kW/kg in the slow wind to around 10 kW/kg in the fast wind, in remarkable agreement with the rate of energy observed by previous authors to cascade in solar wind's MHD turbulence at 1 AU. These results therefore support the idea of proton turbulent heating in the solar wind.

Comparison of temperature estimates from heat transport model and electrical resistivity tomography during a shallow heat injection and storage experiment

OpenAIRE

Hermans, Thomas; Daoudi, Moubarak; Vandenbohede, Alexander; Robert, Tanguy; Caterina, David; Nguyen, Frédéric

2012-01-01

Groundwater resources are increasingly used around the world as geothermal systems. Understanding physical processes and quantification of parameters determining heat transport in porous media is therefore important. Geophysical methods may be useful in order to yield additional information with greater coverage than conventional wells. We report a heat transport study during a shallow heat injection and storage field test. Heated water (about 50°C) was injected for 6 days at the rate of 80 l...

Cellular neural network to the spherical harmonics approximation of neutron transport equation in x–y geometry

International Nuclear Information System (INIS)

Pirouzmand, Ahmad; Hadad, Kamal

2012-01-01

Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.

Heat transfer enhancement in nanofluids. A numerical approach

International Nuclear Information System (INIS)

Fariñas Alvariño, P; Sáiz Jabardo, J M; Arce, A; Llamas Galdo, M I

2012-01-01

The aim of the reported investigation is to asses the effect of brownian and thermophoretic diffusion in nanofluids convective heat transfer. In order to capture these effects, a new equation for particles distribution had to be consider. Momentum and energy equations have been reformulated in order to include brownian and thermophretic diffusion. These modes of diffusion have been suggested extensively in the literature but their effect on momentum and energy transport has not yet been numerically analyzed. In order to obtain a solution for the modified set of governing equations, a new CFD solver had to be devised. The new solver has been applied to a case study involving hydrodynamic and thermally developing laminar flow regime in a pipe. Pure base fluid solutions have been used to asses the accuracy of the model. Numerical nanofluid solutions compare reasonably well with both experimental results obtained elsewhere and the Churchill and Ozoe correlation. The observed heat transfer enhancement by the nanofluid has been attributed to its transport properties rather than to another transport mechanism.

Resolution of the neutron transport equation by a three-dimensional least square method

International Nuclear Information System (INIS)

Varin, Elisabeth

2001-01-01

The knowledge of space and time distribution of neutrons with a certain energy or speed allows the exploitation and control of a nuclear reactor and the assessment of the irradiation dose about an irradiated nuclear fuel storage site. The neutron density is described by a transport equation. The objective of this research thesis is to develop a software for the resolution of this stationary equation in a three-dimensional Cartesian domain by means of a deterministic method. After a presentation of the transport equation, the author gives an overview of the different deterministic resolution approaches, identifies their benefits and drawbacks, and discusses the choice of the Ressel method. The least square method is precisely described and then applied. Numerical benchmarks are reported for validation purposes

Dose concept of oncological hyperthermia: Heat-equation considering the cell destruction

Directory of Open Access Journals (Sweden)

Szasz A

2006-01-01

Full Text Available We shall assume, of course, that the objective of hyperthermia is to destroy the malignant cells. Destruction definitely needs energy. Description and quality assurance of hyperthermia use the Pennes heat equation to describe the processes. However the energy balance of the Pennes-equation does not contain the hyperthermic cell-destruction energy, which is a mandatory factor of the process. We propose a generalization of the Pennes-equation, inducing the entire energy balance. The new paradigm could be a theoretical basis of the till now empirical dose-construction for oncological hyperthermia. The cell destruction is a non-equilibrium thermodynamical process, described by the equations of chemical reactions. The dynamic behavior (time dependence has to be considered in this approach. We are going to define also a dose concept that can be objectively compared with other oncological methods. We show how such empirical dose as CEM43oC could be based theoretically as well.

Assessment of intermittency transport equations for modeling transition in boundary layers subjected to freestream turbulence

International Nuclear Information System (INIS)

Suluksna, Keerati; Juntasaro, Ekachai

2008-01-01

The γ-Re θ transition model of Menter et al. [Menter, F.R., Langtry, R.B., Volker, S., Huang, P.G., 2005. Transition modelling for general purpose CFD codes. ERCOFTAC International Symposium Engineering Turbulence Modelling and Measurements] is a highly generalized transport equation model in which it has been developed based on the concept of local variables compatible with modern CFD methods where the unstructured grid and the parallel computing technique are usually integrated in. To perform the prediction with this model, two essential parameters, F length which is used to control the length of the transition region and Re θc which is used to control the onset of the transition location, must be specified to close the model. At present, both parameters are proprietary and their formulations are unpublished. For the first time here, the relations for both parameters are formulated by means of numerical experiments and analysis under the assumption of Re θc = Re θt corresponding with the bypass transition behavior. Based on this analysis, the optimized values of the parameters are found and their relations can be constructed as follows: Re θc = 803.73(Tu ∞ , le + 0.6067) -1.027 and F length = 163 ln(Tu ∞ , le ) + 3.625. The performance of this transition model is assessed by testing with the experimental cases of T3AM, T3A, and T3B. Detailed comparisons with the predicted results by the transition models of Suzen and Huang [Suzen, Y.B., Huang, P.G., 2000. Modeling of flow transition using an intermittency transport equation. J. Fluids Eng. 122, 273-284] and Lodefier et al. [Lodefier, K., Merci, B., De Langhe, C., Dick, E., 2003. Transition modelling with the SST turbulence model and intermittency transport equation. ASME Turbo Expo, Atlanta, GA, USA, June 16-19], and also with the predicted results by the k-ε model of Launder and Sharma [Launder, B.E., Sharma, B., 1974. Application of the energy dissipation model of turbulence to the calculation of

Numerical approximation of null controls for the heat equation: Ill-posedness and remedies

International Nuclear Information System (INIS)

Münch, Arnaud; Zuazua, Enrique

2010-01-01

The numerical approximation of exact or trajectory controls for the wave equation is known to be a delicate issue, since the pioneering work of Glowinski–Lions in the nineties, because of the anomalous behavior of the high-frequency spurious numerical waves. Various efficient remedies have been developed and analyzed in the last decade to filter out these high-frequency components: Fourier filtering, Tychonoff's regularization, mixed finite-element methods, multi-grid strategies, etc. Recently convergence rate results have also been obtained. This work is devoted to analyzing this issue for the heat equation, which is the opposite paradigm because of its strong dissipativity and smoothing properties. The existing analytical results guarantee that, at least in some simple situations, as in the finite-difference scheme in 1 − d, the null or trajectory controls for numerical approximation schemes converge. This is due to the intrinsic high-frequency damping of the heat equation that is inherited by its numerical approximation schemes. But when developing numerical simulations the topic appears to be much more subtle and difficult. In fact, efficiently computing the null control for a numerical approximation scheme of the heat equation is a difficult problem in itself. The difficulty is strongly related to the regularizing effect of the heat kernel. The controls of minimal L 2 -norm are characterized as minima of quadratic functionals on the solutions of the adjoint heat equation, or its numerical versions. These functionals are shown to be coercive in very large spaces of solutions, sufficient to guarantee the L 2 character of controls, but very far from being identifiable as energy spaces for the adjoint system. The very weak coercivity of the functionals under consideration makes the approximation problem exponentially ill-posed and the functional framework far from being well adapted to standard techniques in numerical analysis. In practice, the controls of the

MFE revisited : part 1: adaptive grid-generation using the heat equation

NARCIS (Netherlands)

Zegeling, P.A.

1996-01-01

In this paper the moving-nite-element method (MFE) is used to solve the heat equation, with an articial time component, to give a non-uniform (steady-state) grid that is adapted to a given prole. It is known from theory and experiments that MFE, applied to parabolic PDEs, gives adaptive grids which

Interpretation of heat and density pulse propagation in tokamaks

International Nuclear Information System (INIS)

Sips, A.C.C.; Costley, A.E.; O'Rourke, J.O.

1991-01-01

This paper addresses two key issues in current research on sawtooth induced heat and density pulse measurements in Tokamaks and their interpretation. First, heat and density pulses in JET and TXT show different qualitative behaviour implying substantially different transport coefficients. Second, a new description of the heat pulse has been used to describe measurements cannot be simulated with the widely used diffusive model. In this paper, we show that consistency between all these measurements can be obtained assuming a diffusive propagation for the heat and density pulses and using linearised coupled transport equations. (author) 6 refs., 5 figs

Changing storm track diffusivity and the upper limit to poleward latent heat transport

Science.gov (United States)

Caballero, R.

2010-12-01

Poleward atmospheric energy transport plays a key role in the climate system by helping set the mean equator-pole temperature gradient. The mechanisms controlling the response of poleward heat flux to climate change are still poorly understood. Recent work shows that midlatitude poleward latent heat flux in atmospheric GCMs generally increases as the climate warms but reaches an upper limit at sufficiently high temperature and decreases with further warming. The reasons for this non-monotonic behavior have remained unclear. Simple arguments suggests that the latent heat flux Fl should scale as Fl ˜ vref qs, where vref is a typical meridional velocity in the baroclinic zone and qs is saturation humidity. While vref decreases with temperature, qs increases much more rapidly, so this scaling implies monotonically increasing moisture flux. We study this problem using a series of simulations employing NCAR’s CAM3 GCM coupled to a slab-ocean aquaplanet and spanning a wide range of atmospheric CO2 concentrations. We find that a modified scaling, Fl ˜ vref2 qs, describes the changes in moisture flux much more accurately. Using Lagrangian trajectory analysis, we explain the success of this scaling in terms of changes in the mixing length, which contracts proportionally to vref.

Solution of linear transport equation using Chebyshev polynomials and Laplace transform

International Nuclear Information System (INIS)

Cardona, A.V.; Vilhena, M.T.M.B. de

1994-01-01

The Chebyshev polynomials and the Laplace transform are combined to solve, analytically, the linear transport equation in planar geometry, considering isotropic scattering and the one-group model. Numerical simulation is presented. (author)

Numerical methods to solve the two-dimensional heat conduction equation

International Nuclear Information System (INIS)

Santos, R.S. dos.

1981-09-01

A class of numerical methods, called 'Hopscotch Algorithms', was used to solve the heat conduction equation in cylindrical geometry. Using a time dependent heat source, the temperature versus time behaviour of cylindric rod was analysed. Numerical simulation was used to study the stability and the convergence of each different method. Another test had the temperature specified on the outer surface as boundary condition. The various Hopscotch methods analysed exhibit differing degrees of accuracy, few of them being so accurate as the ADE method, but requiring more computational operations than the later, were observed. Finally, compared with the so called ODD-EVEN method, two other Hopscotch methods, are more time consuming. (Author) [pt

Adomian decomposition method for solving the telegraph equation in charged particle transport

International Nuclear Information System (INIS)

Abdou, M.A.

2005-01-01

In this paper, the analysis for the telegraph equation in case of isotropic small angle scattering from the Boltzmann transport equation for charged particle is presented. The Adomian decomposition is used to solve the telegraph equation. By means of MAPLE the Adomian polynomials of obtained series (ADM) solution have been calculated. The behaviour of the distribution function are shown graphically. The results reported in this article provide further evidence of the usefulness of Adomain decomposition for obtaining solution of linear and nonlinear problems

Numerical model to simulate the isotopic and heat release and transport through the geosphere from a geological repository of radioactive wastes

International Nuclear Information System (INIS)

Hidalgo Lopez, A.

2002-01-01

The aim of this research is to simulate the isotopic and heat release and transport through the geosphere, from a geological repository of high level nuclear waste. in order to achieve it, different physical processes, that have to do with the problem, are considered: groundwater flow, radioactive decay, nuclide dissolution in groundwater, heat generation, mass and heat transport. Some of these phenomena are related among the, which allows to build a coupled model,which is the starting point to generate a FORTRAN code. The flow and transport models are developed in two spatial dimensions and are integrated in space by means of a finite volume method. The time integration is fulfilled by a θ-method. Moreover, the advection-diffusion equation is solved by two finite volume techniques. In the first one a linear interpolation is used whereas in the second it is used a quadratic one. Also, a consistency an stability study of both methods is carried out in order to compare their stability zones and the errors appearing. Stability is analysed by applying the von Neumann method, which is based upon Fourier series. Although it is a classical technique when dealing with finite-difference schemes, it is here applied to two finite volume schemes. (Author)

Molecular dynamics study on heat transport from single-walled carbon nanotubes to Si substrate

Energy Technology Data Exchange (ETDEWEB)

Feng, Ya; Zhu, Jie, E-mail: zhujie@iet.cn; Tang, Da-Wei

2015-02-06

In this paper, non-equilibrium molecular dynamics simulations were performed to investigate the heat transport between a vertically aligned single-walled carbon nanotube (SWNT) and Si substrate, to find out the influence of temperature and system sizes, including diameter and length of SWNT and measurements of substrate. Results revealed that high temperature hindered heat transport in SWNT itself but was a beneficial stimulus for heat transport at interface of SWNT and Si. Furthermore, the system sizes strongly affected the peaks in vibrational density of states of Si, which led to interfacial thermal conductance dependent on system sizes. - Highlights: • NEMD is performed to simulate the heat transport from SWNT to Si substrate. • We analyze both interfacial thermal conductance and thermal conductivity of SWNT. • High temperature is a beneficial stimulus for heat transport at the interface. • Interfacial thermal conductance strongly depends on the sizes of SWNT and substrate. • We calculate VDOS of C and Si atoms to analyze phonon couplings between them.

Application of Trotter approximation for solving time dependent neutron transport equation

International Nuclear Information System (INIS)

Stancic, V.

1987-01-01

A method is proposed to solve multigroup time dependent neutron transport equation with arbitrary scattering anisotropy. The recurrence relation thus obtained is simple, numerically stable and especially suitable for treatment of complicated geometries. (author)

Circum-Antarctic Shoreward Heat Transport Derived From an Eddy- and Tide-Resolving Simulation

Science.gov (United States)

Stewart, Andrew L.; Klocker, Andreas; Menemenlis, Dimitris

2018-01-01

Almost all heat reaching the bases of Antarctica's ice shelves originates from warm Circumpolar Deep Water in the open Southern Ocean. This study quantifies the roles of mean and transient flows in transporting heat across almost the entire Antarctic continental slope and shelf using an ocean/sea ice model run at eddy- and tide-resolving (1/48°) horizontal resolution. Heat transfer by transient flows is approximately attributed to eddies and tides via a decomposition into time scales shorter than and longer than 1 day, respectively. It is shown that eddies transfer heat across the continental slope (ocean depths greater than 1,500 m), but tides produce a stronger shoreward heat flux across the shelf break (ocean depths between 500 m and 1,000 m). However, the tidal heat fluxes are approximately compensated by mean flows, leaving the eddy heat flux to balance the net shoreward heat transport. The eddy-driven cross-slope overturning circulation is too weak to account for the eddy heat flux. This suggests that isopycnal eddy stirring is the principal mechanism of shoreward heat transport around Antarctica, though likely modulated by tides and surface forcing.

Characteristics of convective heat transport in a packed pebble-bed reactor

Energy Technology Data Exchange (ETDEWEB)

Abdulmohsin, Rahman S., E-mail: rsar62@mst.edu [Department of Chemical and Biochemical Engineering, Missouri University of Science and Technology, 400 West 11th Street/231 Schrenk Hall, Rolla, MO 65409-1230 (United States); Al-Dahhan, Muthanna H., E-mail: aldahhanm@mst.edu [Department of Chemical and Biochemical Engineering, Missouri University of Science and Technology, 400 West 11th Street/231 Schrenk Hall, Rolla, MO 65409-1230 (United States); Department of Nuclear Engineering, 301 W. 14th St./222 Fulton Hall (United States)

2015-04-01

Highlights: • A fast-response heat transfer probe has been developed and used in this work. • Heat transport has been quantified in terms of local heat transfer coefficients. • The method of the electrically heated single sphere in packing has been applied. • The heat transfer coefficient increases from the center to the wall of packed bed. • This work advancing the knowledge of heat transport in the studied packed bed. - Abstract: Obtaining more precise results and a better understanding of the heat transport mechanism in the dynamic core of packed pebble-bed reactors is needed because this mechanism poses extreme challenges to the reliable design and efficient operation of these reactors. This mechanism can be quantified in terms of a solid-to-gas convective heat transfer coefficient. Therefore, in this work, the local convective heat transfer coefficients and their radial profiles were measured experimentally in a separate effect pilot-plant scale and cold-flow experimental setup of 0.3 m in diameter, using a sophisticated noninvasive heat transfer probe of spherical type. The effect of gas velocity on the heat transfer coefficient was investigated over a wide range of Reynolds numbers of practical importance. The experimental investigations of this work include various radial locations along the height of the bed. It was found that an increase in coolant gas flow velocity causes an increase in the heat transfer coefficient and that effect of the gas flow rate varies from laminar to turbulent flow regimes at all radial positions of the studied packed pebble-bed reactor. The results show that the local heat transfer coefficient increases from the bed center to the wall due to the change in the bed structure, and hence, in the flow pattern of the coolant gas. The findings clearly indicate that one value of an overall heat transfer coefficient cannot represent the local heat transfer coefficients within the bed; therefore, correlations are needed to

Hydromagnetic transport phenomena from a stretching or shrinking nonlinear nanomaterial sheet with Navier slip and convective heating: A model for bio-nano-materials processing

Energy Technology Data Exchange (ETDEWEB)

Uddin, M.J., E-mail: jashim_74@yahoo.com [Department of Mathematics, American International University-Bangladesh, Banani Dhaka 1213 (Bangladesh); Bég, O. Anwar [Gort Engovation Research (Propulsion/Biomechanics), Gabriel' s Wing House, 15 Southmere Ave., Bradford, BD7 3NU England (United Kingdom); Amin, N. [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor (Malaysia)

2014-11-15

Steady two-dimensional magnetohydrodynamic laminar free convective boundary layer slip flow of an electrically conducting Newtonian nanofluid from a translating stretching/shrinking sheet in a quiescent fluid is studied. A convective heating boundary condition is incorporated. The transport equations along with the boundary conditions are first converted into dimensionless form and following the implementation of a 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 from Maple. Validation of the Maple solutions is achieved with previous non-magnetic published results. The effects of the emerging thermophysical parameters; namely, stretching/shrinking, velocity slip, magnetic field, convective heat transfer and buoyancy ratio parameters, on the dimensionless velocity, temperature and concentration (nanoparticle fraction) are depicted graphically and interpreted at length. It is found that velocity increases whilst temperature and concentration reduce with the velocity slip. Magnetic field causes to reduce velocity and enhances temperature and concentration. Velocity, temperature as well as concentration rises with convective heating parameter. The study is relevant to the synthesis of bio-magnetic nanofluids of potential interest in wound treatments, skin repair and smart coatings for biological devices. - Highlights: • This paper analyses MHD slip flow of nofluid with convective boundary conditions. • Group method is used to transform governing equations into similarity equations. • The Runge–Kutta–Fehlberg method is used for numerical computations. • The study is relevant to synthesis of bio-magnetic nanofluids.

The discontinuous finite element method for solving Eigenvalue problems of transport equations

International Nuclear Information System (INIS)

Yang, Shulin; Wang, Ruihong

2011-01-01

In this paper, the multigroup transport equations for solving the eigenvalues λ and K_e_f_f under two dimensional cylindrical coordinate are discussed. Aimed at the equations, the discretizing way combining discontinuous finite element method (DFE) with discrete ordinate method (SN) is developed, and the iterative algorithms and steps are studied. The numerical results show that the algorithms are efficient. (author)

The H-N method for solving linear transport equation: theory and application

International Nuclear Information System (INIS)

Kaskas, A.; Gulecyuz, M.C.; Tezcan, C.

2002-01-01

The system of singular integral equation which is obtained from the integro-differential form of the linear transport equation as a result of Placzec lemma is solved. Application are given using the exit distributions and the infinite medium Green's function. The same theoretical results are also obtained with the use of the singular eigenfunction of the method of elementary solutions

Master equation and two heat reservoirs.

Science.gov (United States)

Trimper, Steffen

2006-11-01

A simple spin-flip process is analyzed under the presence of two heat reservoirs. While one flip process is triggered by a bath at temperature T, the inverse process is activated by a bath at a different temperature T'. The situation can be described by using a master equation approach in a second quantized Hamiltonian formulation. The stationary solution leads to a generalized Fermi-Dirac distribution with an effective temperature Te. Likewise the relaxation time is given in terms of Te. Introducing a spin representation we perform a Landau expansion for the averaged spin as order parameter and consequently, a free energy functional can be derived. Owing to the two reservoirs the model is invariant with respect to a simultaneous change sigma-sigma and TT'. This symmetry generates a third order term in the free energy which gives rise a dynamically induced first order transition.

Predicting fractional bed load transport rates: Application of the Wilcock‐Crowe equations to a regulated gravel bed river

Science.gov (United States)

Gaeuman, David; Andrews, E.D.; Krause, Andreas; Smith, Wes

2009-01-01

Bed load samples from four locations in the Trinity River of northern California are analyzed to evaluate the performance of the Wilcock‐Crowe bed load transport equations for predicting fractional bed load transport rates. Bed surface particles become smaller and the fraction of sand on the bed increases with distance downstream from Lewiston Dam. The dimensionless reference shear stress for the mean bed particle size (τ*rm) is largest near the dam, but varies relatively little between the more downstream locations. The relation between τ*rm and the reference shear stresses for other size fractions is constant across all locations. Total bed load transport rates predicted with the Wilcock‐Crowe equations are within a factor of 2 of sampled transport rates for 68% of all samples. The Wilcock‐Crowe equations nonetheless consistently under‐predict the transport of particles larger than 128 mm, frequently by more than an order of magnitude. Accurate prediction of the transport rates of the largest particles is important for models in which the evolution of the surface grain size distribution determines subsequent bed load transport rates. Values of τ*rm estimated from bed load samples are up to 50% larger than those predicted with the Wilcock‐Crowe equations, and sampled bed load transport approximates equal mobility across a wider range of grain sizes than is implied by the equations. Modifications to the Wilcock‐Crowe equation for determining τ*rm and the hiding function used to scale τ*rm to other grain size fractions are proposed to achieve the best fit to observed bed load transport in the Trinity River.

Neoclassical transport analysis for a class of high-β tokamak equilibria

International Nuclear Information System (INIS)

Rieser, H.; Werthmann, H.; Kuhn, S.

1995-01-01

Balescu's neoclassical transport theory is extended to the case of non-circular flux-surface geometries. Modified classical and neoclassical transport equations, governing particle and heat fluxes in the short- and long-mean-free-path regimes, are derived. These equations are shown to coincide to leading order with the corresponding equations given by Hirshman and Sigmar. They are then applied to an ideal MHD equilibrium, suitable as a simplified but analytically tractable model of a high-β tokamak. Numerical results for the radial profiles of the global (i.e. flux-surface integrated) particle and heat fluxes in the classical, Pfirsch-Schlueter and banana regimes are presented for geometry and plasma parameters realized in some tokamaks, like the divertor and injection tokamak experiment (DITE). This spatial representation provides direct insight into the overall collisional transport behaviour of a given equilibrium, whereas the anomalous transport problem is not addressed here. Our results demonstrate that for a given pressure profile the global neoclassical fluxes may depend very sensitively on the temperature profiles and that, in particular, the global classical and neoclassical ion heat fluxes exhibit a characteristic non-monotonic behaviour. (author)

Second order time evolution of the multigroup diffusion and P1 equations for radiation transport

International Nuclear Information System (INIS)

Olson, Gordon L.

2011-01-01

Highlights: → An existing multigroup transport algorithm is extended to be second-order in time. → A new algorithm is presented that does not require a grey acceleration solution. → The two algorithms are tested with 2D, multi-material problems. → The two algorithms have comparable computational requirements. - Abstract: An existing solution method for solving the multigroup radiation equations, linear multifrequency-grey acceleration, is here extended to be second order in time. This method works for simple diffusion and for flux-limited diffusion, with or without material conduction. A new method is developed that does not require the solution of an averaged grey transport equation. It is effective solving both the diffusion and P 1 forms of the transport equation. Two dimensional, multi-material test problems are used to compare the solution methods.

A low-frequency wave motion mechanism enables efficient energy transport in carbon nanotubes at high heat fluxes.

Science.gov (United States)

Zhang, Xiaoliang; Hu, Ming; Poulikakos, Dimos

2012-07-11

The great majority of investigations of thermal transport in carbon nanotubes (CNTs) in the open literature focus on low heat fluxes, that is, in the regime of validity of the Fourier heat conduction law. In this paper, by performing nonequilibrium molecular dynamics simulations we investigated thermal transport in a single-walled CNT bridging two Si slabs under constant high heat flux. An anomalous wave-like kinetic energy profile was observed, and a previously unexplored, wave-dominated energy transport mechanism is identified for high heat fluxes in CNTs, originated from excited low frequency transverse acoustic waves. The transported energy, in terms of a one-dimensional low frequency mechanical wave, is quantified as a function of the total heat flux applied and is compared to the energy transported by traditional Fourier heat conduction. The results show that the low frequency wave actually overtakes traditional Fourier heat conduction and efficiently transports the energy at high heat flux. Our findings reveal an important new mechanism for high heat flux energy transport in low-dimensional nanostructures, such as one-dimensional (1-D) nanotubes and nanowires, which could be very relevant to high heat flux dissipation such as in micro/nanoelectronics applications.

A time dependent mixing model to close PDF equations for transport in heterogeneous aquifers

Science.gov (United States)

Schüler, L.; Suciu, N.; Knabner, P.; Attinger, S.

2016-10-01

Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. The mixing model, describing the transport of the PDF in concentration space, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.

Mobile heat accumulators for lorry or train transport?; Mobile Waermespeicher fuer den LKW- oder Zugtransport?

Energy Technology Data Exchange (ETDEWEB)

Goldenberg, Philipp

2013-07-01

Where heat grids cannot be laid for geographic reasons, mobile heat accumulators may be appropriate. The mobile heat accumulators are transported by lorry or train between the heat source and the heat sink. The waste heat can be decoupled from biogas plants, waste incineration plants or industrial sites. Existing road or rail networks can be used for transportation. Decisive factors to achieve low heat production costs are: free waste heat, large and continuous heat quantities as well as a short distance between the heat source and the heat sink. (orig.)

Latent heat increases storage capacity. Heat transport by truck; Latente warmte vergroot opslagcapaciteit. Warmtetransport per vrachtauto is soms heel slim

Energy Technology Data Exchange (ETDEWEB)

De Jong, K.

2012-11-15

The project-group Biomass CHP (combined production of heat and power) organized a tour with a workshop in Dortmund, Germany, September 26, 2012, on storage and transport of heat and biogas. There are several projects in Germany involving road transport of heat by means of containers. A swimming pool in Dortmund already is using this option since 2008. Waste heat from a CHP-installation for landfill gas is collected from a waste dump [Dutch] De projectgroep Biomassa en WKK organiseerde 26 September een excursie met workshop in Dortmund over opslag en transport van warmte en biogas. Er zijn in Duitsland al meerdere projecten waarbij warmte per container over de weg wordt vervoerd. Een Dortmunds zwembad werkt hier al sinds 2008 mee. De restwarmte van een wkk op stortgas wordt opgehaald bij een afvalstortplaats.

Heat transport in low-dimensional materials: A review and perspective

Directory of Open Access Journals (Sweden)

Zhiping Xu

2016-05-01

Full Text Available Heat transport is a key energetic process in materials and devices. The reduced sample size, low dimension of the problem and the rich spectrum of material imperfections introduce fruitful phenomena at nanoscale. In this review, we summarize recent progresses in the understanding of heat transport process in low-dimensional materials, with focus on the roles of defects, disorder, interfaces, and the quantum-mechanical effect. New physics uncovered from computational simulations, experimental studies, and predictable models will be reviewed, followed by a perspective on open challenges.

Transport methods: general. 3. An Additive Angular-Dependent Re-balance Acceleration Method for Neutron Transport Equations

International Nuclear Information System (INIS)

Cho, Nam Zin; Park, Chang Je

2001-01-01

An additive angular-dependent re-balance (AADR) factor acceleration method is described to accelerate the source iteration of discrete ordinates transport calculation. The formulation of the AADR method follows that of the angular-dependent re-balance (ADR) method in that the re-balance factor is defined only on the cell interface and in that the low-order equation is derived by integrating the transport equation (high-order equation) over angular subspaces. But, the re-balance factor is applied additively. While the AADR method is similar to the boundary projection acceleration and the alpha-weighted linear acceleration, it is more general and does have distinct features. The method is easily extendible to DP N and low-order S N re-balancing, and it does not require consistent discretizations between the high- and low-order equations as in diffusion synthetic acceleration. We find by Fourier analysis and numerical results that the AADR method with a chosen form of weighting functions is unconditionally stable and very effective. There also exists an optimal weighting parameter that leads to the smallest spectral radius. The AADR acceleration method described in this paper is simple to implement, unconditionally stable, and very effective. It uses a physically based weighting function with an optimal parameter, leading to the best spectral radius of ρ<0.1865, compared to ρ<0.2247 of DSA. The application of the AADR acceleration method with the LMB scheme on a test problem shows encouraging results

Linear fractional diffusion-wave equation for scientists and engineers

CERN Document Server

Povstenko, Yuriy

2015-01-01

This book systematically presents solutions to the linear time-fractional diffusion-wave equation. It introduces the integral transform technique and discusses the properties of the Mittag-Leffler, Wright, and Mainardi functions that appear in the solutions. The time-nonlocal dependence between the flux and the gradient of the transported quantity with the “long-tail” power kernel results in the time-fractional diffusion-wave equation with the Caputo fractional derivative. Time-nonlocal generalizations of classical Fourier’s, Fick’s and Darcy’s laws are considered and different kinds of boundary conditions for this equation are discussed (Dirichlet, Neumann, Robin, perfect contact). The book provides solutions to the fractional diffusion-wave equation with one, two and three space variables in Cartesian, cylindrical and spherical coordinates. The respective sections of the book can be used for university courses on fractional calculus, heat and mass transfer, transport processes in porous media and ...

Mathematical Analysis of the Solidification Behavior of Plain Steel Based on Solute- and Heat-Transfer Equations in the Liquid-Solid Zone

Science.gov (United States)

Fujimura, Toshio; Takeshita, Kunimasa; Suzuki, Ryosuke O.

2018-04-01

An analytical approximate solution to non-linear solute- and heat-transfer equations in the unsteady-state mushy zone of Fe-C plain steel has been obtained, assuming a linear relationship between the solid fraction and the temperature of the mushy zone. The heat transfer equations for both the solid and liquid zone along with the boundary conditions have been linked with the equations to solve the whole equations. The model predictions ( e.g., the solidification constants and the effective partition ratio) agree with the generally accepted values and with a separately performed numerical analysis. The solidus temperature predicted by the model is in the intermediate range of the reported formulas. The model and Neuman's solution are consistent in the low carbon range. A conventional numerical heat analysis ( i.e., an equivalent specific heat method using the solidus temperature predicted by the model) is consistent with the model predictions for Fe-C plain steels. The model presented herein simplifies the computations to solve the solute- and heat-transfer simultaneous equations while searching for a solidus temperature as a part of the solution. Thus, this model can reduce the complexity of analyses considering the heat- and solute-transfer phenomena in the mushy zone.

Exponentially-convergent Monte Carlo for the 1-D transport equation

International Nuclear Information System (INIS)

Peterson, J. R.; Morel, J. E.; Ragusa, J. C.

2013-01-01

We define a new exponentially-convergent Monte Carlo method for solving the one-speed 1-D slab-geometry transport equation. This method is based upon the use of a linear discontinuous finite-element trial space in space and direction to represent the transport solution. A space-direction h-adaptive algorithm is employed to restore exponential convergence after stagnation occurs due to inadequate trial-space resolution. This methods uses jumps in the solution at cell interfaces as an error indicator. Computational results are presented demonstrating the efficacy of the new approach. (authors)

Single-phase pump model for analysis of LMFBR heat transport systems

International Nuclear Information System (INIS)

Madni, I.K.; Cazzoli, E.

1978-05-01

A single-phase pump model for transient and steady-state analysis of LMFBR heat transport systems is presented. Fundamental equations of the model are angular momentum balance to determine transient impeller speed and mass balance (including thermal expansion effects) to determine the level of sodium in the pump tank. Pump characteristics are modeled by homologous head and torque relations. All regions of pump operation are represented with reverse rotation allowed. The model also includes option for enthalpy rise calculations and pony motor operation. During steady state, the pump operating speed is determined by matching required head with total load in the circuit. Calculated transient results are presented for pump coastdown and double-ended pipe break accidents. The report examines the influence of frictional torque and specific speed on predicted response for the pump coastdown to natural circulation transient. The results for a double-ended pipe break accident indicate the necessity of including all regions of operation for pump characteristics

Non-local model analysis of heat pulse propagation and simulation of experiments in W7-AS

International Nuclear Information System (INIS)

Iwasaki, Takuya; Itoh, Sanae-I.; Yagi, Masatoshi; Itoh, Kimitaka; Stroth, U.

1999-01-01

A new model equation which includes the non-local effect in the hear flux is introduced to study the transient transport phenomena. A non-local heat flux, which is expressed in terms of the integral equation, is superimposed on the conventional form of the heat flux. This model is applied to describe the experimental results from the power switching [U. Stroth et al.: Plasma Phys. Control. Fusion 38 (1996) 1087] and the power modulation experiments [L. Giannone et al.: Nucl. Fusion 32 (1992) 1985] in the W7-AS stellarator. A small fraction of non-local component in the heat flux is found to be very effective in modifying the response against an external modulation. The transient feature of the transport property, which are observed in the response of heat pulse propagation, are qualitatively reproduced by the transport simulations based on this model. A possibility is discussed to estimate the correlation length of the non-local effect experimentally by use of the results of transport simulations. (author)

Application of Quasi-Heat-Pulse Solutions for Luikov’s Equations of Heat and Moisture Transfer for Calibrating and Utilizing Thermal Properties Apparatus

Science.gov (United States)

Mark A. Dietenberger; Charles R. Boardman

2014-01-01

Several years ago the Laplace transform solutions of Luikov’s differential equations were presented for one-dimensional heat and moisture transfer in porous hydroscopic orthotropic materials for the boundary condition of a gradual heat pulse applied to both surfaces of a flat slab. This paper presents calibration methods and data for the K-tester 637 (Lasercomp),...

Seasonal and mesoscale variability of oceanic transport of anthropogenic CO2

Directory of Open Access Journals (Sweden)

J.-C. Dutay

2009-11-01

Full Text Available Estimates of the ocean's large-scale transport of anthropogenic CO2 are based on one-time hydrographic sections, but the temporal variability of this transport has not been investigated. The aim of this study is to evaluate how the seasonal and mesoscale variability affect data-based estimates of anthropogenic CO2 transport. To diagnose this variability, we made a global anthropogenic CO2 simulation using an eddy-permitting version of the coupled ocean sea-ice model ORCA-LIM. As for heat transport, the seasonally varying transport of anthropogenic CO2 is largest within 20° of the equator and shows secondary maxima in the subtropics. Ekman transport generally drives most of the seasonal variability, but the contribution of the vertical shear becomes important near the equator and in the Southern Ocean. Mesoscale variabilty contributes to the annual-mean transport of both heat and anthropogenic CO2 with strong poleward transport in the Southern Ocean and equatorward transport in the tropics. This "rectified" eddy transport is largely baroclinic in the tropics and barotropic in the Southern Ocean due to a larger contribution from standing eddies. Our analysis revealed that most previous hydrographic estimates of meridional transport of anthropogenic CO2 are severely biased because they neglect temporal fluctuations due to non-Ekman velocity variations. In each of the three major ocean basins, this bias is largest near the equator and in the high southern latitudes. In the subtropical North Atlantic, where most of the hydrographic-based estimates have been focused, this uncertainty represents up to 20% and 30% of total meridional transport of heat and CO2. Generally though, outside the tropics and Southern Ocean, there are only small variations in meridional transport due to seasonal variations in tracer fields and time variations in eddy transport. For the North Atlantic, eddy variability accounts for up to 10% and 15% of the total transport of

An introduction to the Boltzmann equation and transport processes in gases

CERN Document Server

Kremer, Gilberto M; Colton, David

2010-01-01

This book covers classical kinetic theory of gases, presenting basic principles in a self-contained framework and from a more rigorous approach based on the Boltzmann equation. Uses methods in kinetic theory for determining the transport coefficients of gases.

The Role of Ocean and Atmospheric Heat Transport in the Arctic Amplification

Science.gov (United States)

Vargas Martes, R. M.; Kwon, Y. O.; Furey, H. H.

2017-12-01

Observational data and climate model projections have suggested that the Arctic region is warming around twice faster than the rest of the globe, which has been referred as the Arctic Amplification (AA). While the local feedbacks, e.g. sea ice-albedo feedback, are often suggested as the primary driver of AA by previous studies, the role of meridional heat transport by ocean and atmosphere is less clear. This study uses the Community Earth System Model version 1 Large Ensemble simulation (CESM1-LE) to seek deeper understanding of the role meridional oceanic and atmospheric heat transports play in AA. The simulation consists of 40 ensemble members with the same physics and external forcing using a single fully coupled climate model. Each ensemble member spans two time periods; the historical period from 1920 to 2005 using the Coupled Model Intercomparison Project Phase 5 (CMIP5) historical forcing and the future period from 2006 to 2100 using the CMIP5 Representative Concentration Pathways 8.5 (RCP8.5) scenario. Each of the ensemble members are initialized with slightly different air temperatures. As the CESM1-LE uses a single model unlike the CMIP5 multi-model ensemble, the internal variability and the externally forced components can be separated more clearly. The projections are calculated by comparing the period 2081-2100 relative to the time period 2001-2020. The CESM1-LE projects an AA of 2.5-2.8 times faster than the global average, which is within the range of those from the CMIP5 multi-model ensemble. However, the spread of AA from the CESM1-LE, which is attributed to the internal variability, is 2-3 times smaller than that of the CMIP5 ensemble, which may also include the inter-model differences. CESM1LE projects a decrease in the atmospheric heat transport into the Arctic and an increase in the oceanic heat transport. The atmospheric heat transport is further decomposed into moisture transport and dry static energy transport. Also, the oceanic heat

Experimental study of thermal performance of heat pipe with axial trapezoidal grooves

International Nuclear Information System (INIS)

Suh, Jeong Se; Lee, Woon

2003-01-01

Analysis and experiment are performed to investigate the thermal performance of a heat pipe with axial grooves. The heat pipe was designed in a 6.5 mm I.D., 17 axial trapezoidal grooves, 1000 mm long tube of aluminium, and ammonia as working fluid. A mathematical equations for heat pipe with axial grooves is formulated to obtain the capillary limitation on heat transport rate in a steady state. As a result, heat transport factor of heat pipe has the maximum at the operating temperature of 293K in 0m elevation. As the elevation of heat pipe increases, the heat transport factor of the heat pipe is reduced markedly, comparing with that of horizontal elevation of the heat pipe. It may be considered that such behavior of heat pipe is caused by the working fluid swarmed back to the condenser port due to gravity force and supercooled by a coolant of heat exchanger. Analytical results of heat transport factor are in a good agreement with those of experiment

Kinetic and transport theory near the tokamak edge

International Nuclear Information System (INIS)

Hazeltine, R.D.; Catto, P.J.

1995-12-01

Conventional transport orderings employed in the core of a tokamak plasma allow large divergence-free flows in flux surfaces, but only weak radial flows. However, alternate orderings are required in the edge region where radial diffusion must balance the rapid loss due to free-streaming to divertor plates or limiters. Kinetic equations commonly used to study the plasma core do not allow such a balance and are, therefore, inapplicable in the plasma edge. Similarly, core transport formulae cannot be extended to the edge region without major, qualitative alteration. Here the authors address the necessary changes. By deriving and solving a novel kinetic equation, they construct distinctive collisional transport laws for the plasma edge. They find that their edge ordering naturally retains the radial diffusion and parallel flow of particles, momentum and heat to lowest order in the conservation equations. To higher order they find a surprising form for parallel transport in the scrape-off layer, in which the parallel flow of particles and heat are driven by a combination of the conventional gradients, viscosity, and new terms involving radial derivatives. The new terms are not relatively small, and could affect understanding of limiter and divertor operation

Climate in the Absence of Ocean Heat Transport

Science.gov (United States)

Rose, B. E. J.

2015-12-01

The energy transported by the oceans to mid- and high latitudes is small compared to the atmosphere, yet exerts an outsized influence on the climate. A key reason is the strong interaction between ocean heat transport (OHT) and sea ice extent. I quantify this by comparing a realistic control climate simulation with a slab ocean simulation in which OHT is disabled. Using the state-of-the-art CESM with a realistic present-day continental configuration, I show that the absence of OHT leads to a 23 K global cooling and massive expansion of sea ice to near 30º latitude in both hemisphere. The ice expansion is asymmetric, with greatest extent in the South Pacific and South Indian ocean basins. I discuss implications of this enormous and asymmetric climate change for atmospheric circulation, heat transport, and tropical precipitation. Parameter sensitivity studies show that the simulated climate is far more sensitive to small changes in ice surface albedo in the absence of OHT, with some perturbations sufficient to cause a runaway Snowball Earth glaciation. I conclude that the oceans are responsible for an enormous global warming by mitigating an otherwise very potent sea ice albedo feedback, but that the magnitude of this effect is still rather uncertain. I will also present some ideas on adapting the simple energy balance model to account for the enhanced sensitivity of sea ice to heating from the ocean.

Numerical evaluation of the intensity transport equation for well-known wavefronts and intensity distributions

Science.gov (United States)

Campos-García, Manuel; Granados-Agustín, Fermín.; Cornejo-Rodríguez, Alejandro; Estrada-Molina, Amilcar; Avendaño-Alejo, Maximino; Moreno-Oliva, Víctor Iván.

2013-11-01

In order to obtain a clearer interpretation of the Intensity Transport Equation (ITE), in this work, we propose an algorithm to solve it for some particular wavefronts and its corresponding intensity distributions. By simulating intensity distributions in some planes, the ITE is turns into a Poisson equation with Neumann boundary conditions. The Poisson equation is solved by means of the iterative algorithm SOR (Simultaneous Over-Relaxation).

Solution of the Boltzmann-Fokker-Planck transport equation using exponential nodal schemes

International Nuclear Information System (INIS)

Ortega J, R.; Valle G, E. del

2003-01-01

There are carried out charge and energy calculations deposited due to the interaction of electrons with a plate of a certain material, solving numerically the electron transport equation for the Boltzmann-Fokker-Planck approach of first order in plate geometry with a computer program denominated TEOD-NodExp (Transport of Electrons in Discreet Ordinates, Nodal Exponentials), using the proposed method by the Dr. J. E. Morel to carry out the discretization of the variable energy and several spatial discretization schemes, denominated exponentials nodal. It is used the Fokker-Planck equation since it represents an approach of the Boltzmann transport equation that is been worth whenever it is predominant the dispersion of small angles, that is to say, resulting dispersion in small dispersion angles and small losses of energy in the transport of charged particles. Such electrons could be those that they face with a braking plate in a device of thermonuclear fusion. In the present work its are considered electrons of 1 MeV that impact isotropically on an aluminum plate. They were considered three different thickness of plate that its were designated as problems 1, 2 and 3. In the calculations it was used the discrete ordinate method S 4 with expansions of the dispersion cross sections until P 3 order. They were considered 25 energy groups of uniform size between the minimum energy of 0.1 MeV and the maximum of 1.0 MeV; the one spatial intervals number it was considered variable and it was assigned the values of 10, 20 and 30. (Author)

Diffusive and convective transport modelling from analysis of ECRH-stimulated electron heat wave propagation

International Nuclear Information System (INIS)

Erckmann, V.; Gasparino, U.; Giannone, L.

1992-01-01

ECRH power modulation experiments in toroidal devices offer the chance to analyze the electron heat transport more conclusively: the electron heat wave propagation can be observed by ECE (or SX) leading to radial profiles of electron temperature modulation amplitude and time delay (phase shift). Taking also the stationary power balance into account, the local electron heat transport can be modelled by a combination of diffusive and convective transport terms. This method is applied to ECRH discharges in the W7-AS stellarator (B=2.5T, R=2m, a≤18 cm) where the ECRH power deposition is highly localized. In W7-AS, the T e modulation profiles measured by a high resolution ECE system are the basis for the local transport analysis. As experimental errors limit the separation of diffusive and convective terms in the electron heat transport for central power deposition, also ECRH power modulation experiments with off-axis deposition and inward heat wave propagation were performed (with 70 GHz o-mode as well as with 140 GHz x-mode for increased absorption). Because collisional electron-ion coupling and radiative losses are only small, low density ECRH discharges are best candidates for estimating the electron heat flux from power balance. (author) 2 refs., 3 figs

Spatially adaptive hp refinement approach for PN neutron transport equation using spectral element method

International Nuclear Information System (INIS)

Nahavandi, N.; Minuchehr, A.; Zolfaghari, A.; Abbasi, M.

2015-01-01

Highlights: • Powerful hp-SEM refinement approach for P N neutron transport equation has been presented. • The method provides great geometrical flexibility and lower computational cost. • There is a capability of using arbitrary high order and non uniform meshes. • Both posteriori and priori local error estimation approaches have been employed. • High accurate results are compared against other common adaptive and uniform grids. - Abstract: In this work we presented the adaptive hp-SEM approach which is obtained from the incorporation of Spectral Element Method (SEM) and adaptive hp refinement. The SEM nodal discretization and hp adaptive grid-refinement for even-parity Boltzmann neutron transport equation creates powerful grid refinement approach with high accuracy solutions. In this regard a computer code has been developed to solve multi-group neutron transport equation in one-dimensional geometry using even-parity transport theory. The spatial dependence of flux has been developed via SEM method with Lobatto orthogonal polynomial. Two commonly error estimation approaches, the posteriori and the priori has been implemented. The incorporation of SEM nodal discretization method and adaptive hp grid refinement leads to high accurate solutions. Coarser meshes efficiency and significant reduction of computer program runtime in comparison with other common refining methods and uniform meshing approaches is tested along several well-known transport benchmarks

Nature of complex time eigenvalues of the one speed transport equation in a homogeneous sphere

International Nuclear Information System (INIS)

Dahl, E.B.; Sahni, D.C.

1990-01-01

The complex time eigenvalues of the transport equation have been studied for one speed neutrons, scattered isotropically in a homogeneous sphere with vacuum boundary conditions. It is shown that the complex decay constants vary continuously with the radius of the sphere. Our earlier conjecture (Dahl and Sahni (1983-84)) regarding disjoint arcs is thus shown to be true. We also indicate that complex decay constants exist even for large assemblies, though with rapid oscillations in the corresponding eigenvectors. These modes cannot be predicted by the diffusion equation as this behaviour of the eigenvectors contradicts the assumption of 'slowly varying flux' needed to derive the diffusion approximation from the transport equation. For an infinite system, the existence of complex modes is related to the solution of a homogeneous equation. (author)

Development of a polynomial nodal model to the multigroup transport equation in one dimension

International Nuclear Information System (INIS)

Feiz, M.

1986-01-01

A polynomial nodal model that uses Legendre polynomial expansions was developed for the multigroup transport equation in one dimension. The development depends upon the least-squares minimization of the residuals using the approximate functions over the node. Analytical expressions were developed for the polynomial coefficients. The odd moments of the angular neutron flux over the half ranges were used at the internal interfaces, and the Marshak boundary condition was used at the external boundaries. Sample problems with fine-mesh finite-difference solutions of the diffusion and transport equations were used for comparison with the model

FEHM, Finite Element Heat and Mass Transfer Code

International Nuclear Information System (INIS)

Zyvoloski, G.A.

2002-01-01

1 - Description of program or function: FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; and double porosity and double porosity/double permeability capabilities. 2 - Methods: FEHM uses a preconditioned conjugate gradient solution of coupled linear equations and a fully implicit, fully coupled Newton Raphson solution of nonlinear equations. It has the capability of simulating transport using either a advection/diffusion solution or a particle tracking method. 3 - Restriction on the complexity of the problem: Disk space and machine memory are the only limitations

Turbulent transport regimes and the SOL heat flux width

Science.gov (United States)

Myra, J. R.; D'Ippolito, D. A.; Russell, D. A.

2014-10-01

Understanding the responsible mechanisms and resulting scaling of the scrape-off layer (SOL) heat flux width is important for predicting viable operating regimes in future tokamaks, and for seeking possible mitigation schemes. Simulation and theory results using reduced edge/SOL turbulence models have produced SOL widths and scalings in reasonable accord with experiments in many cases. In this work, we attempt to qualitatively and conceptually understand various regimes of edge/SOL turbulence and the role of turbulent transport in establishing the SOL heat flux width. Relevant considerations include the type and spectral characteristics of underlying instabilities, the location of the gradient drive relative to the SOL, the nonlinear saturation mechanism, and the parallel heat transport regime. Recent SOLT turbulence code results are employed to understand the roles of these considerations and to develop analytical scalings. We find a heat flux width scaling with major radius R that is generally positive, consistent with older results reviewed in. The possible relationship of turbulence mechanisms to the heuristic drift mechanism is considered, together with implications for future experiments. Work supported by US DOE grant DE-FG02-97ER54392.

Magnetic-field asymmetry of nonlinear thermoelectric and heat transport

International Nuclear Information System (INIS)

Hwang, Sun-Yong; Sánchez, David; López, Rosa; Lee, Minchul

2013-01-01

Nonlinear transport coefficients do not obey, in general, reciprocity relations. We here discuss the magnetic-field asymmetries that arise in thermoelectric and heat transport of mesoscopic systems. Based on a scattering theory of weakly nonlinear transport, we analyze the leading-order symmetry parameters in terms of the screening potential response to either voltage or temperature shifts. We apply our general results to a quantum Hall antidot system. Interestingly, we find that certain symmetry parameters show a dependence on the measurement configuration. (paper)

Analysis of an upstream weighted collocation approximation to the transport equation

International Nuclear Information System (INIS)

Shapiro, A.; Pinder, G.F.

1981-01-01

The numerical behavior of a modified orthogonal collocation method, as applied to the transport equations, can be examined through the use of a Fourier series analysis. The necessity of such a study becomes apparent in the analysis of several techniques which emulate classical upstream weighting schemes. These techniques are employed in orthogonal collocation and other numerical methods as a means of handling parabolic partial differential equations with significant first-order terms. Divergent behavior can be shown to exist in one upstream weighting method applied to orthogonal collocation

Latent heat transport and microlayer evaporation in nucleate boiling

International Nuclear Information System (INIS)

Jawurek, H.H.

1977-08-01

Part 1 of this work provides a broad overview and, where possible, a quantitative assessment of the complex physical processes which together constitute the mechanism of nucleate boiling heat transfer. It is shown that under a wide range of conditions the primary surface-to-liquid heat flows within an area of bubble influence are so redistributed as to manifest themselves predominantly as latent heat transport, that is, as vaporisation into attached bubbles. Part 2 deals in greater detail with one of the component processes of latent heat transport, namely microlayer evaporation. A literature review reveals the need for synchronised records of microlayer geometry versus time and of normal bubble growth and departure. An apparatus developed to provide such records is described. High-speed cine interference photography from beneath and through a transparent heating surface provided details of microlayer geometry and an image reflection system synchronised these records with the bubble profile views. Results are given for methanol and ethanol boiling at sub-atmospheric pressures and at various heat fluxes and bulk subcoolings. In all cases it is found that microlayers were of sub-micron thickness, that microlayer thinning was restricted to the inner layer edge (with the thickness elsewhere remaining constant or increasing with time) and that the contribution of this visible evaporation to the total vapour flow into bubbles was negligible. The observation of thickening towards the outer microlayer edge, however, demonstrates that a liquid replenishment flow occurred simultaneously with the evaporation process

Numerical modeling of the thermoelectric cooler with a complementary equation for heat circulation in air gaps

Science.gov (United States)

Fang, En; Wu, Xiaojie; Yu, Yuesen; Xiu, Junrui

2017-03-01

In this paper, a numerical model is developed by combining thermodynamics with heat transfer theory. Taking inner and external multi-irreversibility into account, it is with a complementary equation for heat circulation in air gaps of a steady cooling system with commercial thermoelectric modules operating in refrigeration mode. With two modes concerned, the equation presents the heat flowing through air gaps which forms heat circulations between both sides of thermoelectric coolers (TECs). In numerical modelling, a TEC is separated as two temperature controlled constant heat flux reservoirs in a thermal resistance network. In order to obtain the parameter values, an experimental apparatus with a commercial thermoelectric cooler was built to characterize the performance of a TEC with heat source and sink assembly. At constant power dissipation, steady temperatures of heat source and both sides of the thermoelectric cooler were compared with those in a standard numerical model. The method displayed that the relationship between Φf and the ratio Φ_{c}'/Φ_{c} was linear as expected. Then, for verifying the accuracy of proposed numerical model, the data in another system were recorded. It is evident that the experimental results are in good agreement with simulation(proposed model) data at different heat transfer rates. The error is small and mainly results from the instabilities of thermal resistances with temperature change and heat flux, heat loss of the device vertical surfaces and measurements.

Weak Solution and Weakly Uniformly Bounded Solution of Impulsive Heat Equations Containing “Maximum” Temperature

Directory of Open Access Journals (Sweden)

Oyelami, Benjamin Oyediran

2013-09-01

Full Text Available In this paper, criteria for the existence of weak solutions and uniformly weak bounded solution of impulsive heat equation containing maximum temperature are investigated and results obtained. An example is given for heat flow system with impulsive temperature using maximum temperature simulator and criteria for the uniformly weak bounded of solutions of the system are obtained.

Fundamental experiment of potassium heat exchanger using principle of heat pipe

International Nuclear Information System (INIS)

Sumida, Isao; Kotani, Koichi

1976-01-01

In order to provide compact and reliable sodium equipments including a steam generator, performance tests are conducted with a potassium heat exchanger, which is featured by the separate construction of primary and secondary coolant systems. A small amount of potassium plays a role as an intermediate media of heat transportation between these two coolant systems. Heat is transferred by evaporation and condensation of potassium on the surface of the primary and the secondary coolant pipings, respectively. The tests are performed in the temperature range of 200 -- 300 0 C and the maximum heat transfer reaches 1.3kW (heat transfer rate at the primary heating source: 8.6W/cm 2 at 300 0 C). The experimental results are analyzed by using Langmuir's and Schrage's equation and close agreement between experiment and theory is obtained. (auth.)

New numerical method for solving the solute transport equation

International Nuclear Information System (INIS)

Ross, B.; Koplik, C.M.

1978-01-01

The solute transport equation can be solved numerically by approximating the water flow field by a network of stream tubes and using a Green's function solution within each stream tube. Compared to previous methods, this approach permits greater computational efficiency and easier representation of small discontinuities, and the results are easier to interpret physically. The method has been used to study hypothetical sites for disposal of high-level radioactive waste

Equations governing the liquid-film flow over a plane with heat flux and interfacial phase change

International Nuclear Information System (INIS)

Spindler, B.

1983-01-01

The purpose of the study is to find a system of equations which can be used to study the linear stability of a liquid film flow over a plane exhibiting wall heat flux and interfacial phase change. The flow of such a film is governed by four groups of equations: the equations for mass balance, momentum and energy in the liquid; equations for the balance in the steam; equations for the balance at the liquid-steam interface; and the boundary conditions. Two flow patterns are considered - flow with upstream film and film condensation. Stability is studied by perturbation methods

Equations governing the liquid-film flow over a plane with heat flux and interfacial phase change

Science.gov (United States)

Spindler, B.

1983-08-01

The purpose of the study is to find a system of equations which can be used to study the linear stability of a liquid film flow over a plane exhibiting wall heat flux and interfacial phase change. The flow of such a film is governed by four groups of equations: the equations for mass balance, momentum and energy in the liquid; equations for the balance in the steam; equations for the balance at the liquid-steam interface; and the boundary conditions. Two flow patterns are considered - flow with upstream film and film condensation. Stability is studied by perturbation methods.

Water, solute and heat transport in the soil: the Australian connection

Science.gov (United States)

Knight, John

2016-04-01

The interest of Peter Raats in water, solute and heat transport in the soil has led to scientific and/or personal interactions with several Australian scientists such as John Philip, David Smiles, Greg Davis and John Knight. Along with John Philip and Robin Wooding, Peter was an early user of the Gardner (1958) linearised model of soil water flow, which brought him into competition with John Philip. I will discuss some of Peter's solutions relevant to infiltration from line and point sources, cavities and basins. A visit to Canberra, Australia in the early 1980s led to joint work on soil water flow, and on combined water and solute movement with David Smiles and others. In 1983 Peter was on the PhD committee for Greg Davis at the University of Wollongong, and some of the methods in his thesis 'Mathematical modelling of rate-limiting mechanisms of pyritic oxidation in overburden dumps' were later used by Peter's student Sjoerd van der Zee. David Smiles and Peter wrote a survey article 'Hydrology of swelling clay soils' in 2005. In the last decade Peter has been investigating the history of groundwater and vadose zone hydrology, and recently he and I have been bringing to light the largely forgotten work of Lewis Fry Richardson on finite difference solution of the heat equation, drainage theory, soil physics, and the soil-plant-atmosphere continuum.

Coupled Transport Phenomena in the Opalinus Clay: Implications for Radionuclide Transport

International Nuclear Information System (INIS)

Soler, J.M.

1999-09-01

Coupled phenomena (thermal and chemical osmosis, hyperfiltration, coupled diffusion, thermal diffusion, thermal filtration, Dufour effect) may play an important role in fluid, solute and heat transport in clay-rich formations, such as the Opalinus Clay (OPA), which are being considered as potential hosts for radioactive waste repositories. In this study, the potential effects of coupled phenomena on radionuclide transport in the vicinity of a repository for vitrified high-level radioactive waste (HLW) and spent nuclear fuel (SF) hosted by the Opalinus Clay, at times equal to or greater than the expected lifetime of the waste canisters (about 1000 years), have been addressed. Firstly, estimates of the solute fluxes associated with chemical osmosis, hyperfiltration, thermal diffusion and thermal osmosis have been calculated. Available experimental data concerning coupled transport phenomena in compacted clays, and the hydrogeological and geochemical conditions to which the Opalinus Clay is subject, have been used for these estimates. These estimates suggest that thermal osmosis is the only coupled transport mechanism that could have a strong impact on solute and fluid transport in the vicinity of the repository. Secondly, estimates of the heat fluxes associated with thermal filtration and the Dufour effect in the vicinity of the repository have been calculated. The calculated heat fluxes are absolutely negligible compared to the heat flux caused by thermal conduction. As a further step to obtain additional insight into the effects of coupled phenomena on solute transport, the solute fluxes associated with advection, chemical diffusion, thermal and chemical osmosis, hyperfiltration and thermal diffusion have been incorporated into a simple one-dimensional transport equation. The analytical solution of this equation, with appropriate parameters, shows again that thermal osmosis is the only coupled transport mechanism that could have a strong effect on repository

Coupled Transport Phenomena in the Opalinus Clay: Implications for Radionuclide Transport

Energy Technology Data Exchange (ETDEWEB)

Soler, J.M.

1999-09-01

Coupled phenomena (thermal and chemical osmosis, hyperfiltration, coupled diffusion, thermal diffusion, thermal filtration, Dufour effect) may play an important role in fluid, solute and heat transport in clay-rich formations, such as the Opalinus Clay (OPA), which are being considered as potential hosts for radioactive waste repositories. In this study, the potential effects of coupled phenomena on radionuclide transport in the vicinity of a repository for vitrified high-level radioactive waste (HLW) and spent nuclear fuel (SF) hosted by the Opalinus Clay, at times equal to or greater than the expected lifetime of the waste canisters (about 1000 years), have been addressed. Firstly, estimates of the solute fluxes associated with chemical osmosis, hyperfiltration, thermal diffusion and thermal osmosis have been calculated. Available experimental data concerning coupled transport phenomena in compacted clays, and the hydrogeological and geochemical conditions to which the Opalinus Clay is subject, have been used for these estimates. These estimates suggest that thermal osmosis is the only coupled transport mechanism that could have a strong impact on solute and fluid transport in the vicinity of the repository. Secondly, estimates of the heat fluxes associated with thermal filtration and the Dufour effect in the vicinity of the repository have been calculated. The calculated heat fluxes are absolutely negligible compared to the heat flux caused by thermal conduction. As a further step to obtain additional insight into the effects of coupled phenomena on solute transport, the solute fluxes associated with advection, chemical diffusion, thermal and chemical osmosis, hyperfiltration and thermal diffusion have been incorporated into a simple one-dimensional transport equation. The analytical solution of this equation, with appropriate parameters, shows again that thermal osmosis is the only coupled transport mechanism that could have a strong effect on repository

Interfacial area transport of subcooled boiling flow in a vertical annulus

Energy Technology Data Exchange (ETDEWEB)

Brooks, Caleb S.; Ozar, Basar; Hibiki, Takashi; Ishii, Mamoru, E-mail: ishii@purdue.edu

2014-03-15

Highlights: • Discussion of boiling and wall nucleation dataset obtained in a vertical annulus. • Overview of the interfacial area transport equation modeling in boiling flow. • Comparison of bubble departure diameter and frequency with existing models. • Evaluation of the interfacial area transport equation prediction in boiling flow. - Abstract: In an effort to improve the prediction of void fraction and heat transfer characteristics in two-phase systems, the two-group interfacial area transport equation has been developed for use with the two-group two-fluid model. The two-group approach treats spherical/distorted bubbles as Group-1 and cap/slug/churn-turbulent bubbles as Group-2. Therefore, the interfacial area transport of steam-water two-phase flow in a vertical annulus has been investigated experimentally, including bulk flow parameters and wall nucleation characteristics. The theoretical modeling of interfacial area transport equation with phase change terms is introduced and discussed along with the experimental results. Benchmark of the interfacial area transport equation is performed considering the effects of bubble interaction mechanisms such as bubble break-up and coalescence, as well as, effects of phase change mechanisms such as wall nucleation and condensation for subcooled boiling. From the benchmark, sensitivity in the constitutive relations for Group-1 phase change mechanisms, such as wall nucleation and condensation is clear. The Group-2 interfacial area transport is shown to be dominated by the interfacial heat transfer mechanism causing expansion of Group-1 bubbles into Group-2 bubbles in the boiling flow.

Surface perturbations of a shallow viscous fluid heated from below and the (2+1)-dimensional Burgers equation

International Nuclear Information System (INIS)

Kraenkel, R.A.; Pereira, J.G.; Manna, M.A.

1991-01-01

The (2+1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfy the condition R ≠ 30. A solution to this equation is explicity exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink. (author)

Large eddy simulations of turbulent flows with heat transfer

International Nuclear Information System (INIS)

Chatelain, Alexandre

2004-01-01

LES of turbulent flows with heat transfer was used within the framework of conjugate heat transfer problems. The objective of this work lies not only in identifying the various elements likely to impair temperature fluctuations estimations at the fluid/solid interface but also to introduce adequate wall modeling. The choice of a proper convection scheme for the transport of passive scalars led to the adoption of a high order upwind scheme with slope limiter. The use of classical wall models having shown some weaknesses as for the estimation of parietal temperature fluctuations, two new approaches are proposed and tested. The first one relies on a complete resolution of the Navier-Stokes equations on a refined grid close to the wall making it possible to rebuild the temperature fluctuations near the wall. The second one relies on the simultaneous and one dimensional resolution of a turbulent boundary layer equation and a variance transport equation near the wall. (author) [fr

Thermophysical and heat transfer properties of phase change material candidate for waste heat transportation system

Science.gov (United States)

Kaizawa, Akihide; Maruoka, Nobuhiro; Kawai, Atsushi; Kamano, Hiroomi; Jozuka, Tetsuji; Senda, Takeshi; Akiyama, Tomohiro

2008-05-01

A waste heat transportation system trans-heat (TH) system is quite attractive that uses the latent heat of a phase change material (PCM). The purpose of this paper is to study the thermophysical properties of various sugars and sodium acetate trihydrate (SAT) as PCMs for a practical TH system and the heat transfer property between PCM selected and heat transfer oil, by using differential scanning calorimetry (DSC), thermogravimetry-differential thermal analysis (TG-DTA) and a heat storage tube. As a result, erythritol, with a large latent heat of 344 kJ/kg at melting point of 117°C, high decomposition point of 160°C and excellent chemical stability under repeated phase change cycles was found to be the best PCM among them for the practical TH system. In the heat release experiments between liquid erythritol and flowing cold oil, we observed foaming phenomena of encapsulated oil, in which oil droplet was coated by solidification of PCM.

Finite moments approach to the time-dependent neutron transport equation

International Nuclear Information System (INIS)

Kim, Sang Hyun

1994-02-01

Currently, nodal techniques are widely used in solving the multidimensional diffusion equation because of savings in computing time and storage. Thanks to the development of computer technology, one can now solve the transport equation instead of the diffusion equation to obtain more accurate solution. The finite moments method, one of the nodal methods, attempts to represent the fluxes in the cell and on cell surfaces more rigorously by retaining additional spatial moments. Generally, there are two finite moments schemes to solve the time-dependent transport equation. In one, the time variable is treated implicitly with finite moments method in space variable (implicit finite moments method), the other method uses finite moments method in both space and time (space-time finite moments method). In this study, these two schemes are applied to two types of time-dependent neutron transport problems. One is a fixed source problem, the other a heterogeneous fast reactor problem with delayed neutrons. From the results, it is observed that the two finite moments methods give almost the same solutions in both benchmark problems. However, the space-time finite moments method requires a little longer computing time than that of the implicit finite moments method. In order to reduce the longer computing time in the space-time finite moments method, a new iteration strategy is exploited, where a few time-stepwise calculation, in which original time steps are grouped into several coarse time divisions, is performed sequentially instead of performing iterations over the entire time steps. This strategy results in significant reduction of the computing time and we observe that 2-or 3-stepwise calculation is preferable. In addition, we propose a new finite moments method which is called mixed finite moments method in this thesis. Asymptotic analysis for the finite moments method shows that accuracy of the solution in a heterogeneous problem mainly depends on the accuracy of the

CACTUS, a characteristics solution to the neutron transport equations in complicated geometries

International Nuclear Information System (INIS)

Halsall, M.J.

1980-04-01

CACTUS has been written to solve the multigroup neutron transport equation in a general two-dimensional geometry. The method is based upon a characteristics formulation for the problem in which the transport equation is integrated explicitly along straight line tracks that are suitably distributed throughout the problem. Source distributions and scattering are assumed to be isotropic, but the only restriction on geometry is that the outer boundary should be rectangular. Within this rectangular boundary the user is free to build his problem geometry using any combination of intersecting straight lines and circular arcs. The theory of the method is described, followed by some details of a coding, a sensitivity study on the number of tracks required to integrate fluxes in a particular problem, a user's guide, and a few test cases. (author)

First-principles simulations of heat transport

Science.gov (United States)

Puligheddu, Marcello; Gygi, Francois; Galli, Giulia

2017-11-01

Advances in understanding heat transport in solids were recently reported by both experiment and theory. However an efficient and predictive quantum simulation framework to investigate thermal properties of solids, with the same complexity as classical simulations, has not yet been developed. Here we present a method to compute the thermal conductivity of solids by performing ab initio molecular dynamics at close to equilibrium conditions, which only requires calculations of first-principles trajectories and atomic forces, thus avoiding direct computation of heat currents and energy densities. In addition the method requires much shorter sequential simulation times than ordinary molecular dynamics techniques, making it applicable within density functional theory. We discuss results for a representative oxide, MgO, at different temperatures and for ordered and nanostructured morphologies, showing the performance of the method in different conditions.

Heat transport in an anharmonic crystal

Science.gov (United States)

Acharya, Shiladitya; Mukherjee, Krishnendu

2018-04-01

We study transport of heat in an ordered, anharmonic crystal in the form of slab geometry in three dimensions. Apart from attaching baths of Langevin type to two extreme surfaces, we also attach baths of same type to the intermediate surfaces of the slab. Since the crystal is uninsulated, it exchanges energy with the intermediate heat baths. We find that both Fourier’s law of heat conduction and the Newton’s law of cooling hold to leading order in anharmonic coupling. The leading behavior of the temperature profile is exponentially falling from high to low temperature surface of the slab. As the anharmonicity increases, profiles fall more below the harmonic one in the log plot. In the thermodynamic limit thermal conductivity remains independent of the environment temperature and its leading order anharmonic contribution is linearly proportional to the temperature change between the two extreme surfaces of the slab. A fast crossover from one-dimensional (1D) to three-dimensional (3D) behavior of the thermal conductivity is observed in the system.

Mesoscale Eddies in the Northwestern Pacific Ocean: Three-Dimensional Eddy Structures and Heat/Salt Transports

Science.gov (United States)

Dong, Di; Brandt, Peter; Chang, Ping; Schütte, Florian; Yang, Xiaofeng; Yan, Jinhui; Zeng, Jisheng

2017-12-01

The region encompassing the Kuroshio Extension (KE) in the Northwestern Pacific Ocean (25°N-45°N and 130°E-180°E) is one of the most eddy-energetic regions of the global ocean. The three-dimensional structures and transports of mesoscale eddies in this region are comprehensively investigated by combined use of satellite data and Argo profiles. With the allocation of Argo profiles inside detected eddies, the spatial variations of structures of eddy temperature and salinity anomalies are analyzed. The results show that eddies predominantly have subsurface (near-surface) intensified temperature and salinity anomalies south (north) of the KE jet, which is related to different background stratifications between these regions. A new method based on eddy trajectories and the inferred three-dimensional eddy structures is proposed to estimate heat and salt transports by eddy movements in a Lagrangian framework. Spatial distributions of eddy transports are presented over the vicinity of the KE for the first time. The magnitude of eddy-induced meridional heat (freshwater volume) transport is on the order of 0.01 PW (103 m3/s). The eddy heat transport divergence results in an oceanic heat loss south and heat gain north of the KE, thereby reinforcing and counteracting the oceanic heat loss from air-sea fluxes south and north of the KE jet, respectively. It also suggests a poleward heat transport across the KE jet due to eddy propagation.

Solar-energy heats a transportation test center--Pueblo, Colorado

Science.gov (United States)

1981-01-01

Petroleum-base, thermal energy transport fluid circulating through 583 square feet of flat-plate solar collectors accumulates majority of energy for space heating and domestic hot-water of large Test Center. Report describes operation, maintenance, and performance of system which is suitable for warehouses and similar buildings. For test period from February 1979 to January 1980, solar-heating fraction was 31 percent, solar hot-water fraction 79 percent.

On the physical solutions to the heat equation subjected to nonlinear boundary conditions

International Nuclear Information System (INIS)

Gama, R.M.S. da.

1990-01-01

This work consists of a discussion on the physical solutions to the steady-state heat transfer equation, when it is subjected to nonlinear boundary conditions. It will be presented a functional, whose minimum occurs for the (unique) physical solution to the condidered heat transfer problem, suitable for a large class of typical (nonlinear) boundary conditions (representing the radiative/convective loss from the body to the environment). It will be demonstrated that these problems admit-always one, and only one, physical solution (which represents the absolute temperature). (author)

Neoclassical and anomalous transport in axisymmetric toroidal plasmas with electrostatic turbulence

International Nuclear Information System (INIS)

Sugama, H.; Horton, W.

1995-01-01

Neoclassical and anomalous transport fluxes are determined for axisymmetric toroidal plasmas with weak electrostatic fluctuations. The neoclassical and anomalous fluxes are defined based on the ensemble-averaged kinetic equation with the statistically averaged nonlinear term. The anomalous forces derived from that quasilinear term induce the anomalous particle and heat fluxes. The neoclassical banana-plateau particle and heat fluxes and the bootstrap current are also affected by the fluctuations through the parallel anomalous forces and the modified parallel viscosities. The quasilinear term, the anomalous forces, and the anomalous particle and heat fluxes are evaluated from the fluctuating part of the drift kinetic equation. The averaged drift kinetic equation with the quasilinear term is solved for the plateau regime to derive the parallel viscosities modified by the fluctuations. The entropy production rate due to the anomalous transport processes is formulated and used to identify conjugate pairs of the anomalous fluxes and forces, which are connected by the matrix with the Onsager symmetry. copyright 1995 American Institute of Physics

Neoclassical and anomalous transport in axisymmetric toroidal plasmas with electrostatic turbulence

International Nuclear Information System (INIS)

Sugama, H.; Horton, W.

1995-05-01

Neoclassical and anomalous transport fluxes are determined for axisymmetric toroidal plasmas with weak electrostatic fluctuations. The neoclassical and anomalous fluxes are defined based on the ensemble-averaged kinetic equation with the statistically averaged nonlinear term. The anomalous forces derived from that quasilinear term induce the anomalous particle and heat fluxes. The neoclassical banana-plateau particle and heat fluxes and the bootstrap current are also affected by the fluctuations through the parallel anomalous forces and the modified parallel viscosities. The quasilinear term, the anomalous forces, and the anomalous particle and heat fluxes are evaluated from the fluctuating part of the drift kinetic equation. The averaged drift kinetic equation with the quasilinear term is solved for the plateau regime to derive the parallel viscosities modified by the fluctuations. The entropy production rate due to the anomalous transport processes is formulated and used to identify conjugate pairs of the anomalous fluxes and forces, which are connected by the matrix with the Onsager symmetry. (author)

RTk/SN Solutions of the Two-Dimensional Multigroup Transport Equations in Hexagonal Geometry

International Nuclear Information System (INIS)

Valle, Edmundo del; Mund, Ernest H.

2004-01-01

This paper describes an extension to the hexagonal geometry of some weakly discontinuous nodal finite element schemes developed by Hennart and del Valle for the two-dimensional discrete ordinates transport equation in quadrangular geometry. The extension is carried out in a way similar to the extension to the hexagonal geometry of nodal element schemes for the diffusion equation using a composite mapping technique suggested by Hennart, Mund, and del Valle. The combination of the weakly discontinuous nodal transport scheme and the composite mapping is new and is detailed in the main section of the paper. The algorithm efficiency is shown numerically through some benchmark calculations on classical problems widely referred to in the literature

The Transport Equation in Optically Thick Media: Discussion of IMC and its Diffusion Limit

Energy Technology Data Exchange (ETDEWEB)

Szoke, A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Brooks, E. D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2016-07-12

We discuss the limits of validity of the Implicit Monte Carlo (IMC) method for the transport of thermally emitted radiation. The weakened coupling between the radiation and material energy of the IMC method causes defects in handling problems with strong transients. We introduce an approach to asymptotic analysis for the transport equation that emphasizes the fact that the radiation and material temperatures are always different in time-dependent problems, and we use it to show that IMC does not produce the correct diffusion limit. As this is a defect of IMC in the continuous equations, no improvement to its discretization can remedy it.

Modeling Blazar Spectra by Solving an Electron Transport Equation

Science.gov (United States)

Lewis, Tiffany; Finke, Justin; Becker, Peter A.

2018-01-01

Blazars are luminous active galaxies across the entire electromagnetic spectrum, but the spectral formation mechanisms, especially the particle acceleration, in these sources are not well understood. We develop a new theoretical model for simulating blazar spectra using a self-consistent electron number distribution. Specifically, we solve the particle transport equation considering shock acceleration, adiabatic expansion, stochastic acceleration due to MHD waves, Bohm diffusive particle escape, synchrotron radiation, and Compton radiation, where we implement the full Compton cross-section for seed photons from the accretion disk, the dust torus, and 26 individual broad lines. We used a modified Runge-Kutta method to solve the 2nd order equation, including development of a new mathematical method for normalizing stiff steady-state ordinary differential equations. We show that our self-consistent, transport-based blazar model can qualitatively fit the IR through Fermi g-ray data for 3C 279, with a single-zone, leptonic configuration. We use the solution for the electron distribution to calculate multi-wavelength SED spectra for 3C 279. We calculate the particle and magnetic field energy densities, which suggest that the emitting region is not always in equipartition (a common assumption), but sometimes matter dominated. The stratified broad line region (based on ratios in quasar reverberation mapping, and thus adding no free parameters) improves our estimate of the location of the emitting region, increasing it by ~5x. Our model provides a novel view into the physics at play in blazar jets, especially the relative strength of the shock and stochastic acceleration, where our model is well suited to distinguish between these processes, and we find that the latter tends to dominate.

An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media

KAUST Repository

Sun, Shuyu

2012-06-02

A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.

An Equation-Type Approach for the Numerical Solution of the Partial Differential Equations Governing Transport Phenomena in Porous Media

KAUST Repository

Sun, Shuyu; Salama, Amgad; El-Amin, Mohamed

2012-01-01

A new technique for the numerical solution of the partial differential equations governing transport phenomena in porous media is introduced. In this technique, the governing equations as depicted from the physics of the problem are used without extra manipulations. In other words, there is no need to reduce the number of governing equations by some sort of mathematical manipulations. This technique enables the separation of the physics part of the problem and the solver part, which makes coding more robust and could be used in several other applications with little or no modifications (e.g., multi-phase flow in porous media). In this method, one abandons the need to construct the coefficient matrix for the pressure equation. Alternatively, the coefficients are automatically generated within the solver routine. We show examples of using this technique to solving several flow problems in porous media.

Approximate method for solving the velocity dependent transport equation in a slab lattice

International Nuclear Information System (INIS)

Ferrari, A.

1966-01-01

A method is described that is intended to provide an approximate solution of the transport equation in a medium simulating a water-moderated plate filled reactor core. This medium is constituted by a periodic array of water channels and absorbing plates. The velocity dependent transport equation in slab geometry is included. The computation is performed in a water channel: the absorbing plates are accounted for by the boundary conditions. The scattering of neutrons in water is assumed isotropic, which allows the use of a double Pn approximation to deal with the angular dependence. This method is able to represent the discontinuity of the angular distribution at the channel boundary. The set of equations thus obtained is dependent only on x and v and the coefficients are independent on x. This solution suggests to try solutions involving Legendre polynomials. This scheme leads to a set of equations v dependent only. To obtain an explicit solution, a thermalization model must now be chosen. Using the secondary model of Cadilhac a solution of this set is easy to get. The numerical computations were performed with a particular secondary model, the well-known model of Wigner and Wilkins. (author) [fr

A numerical spectral approach to solve the dislocation density transport equation

International Nuclear Information System (INIS)

Djaka, K S; Taupin, V; Berbenni, S; Fressengeas, C

2015-01-01

A numerical spectral approach is developed to solve in a fast, stable and accurate fashion, the quasi-linear hyperbolic transport equation governing the spatio-temporal evolution of the dislocation density tensor in the mechanics of dislocation fields. The approach relies on using the Fast Fourier Transform algorithm. Low-pass spectral filters are employed to control both the high frequency Gibbs oscillations inherent to the Fourier method and the fast-growing numerical instabilities resulting from the hyperbolic nature of the transport equation. The numerical scheme is validated by comparison with an exact solution in the 1D case corresponding to dislocation dipole annihilation. The expansion and annihilation of dislocation loops in 2D and 3D settings are also produced and compared with finite element approximations. The spectral solutions are shown to be stable, more accurate for low Courant numbers and much less computation time-consuming than the finite element technique based on an explicit Galerkin-least squares scheme. (paper)

A general analytical approach to the one-group, one-dimensional transport equation

International Nuclear Information System (INIS)

Barichello, L.B.; Vilhena, M.T.

1993-01-01

The main feature of the presented approach to solve the neutron transport equation consists in the application of the Laplace transform to the discrete ordinates equations, which yields a linear system of order N to be solved (LTS N method). In this paper this system is solved analytically and the inversion is performed using the Heaviside expansion technique. The general formulation achieved by this procedure is then applied to homogeneous and heterogeneous one-group slab-geometry problems. (orig.) [de

Systems with a constant heat flux with applications to radiative heat transport across nanoscale gaps and layers

Science.gov (United States)

Budaev, Bair V.; Bogy, David B.

2018-06-01

We extend the statistical analysis of equilibrium systems to systems with a constant heat flux. This extension leads to natural generalizations of Maxwell-Boltzmann's and Planck's equilibrium energy distributions to energy distributions of systems with a net heat flux. This development provides a long needed foundation for addressing problems of nanoscale heat transport by a systematic method based on a few fundamental principles. As an example, we consider the computation of the radiative heat flux between narrowly spaced half-spaces maintained at different temperatures.

An Analytic Approach to Developing Transport Threshold Models of Neoclassical Tearing Modes in Tokamaks

International Nuclear Information System (INIS)

Mikhailovskii, A.B.; Shirokov, M.S.; Konovalov, S.V.; Tsypin, V.S.

2005-01-01

Transport threshold models of neoclassical tearing modes in tokamaks are investigated analytically. An analysis is made of the competition between strong transverse heat transport, on the one hand, and longitudinal heat transport, longitudinal heat convection, longitudinal inertial transport, and rotational transport, on the other hand, which leads to the establishment of the perturbed temperature profile in magnetic islands. It is shown that, in all these cases, the temperature profile can be found analytically by using rigorous solutions to the heat conduction equation in the near and far regions of a chain of magnetic islands and then by matching these solutions. Analytic expressions for the temperature profile are used to calculate the contribution of the bootstrap current to the generalized Rutherford equation for the island width evolution with the aim of constructing particular transport threshold models of neoclassical tearing modes. Four transport threshold models, differing in the underlying competing mechanisms, are analyzed: collisional, convective, inertial, and rotational models. The collisional model constructed analytically is shown to coincide exactly with that calculated numerically; the reason is that the analytical temperature profile turns out to be the same as the numerical profile. The results obtained can be useful in developing the next generation of general threshold models. The first steps toward such models have already been made

The role of the velocity gradient in laminar convective heat transfer through a tube with a uniform wall heat flux

International Nuclear Information System (INIS)

Wang Liangbi; Zhang Qiang; Li Xiaoxia

2009-01-01

This paper aims to contribute to a better understanding of convective heat transfer. For this purpose, the reason why thermal diffusivity should be placed before the Laplacian operator of the heat flux, and the role of the velocity gradient in convective heat transfer are analysed. The background to these analyses is that, when the energy conservation equation of convective heat transfer is used to explain convective heat transfer there are two points that are difficult for teachers to explain and for undergraduates to understand: thermal diffusivity is placed before the Laplacian operator of temperature; on the wall surface (the fluid side) the velocity is zero, a diffusion equation of temperature is gained from energy conservation equation, however, temperature cannot be transported. Consequently, the real physical meaning of thermal diffusivity is not clearly reflected in the energy conservation equation, and whether heat transfer occurs through a diffusion process or a convection process on the wall surface is not clear. Through a simple convective heat transfer case: laminar convective heat transfer in a tube with a uniform wall heat flux on the tube wall, this paper explains these points more clearly. The results declare that it is easier for teachers to explain and for undergraduates to understand these points when a description of heat transfer in terms of the heat flux is used. In this description, thermal diffusivity is placed before the Laplacian operator of the heat flux; the role of the velocity gradient in convective heat transfer appears, on the wall surface, the fact whether heat transfer occurs through a diffusion process or a convection process can be explained and understood easily. The results are not only essential for teachers to improve the efficiency of university-level physics education regarding heat transfer, but they also enrich the theories for understanding heat transfer

Neoclassical MHD equations for tokamaks

International Nuclear Information System (INIS)

Callen, J.D.; Shaing, K.C.

1986-03-01

The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion

New equations for density, entropy, heat capacity, and potential temperature of a saline thermal fluid

Science.gov (United States)

Sun, Hongbing; Feistel, Rainer; Koch, Manfred; Markoe, Andrew

2008-10-01

A set of fitted polynomial equations for calculating the physical variables density, entropy, heat capacity and potential temperature of a thermal saline fluid for a temperature range of 0-374 °C, pressure range of 0.1-100 MPa and absolute salinity range of 0-40 g/kg is established. The freshwater components of the equations are extracted from the recently released tabulated data of freshwater properties of Wagner and Pruß [2002. The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Journal of Physical and Chemical Reference Data 31, 387-535]. The salt water component of the equation is based on the near-linear relationship between density, salinity and specific heat capacity and is extracted from the data sets of Feistel [2003. A new extended Gibbs thermodynamic potential of seawater. Progress in Oceanography 58, 43-114], Bromley et al. [1970. Heat capacities and enthalpies of sea salt solutions to 200 °C. Journal of Chemical and Engineering Data 15, 246-253] and Grunberg [1970. Properties of sea water concentrates. In: Third International Symposium on Fresh Water from the Sea, vol. 1, pp. 31-39] in a temperature range 0-200 °C, practical salinity range 0-40, and varying pressure and is also calibrated by the data set of Millero et al. [1981. Summary of data treatment for the international high pressure equation of state for seawater. UNESCO Technical Papers in Marine Science 38, 99-192]. The freshwater and salt water components are combined to establish a workable multi-polynomial equation, whose coefficients were computed through standard linear regression analysis. The results obtained in this way for density, entropy and potential temperature are comparable with those of existing models, except that our new equations cover a wider temperature—(0-374 °C) than the traditional (0-40 °C) temperature range. One can apply these newly established equations to the calculation of in-situ or

Laplace transform overcoming principle drawbacks in application of the variational iteration method to fractional heat equations

Directory of Open Access Journals (Sweden)

Wu Guo-Cheng

2012-01-01

Full Text Available This note presents a Laplace transform approach in the determination of the Lagrange multiplier when the variational iteration method is applied to time fractional heat diffusion equation. The presented approach is more straightforward and allows some simplification in application of the variational iteration method to fractional differential equations, thus improving the convergence of the successive iterations.

1D equation for toroidal momentum transport in a tokamak

International Nuclear Information System (INIS)

Rozhansky, V A; Senichenkov, I Yu

2010-01-01

A 1D equation for toroidal momentum transport is derived for a given set of turbulent transport coefficients. The averaging is performed taking account of the poloidal variation of the toroidal fluxes and is based on the ambipolar condition of the zero net radial current through the flux surface. It is demonstrated that taking account of the Pfirsch-Schlueter fluxes leads to a torque in the toroidal direction which is proportional to the gradient of the ion temperature. This effect is new and has not been discussed before. The boundary condition at the separatrix, which is based on the results of the 2D simulations of the edge plasma, is formulated.

Oxygen transport membrane system and method for transferring heat to catalytic/process reactors

Science.gov (United States)

Kelly, Sean M; Kromer, Brian R; Litwin, Michael M; Rosen, Lee J; Christie, Gervase Maxwell; Wilson, Jamie R; Kosowski, Lawrence W; Robinson, Charles

2014-01-07

A method and apparatus for producing heat used in a synthesis gas production is provided. The disclosed method and apparatus include a plurality of tubular oxygen transport membrane elements adapted to separate oxygen from an oxygen containing stream contacting the retentate side of the membrane elements. The permeated oxygen is combusted with a hydrogen containing synthesis gas stream contacting the permeate side of the tubular oxygen transport membrane elements thereby generating a reaction product stream and radiant heat. The present method and apparatus also includes at least one catalytic reactor containing a catalyst to promote the stream reforming reaction wherein the catalytic reactor is surrounded by the plurality of tubular oxygen transport membrane elements. The view factor between the catalytic reactor and the plurality of tubular oxygen transport membrane elements radiating heat to the catalytic reactor is greater than or equal to 0.5.

Oxygen transport membrane system and method for transferring heat to catalytic/process reactors

Science.gov (United States)

Kelly, Sean M.; Kromer, Brian R.; Litwin, Michael M.; Rosen, Lee J.; Christie, Gervase Maxwell; Wilson, Jamie R.; Kosowski, Lawrence W.; Robinson, Charles

2016-01-19

A method and apparatus for producing heat used in a synthesis gas production process is provided. The disclosed method and apparatus include a plurality of tubular oxygen transport membrane elements adapted to separate oxygen from an oxygen containing stream contacting the retentate side of the membrane elements. The permeated oxygen is combusted with a hydrogen containing synthesis gas stream contacting the permeate side of the tubular oxygen transport membrane elements thereby generating a reaction product stream and radiant heat. The present method and apparatus also includes at least one catalytic reactor containing a catalyst to promote the steam reforming reaction wherein the catalytic reactor is surrounded by the plurality of tubular oxygen transport membrane elements. The view factor between the catalytic reactor and the plurality of tubular oxygen transport membrane elements radiating heat to the catalytic reactor is greater than or equal to 0.5

Numerical simulation of the transport phenomena due to sudden heating in porous media

Energy Technology Data Exchange (ETDEWEB)

Lei, S.Y.; Zheng, G.Y.; Wang, B.X.; Yang, R.G.; Xia, C.M.

1997-07-01

Such process as wet porous media suddenly heated by hot fluids frequently occurs in nature and in industrial applications. The three-variable simulation model was developed to predict violent transport phenomena due to sudden heating in porous media. Two sets of independent variables were applied to different regions in porous media in the simulation. For the wet zone, temperature, wet saturation and air pressure were used as the independent variables. For the dry zone, the independent variables were temperature, vapor pressure and air pressure. The model simulated two complicated transport processes in wet unsaturated porous media which is suddenly heated by melting metal or boiling water. The effect of the gas pressure is also investigated on the overall transport phenomena.

An Analysis of the Relationship Between Atmospheric Heat Transport and the Position of the ITCZ in NASA NEWS products, CMIP5 GCMs, and Multiple Reanalyses

Science.gov (United States)

Stanfield, R.; Dong, X.; Su, H.; Xi, B.; Jiang, J. H.

2016-12-01

In the past few years, studies have found a strong connection between atmospheric heat transport across the equator (AHTEQ) and the position of the ITCZ. This study investigates the seasonal, annual-mean and interannual variability of the ITCZ position and explores the relationships between the ITCZ position and inter-hemispheric energy transport in NASA NEWS products, multiple reanalyses datasets, and CMIP5 simulations. We find large discrepancies exist in the ITCZ-AHTEQ relationships in these datasets and model simulations. The components of energy fluxes are examined to identify the primary sources for the discrepancies among the datasets and models results.

Transport and attenuation of radiations

CERN Document Server

Nimal, J C

2003-01-01

This article treats of the calculation methods used for the dimensioning of the protections against radiations. The method consists in determining for a given point the flux of particles coming from a source at a given time. A strong attenuation (of about some few mu Sv.h sup - sup 1) is in general expected between the source and the areas accessible to the personnel or the public. The calculation has to take into account a huge number of radiation-matter interactions and to solve the integral-differential transport equation which links the particles flux to the source. Several methods exist from the simplified physical model with numerical developments to the more or less precise resolution of the transport equation. These methods allows also the calculation of the uncertainties of equivalent dose rates, heat sources, structure damages using the data covariances (efficient cross-sections, modeling, etc..): 1 - transport equation; 2 - Monte-Carlo method; 3 - semi-numerical methods S sub N; 4 - methods based o...

Numerical solution of the radionuclide transport equation

International Nuclear Information System (INIS)

Hadermann, J.; Roesel, F.

1983-11-01

A numerical solution of the one-dimensional geospheric radionuclide chain transport equation based on the pseudospectral method is developed. The advantages of this approach are flexibility in incorporating space and time dependent migration parameters, arbitrary boundary conditions and solute rock interactions as well as efficiency and reliability. As an application the authors investigate the impact of non-linear sorption isotherms on migration in crystalline rock. It is shown that non-linear sorption, in the present case a Freundlich isotherm, may reduce concentration at the geosphere outlet by orders of magnitude provided the migration time is comparable or larger than the half-life of the nuclide in question. The importance of fixing dispersivity within the continuum approach is stressed. (Auth.)

Steady-state transport equation resolution by particle methods, and numerical results

International Nuclear Information System (INIS)

Mercier, B.

1985-10-01

A method to solve steady-state transport equation has been given. Principles of the method are given. The method is studied in two different cases; estimations given by the theory are compared to numerical results. Results got in 1-D (spherical geometry) and in 2-D (axisymmetric geometry) are given [fr

Thermoelectric transport in superlattices

Energy Technology Data Exchange (ETDEWEB)

Reinecke, T L; Broido, D A

1997-07-01

The thermoelectric transport properties of superlattices have been studied using an exact solution of the Boltzmann equation. The role of heat transport along the barrier layers, of carrier tunneling through the barriers, of valley degeneracy and of the well width and energy dependences of the carrier-phonon scattering rates on the thermoelectric figure of merit are given. Calculations are given for Bi{sub 2}Te{sub 3} and for PbTe, and the results of recent experiments are discussed.

A model for the nonlocal transport and the associated distribution function deformation in magnetized laser-plasmas

Science.gov (United States)

Nicolaï, Ph.; Feugeas, J.-L.; Schurtz, G.

2006-06-01

We present a model of nonlocal transport for multidimensional radiation magneto hydrodynamic codes. In laser produced plasmas, it is now believed that the heat transfert can be strongly modified by the nonlocal nature of the electron conduction. Nevertheless other mechanisms as self generated magnetic fields may affect heat transport too. The model described in this work aims at extending the formula of G. Schurtz, Ph. Nicolaï and M. Busquet [1] to magnetized plasmas. A system of nonlocal equations is derived from kinetic equations with self-consistent electric and magnetic fields. These equations are analyzed and applied to a physical problem in order to demonstrate the main features of the model.

VS2DRTI: Simulating Heat and Reactive Solute Transport in Variably Saturated Porous Media.

Science.gov (United States)

Healy, Richard W; Haile, Sosina S; Parkhurst, David L; Charlton, Scott R

2018-01-29

Variably saturated groundwater flow, heat transport, and solute transport are important processes in environmental phenomena, such as the natural evolution of water chemistry of aquifers and streams, the storage of radioactive waste in a geologic repository, the contamination of water resources from acid-rock drainage, and the geologic sequestration of carbon dioxide. Up to now, our ability to simulate these processes simultaneously with fully coupled reactive transport models has been limited to complex and often difficult-to-use models. To address the need for a simple and easy-to-use model, the VS2DRTI software package has been developed for simulating water flow, heat transport, and reactive solute transport through variably saturated porous media. The underlying numerical model, VS2DRT, was created by coupling the flow and transport capabilities of the VS2DT and VS2DH models with the equilibrium and kinetic reaction capabilities of PhreeqcRM. Flow capabilities include two-dimensional, constant-density, variably saturated flow; transport capabilities include both heat and multicomponent solute transport; and the reaction capabilities are a complete implementation of geochemical reactions of PHREEQC. The graphical user interface includes a preprocessor for building simulations and a postprocessor for visual display of simulation results. To demonstrate the simulation of multiple processes, the model is applied to a hypothetical example of injection of heated waste water to an aquifer with temperature-dependent cation exchange. VS2DRTI is freely available public domain software. © 2018, National Ground Water Association.

Turbulent transport regimes and the scrape-off layer heat flux width

Science.gov (United States)

Myra, J. R.; D'Ippolito, D. A.; Russell, D. A.

2015-04-01

Understanding the responsible mechanisms and resulting scaling of the scrape-off layer (SOL) heat flux width is important for predicting viable operating regimes in future tokamaks and for seeking possible mitigation schemes. In this paper, we present a qualitative and conceptual framework for understanding various regimes of edge/SOL turbulence and the role of turbulent transport as the mechanism for establishing the SOL heat flux width. Relevant considerations include the type and spectral characteristics of underlying instabilities, the location of the gradient drive relative to the SOL, the nonlinear saturation mechanism, and the parallel heat transport regime. We find a heat flux width scaling with major radius R that is generally positive, consistent with the previous findings [Connor et al., Nucl. Fusion 39, 169 (1999)]. The possible relationship of turbulence mechanisms to the neoclassical orbit width or heuristic drift mechanism in core energy confinement regimes known as low (L) mode and high (H) mode is considered, together with implications for the future experiments.

Turbulent transport regimes and the scrape-off layer heat flux width

International Nuclear Information System (INIS)

Myra, J. R.; D'Ippolito, D. A.; Russell, D. A.

2015-01-01

Understanding the responsible mechanisms and resulting scaling of the scrape-off layer (SOL) heat flux width is important for predicting viable operating regimes in future tokamaks and for seeking possible mitigation schemes. In this paper, we present a qualitative and conceptual framework for understanding various regimes of edge/SOL turbulence and the role of turbulent transport as the mechanism for establishing the SOL heat flux width. Relevant considerations include the type and spectral characteristics of underlying instabilities, the location of the gradient drive relative to the SOL, the nonlinear saturation mechanism, and the parallel heat transport regime. We find a heat flux width scaling with major radius R that is generally positive, consistent with the previous findings [Connor et al., Nucl. Fusion 39, 169 (1999)]. The possible relationship of turbulence mechanisms to the neoclassical orbit width or heuristic drift mechanism in core energy confinement regimes known as low (L) mode and high (H) mode is considered, together with implications for the future experiments

Tokamak fluidlike equations, with applications to turbulence and transport in H mode discharges

International Nuclear Information System (INIS)

Kim, Y.B.; Biglari, H.; Carreras, B.A.; Diamond, P.H.; Groebner, R.J.; Kwon, O.J.; Spong, D.A.; Callen, J.D.; Chang, Z.; Hollenberg, J.B.; Sundaram, A.K.; Terry, P.W.; Wang, J.F.

1990-01-01

Significant progress has been made in developing tokamak fluidlike equations which are valid in all collisionality regimes in toroidal devices, and their applications to turbulence and transport in tokamaks. The areas highlighted in this paper include: the rigorous derivation of tokamak fluidlike equations via a generalized Chapman-Enskog procedure in various collisionality regimes and on various time scales; their application to collisionless and collisional drift wave models in a sheared slab geometry; applications to neoclassical drift wave turbulence; i.e. neoclassical ion-temperature-gradient-driven turbulence and neoclassical electron-drift-wave turbulence; applications to neoclassical bootstrap-current-driven turbulence; numerical simulation of nonlinear bootstrap-current-driven turbulence and tearing mode turbulence; transport in Hot-Ion H mode discharges. 20 refs., 3 figs

Convective heat transport of high-pressure flows inside active, thick walled-tubes with isothermal outer surfaces: usage of Nusselt correlation equations for an inactive, thin walled-tube

Energy Technology Data Exchange (ETDEWEB)

Campo, Antonio [Idaho State Univ., Nuclear Engineering Dept., Pocatello, ID (United States); Sanchez, Alejo [Universidad de los Andes, Depto. de Ingenieria Mecanica, Merida (Venezuela)

1998-03-01

A semi-analytical analysis was conducted for the prediction of the mean bulk- and interface temperatures of gaseous and liquid fluids moving laminarly at high pressures inside thick-walled metallic tubes. The outer surfaces of the tubes are isothermal. The central goal of this article is to critically examine the thermal response of this kind of in-tube flows utilizing two versions of the 1-D lumped model: one is differential-numerical while the other is differential-algebraic. For the former, the local Nusselt number characterizing an inactive, isothermal tube was taken from correlation equations reported in the heat transfer literature. For the latter, a streamwise-mean Nusselt number associated with an active, isothermal tube was taken from standard correlation equations that appear in text-books on basic heat transfer. For the two different versions of the 1-D lumped model tested, the computed results consistently demonstrate that the differential-algebraic, provides accurate estimates of both the mean bulk- and the interface temperatures when compared with those temperature results computed with formal 2-D differential models. (author)

Theoretical and numerical study of heat transfer deterioration in HPLWR

International Nuclear Information System (INIS)

Palko, D.; Anglart, H.

2007-01-01

A numerical investigation of the Heat Transfer Deterioration (HTD) phenomena is performed using the low-Re k - ω turbulence model. Steady state Reynolds-averaged Navier-Stokes equations are solved together with equations for the transport of enthalpy and turbulence. Equations are solved for the supercritical water flow at different pressures, using water properties from the standard IAPWS tables. All cases are extensively validated against experimental data. The influence of buoyancy on the HTD is demonstrated for different mass flow rates in the heated pipes. Numerical results prove that the RANS low-Re turbulence modeling approach is fully capable to simulate the heat transfer in pipes with the water flow at supercritical pressures. A study of buoyancy influence shows that for the low mass flow rates of coolant, the influence of buoyancy forces on the heat transfer in heated pipes is significant. For the high flow rates, buoyancy influence could be neglected and there are clearly other mechanisms causing the decrease in heat transfer at high coolant flow rates. (author)

On the relativistic transport equation for a discontinuity wave of multiplicity one

International Nuclear Information System (INIS)

Giambo, Sebastiano; Palumbo, Annunziata

1980-01-01

In the framework of the theory of the singular hypersurfaces, the transport equation for the amplitude of a discontinuity wave, corresponding to a simple characteristic of a quasi-linear hyperbolic system, is established in the context of special relativity [fr

Applicability of heat and gas trans-port models in biocover design based on a case study from Denmark

DEFF Research Database (Denmark)

Nielsen, A. A. F.; Binning, Philip John; Kjeldsen, Peter

2015-01-01

Biocovers — layers of mature compost — can oxidise a considerable amount of methane emitted from landfi Different factors can affect oxidation, particularly tempera- ture. For better understanding of the processes and for future biocover designs, two models (analytic and numerical) were developed......) was 0.95 for the analytic model and 0.91 for the numerical model. The models can be used for different design scenarios (e.g. varying methane infl thickness or start of operation), and can also help understand the processes that take place in the system, e.g. how oxygen penetration depends on ambient....... Both models used the heat equation for heat transfer, and the numerical model used advection-diffusion model with dual Monod kinetics for gas transport. The results were validated with data from a Danish landfi The models correlated well with the observed data: the coefficient of determination (R2...

Electron and ion transport equations in computational weakly-ionized plasmadynamics

International Nuclear Information System (INIS)

Parent, Bernard; Macheret, Sergey O.; Shneider, Mikhail N.

2014-01-01

A new set of ion and electron transport equations is proposed to simulate steady or unsteady quasi-neutral or non-neutral multicomponent weakly-ionized plasmas through the drift–diffusion approximation. The proposed set of equations is advantaged over the conventional one by being considerably less stiff in quasi-neutral regions because it can be integrated in conjunction with a potential equation based on Ohm's law rather than Gauss's law. The present approach is advantaged over previous attempts at recasting the system by being applicable to plasmas with several types of positive ions and negative ions and by not requiring changes to the boundary conditions. Several test cases of plasmas enclosed by dielectrics and of glow discharges between electrodes show that the proposed equations yield the same solution as the standard equations but require 10 to 100 times fewer iterations to reach convergence whenever a quasi-neutral region forms. Further, several grid convergence studies indicate that the present approach exhibits a higher resolution (and hence requires fewer nodes to reach a given level of accuracy) when ambipolar diffusion is present. Because the proposed equations are not intrinsically linked to specific discretization or integration schemes and exhibit substantial advantages with no apparent disadvantage, they are generally recommended as a substitute to the fluid models in which the electric field is obtained from Gauss's law as long as the plasma remains weakly-ionized and unmagnetized

Solutions of Heat-Like and Wave-Like Equations with Variable Coefficients by Means of the Homotopy Analysis Method

International Nuclear Information System (INIS)

Alomari, A. K.; Noorani, M. S. M.; Nazar, R.

2008-01-01

We employ the homotopy analysis method (HAM) to obtain approximate analytical solutions to the heat-like and wave-like equations. The HAM contains the auxiliary parameter ħ, which provides a convenient way of controlling the convergence region of series solutions. The analysis is accompanied by several linear and nonlinear heat-like and wave-like equations with initial boundary value problems. The results obtained prove that HAM is very effective and simple with less error than the Adomian decomposition method and the variational iteration method

Multiscale gyrokinetics for rotating tokamak plasmas: fluctuations, transport and energy flows.

Science.gov (United States)

Abel, I G; Plunk, G G; Wang, E; Barnes, M; Cowley, S C; Dorland, W; Schekochihin, A A