Two new theorems in heat conduction.
Heat conduction theorems, discussing steady state system /geometry, conductivities and source strengths/
Lynch, J. H.↗
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Disparate quasiballistic heat conduction regimes from periodic heat sources on a substrate
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charge transport↗
Fractional heat conduction with heat absorption in a sphere under Dirichlet boundary condition
The time-fractional heat conduction equation with the Caputo derivative and with heat absorption term proportional to temperature is considered in a sphere in the case of central symmetry. The fundamental solution to the Dirichlet boundary value problem is found, and the solution to the problem under constant boundary value of temperature is studied. The integral transform technique is used. The solutions are obtained in terms of series containing the Mittag-Leffler functions being the generalization of the exponential function. The numerical results are illustrated graphically.
97 MATHEMATICS AND COMPUTING↗
An application of least squares method to the solution of the inverse problem of heat conduction.
Heat input to a body surface, using least squares method
THERMAL CONDUCTOR↗
Extinction of the Stagnation Point Diffusion Flame: Effect of Conductive Heat Loss into Solid Interior
The flammability boundary of a solid is U-shaped with the ordinate as ambient oxygen percentage (or total pressure) and the abscissa represents flow velocity, gravity level, stretch rate, etc. The left side of the flammability boundary is the quenching branch, and the right side is the blow-off branch. Quenching is due to a weak flame whose heat release from combustion cannot overcome the excessive heat losses from, for example, radiation. Blow-off is due to a short gas residence time that is smaller than the chemical reaction time (traditionally referred to as the small Damköhler number effect). For thick solids, the heat conduction into the solid interior has a long transient after ignition before the solid temperature reaches the steady state. During this slow transient, there is excessive (i.e. more than that at the steady state) gas phase heat conduction into the solid interior. From the viewpoint of the quasi-static gaseous flame, this is an additional heat loss that will affect the gas flame's flammability. In this work, a previously developed one-dimensional axisymmetric stagnation-point diffusion flame model is extended to account for the excessive heat loss into the solid beyond the steady burning state. A non-dimensional excessive conductive heat loss parameter Ψ is defined in the paper to account for the transient solid effect. For each Ψ, the gas phase is considered reaching a quasi-steady state. Extensive numerical computations have been performed to determine the extinction boundary and the characteristics of near-limit flames. The U-shaped flammability boundary is now a series of boundaries with Ψ as a parameter. Flame structures under the same environment condition but with different Ψ are compared. For a given oxygen ambient, the extinction boundary Ψ vs stretch rate is an inverted U-shape. The boundary consists of a blowoff branch and a radiative quenching branch. Extensive computed data including flame and pyrolysis temperatures, burning rate, flame standoff distance, species concentration, and reaction rate are presented along the extinction boundaries. Heat balance analysis is performed for both the gas phase and the gas-solid interface. Along the extinction boundary, the relative importance of conduction, convection, radiation, and chemical reaction are analyzed in detail.
Stagnation point diffusion flame↗
Influence of Multi-Dimension Heat Conduction on Heat Flux Calculation for HFIR LEU Analysis
Steady-state safety margins calculations are an important step in the evaluation of research reactor design. Margins for phenomena such as onset of nucleate boiling and critical heat flux are evaluated by comparing the heat flux leading to those phenomena to a local heat flux. Evaluating properly the magnitude of the heat flux is therefore important and can affect the design. Plate-type research reactors often exhibit significant power peaking on the edges of the plate, near the fuel/cladding interface. The magnitude of the heat flux calculated in these regions can be influenced by the size of the region in which they are evaluated but also by the ability to model heat transport in one or multiple dimensions. The present analysis studies the influence of these two parameters on the heat flux magnitude for the HFIR reactor. From this analysis, a fuel discretization grid is proposed that can generate one-dimension heat flux values relatively close to best estimate values obtained with a high-resolution grid and complex three-dimensional CFD modeling.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Development of soft-sphere contact models for thermal heat conduction in granular flows
Conductive heat transfer to flowing particles occurs when two particles (or a particle and wall) come into contact. The direct conduction between the two bodies depends on the collision dynamics, namely the size of the contact area and the duration of contact. For soft-sphere discrete-particle simulations, it is computationally expensive to resolve the true collision time because doing so would require a restrictively small numerical time step. To improve the computational speed, it is common to increase the 'softness' of the material to artificially increase the collision time, but doing so affects the heat transfer. In this work, two physically-based correction terms are derived to compensate for the increased contact area and time stemming from artificial particle softening. By including both correction terms, the impact that artificial softening has on the conductive heat transfer is removed, thus enabling simulations at greatly reduced computational times without sacrificing physical accuracy.
14 SOLAR ENERGY↗
Large deviations in stochastic heat-conduction processes provide a gradient-flow structure for heat conduction
We consider three one-dimensional continuous-time Markov processes on a lattice, each of which models the conduction of heat: the family of Brownian Energy Processes with parameter m (BEP(m)), a Generalized Brownian Energy Process, and the Kipnis-Marchioro-Presutti (KMP) process. The hydrodynamic limit of each of these three processes is a parabolic equation, the linear heat equation in the case of the BEP(m) and the KMP, and a nonlinear heat equation for the Generalized Brownian Energy Process with parameter a (GBEP(a)). We prove the hydrodynamic limit rigorously for the BEP(m), and give a formal derivation for the GBEP(a). We then formally derive the pathwise large-deviation rate functional for the empirical measure of the three processes. These rate functionals imply gradient-flow structures for the limiting linear and nonlinear heat equations. We contrast these gradient-flow structures with those for processes describing the diffusion of mass, most importantly the class of Wasserstein gradient-flow systems. The linear and nonlinear heat-equation gradient-flow structures are each driven by entropy terms of the form -log ρ; they involve dissipation or mobility terms of order ρ² for the linear heat equation, and a nonlinear function of ρ for the nonlinear heat equation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A conductive heat transfer model for particle flows over immersed surfaces
Not Available
Morris, A. B.↗
Cryogenic regenerator including sarancarbon heat conduction matrix
A saran carbon matrix is employed to conduct heat through the heat storing volume of a cryogenic regenerator. When helium is adsorbed into the saran carbon matrix, the combination exhibits a volumetric specific heat much higher than previously used lead balls. A helium adsorbed saran regenerator should allow much lower refrigerator temperatures than those practically obtainable with lead based regenerators for regenerator type refrigeration systems.
Jones, Jack A.↗
Ballistic magnon heat conduction and possible Poiseuille flow in the helimagnetic insulator Cu 2 OSeO 3
Herein we report on the observation of magnon thermal conductivity κ m ~ 70 W/mK near 5 K in the helimagnetic insulator Cu 2 OSeO 3 , exceeding that measured in any other ferromagnet by almost two orders of magnitude. Ballistic, boundary-limited transport for both magnons and phonons is established below 1 K, and Poiseuille flow of magnons is proposed to explain a magnon mean-free path substantially exceeding the specimen width for the least defective specimens in the range 2 K < T < 10 K. These observations establish Cu 2 OSeO 3 as a model system for studying long-wavelength magnon dynamics.
36 MATERIALS SCIENCE↗
Steady-state-coupled fluid flow and heat conduction analysis of a heat-generating solid, as applied to reactor design
Steady-state-coupled fluid flow and heat conduction analysis of heat-generating solid, as applied to reactor design
SOLIDS↗
Causal explicit algorithm for heat conduction in a plasma
Hyperbolic heat conduction extends standard Spitzer-Harm heat conduction by including a term proportional to the time derivative of the heat flux. The new term arises from a kinetic derivation of the heat flux that includes higher order corrections. Here we present a causal explicit numerical algorithm for solving the nonlinear hyperbolic heat conduction equation in an unmagnetized plasma. The maximum stable timestep for the causal explicit algorithm scales linearly with the cell size, owing to the hyperbolic nature of the problem. This is in contrast to the quadratic scaling of the maximum stable timestep with the cell size for the parabolic forward time centered space algorithm. The favorable scaling of the timestep with the cell size enables a practical explicit implementation of heat conduction in high-performance massively parallel plasma codes. In particular, we have implemented the causal explicit algorithm in the laser plasma interaction code pF3D. We verify the CE algorithm and analyze its convergence rate by simulating a harmonic mode, which has an analytic solution within the context of the HHC model. We also compare simulations using the CE algorithm to those using the forward time centered space algorithm on a pair of test problems: evolution in time of a Gaussian temperature perturbation in a uniform plasma and heat transport in the presence of inverse bremsstrahlung heating by a Gaussian laser speckle.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Heat Rejection from a Variable Conductance Heat Pipe Radiator Panel
A titanium-water heat pipe radiator having an innovative proprietary evaporator configuration was evaluated in a large vacuum chamber equipped with liquid nitrogen cooled cold walls. The radiator was manufactured by Advanced Cooling Technologies, Inc. (ACT), Lancaster, PA, and delivered as part of a Small Business Innovative Research effort. The radiator panel consisted of five titanium-water heat pipes operating as thermosyphons, sandwiched between two polymer matrix composite face sheets. The five variable conductance heat pipes were purposely charged with a small amount of non-condensable gas to control heat flow through the condenser. Heat rejection was evaluated over a wide range of inlet water temperature and flow conditions, and heat rejection was calculated in real-time utilizing a data acquisition system programmed with the Stefan-Boltzmann equation. Thermography through an infra-red transparent window identified heat flow across the panel. Under nominal operation, a maximum heat rejection value of over 2200 Watts was identified. The thermal vacuum evaluation of heat rejection provided critical information on understanding the radiator s performance, and in steady state and transient scenarios provided useful information for validating current thermal models in support of the Fission Power Systems Project.
Jaworske, D. A.↗
Numerical simulation of hyperbolic heat conduction with convection boundary conditions and pulse heating effects
The paper describes the numerical simulation of hyperbolic heat conduction with convection boundary conditions. The effects of a step heat loading, a sudden pulse heat loading, and an internal heat source are considered in conjunction with convection boundary conditions. Two methods of solution are presened for predicting the transient behavior of the propagating thermal disturbances. In the first method, MacCormack's predictor-corrector method is employed for integrating the hyperbolic system of equations. Next, the transfinite element method, which employs specially tailored elements, is used for accurately representing the transient response of the propagating thermal wave fronts. The agreement between the results of various numerical test cases validate the representative behavior of the thermal wave fronts. Both methods represent hyperbolic heat conduction behavior by effectively modeling the sharp discontinuities of the propagating thermal disturbances.
Glass, David E.↗
Feedback controlled variable conductance heat pipes
Variable conductance heat pipes feedback mechanisms for spacecraft electrical temperature control system design, using steady state analysis based performance model
Bienert, W. B.↗
Effects of Aperiodicity and Roughness on Coherent Heat Conduction in Superlattices
Coherent phonon heat conduction has recently been confirmed experimentally in superlattice structures. Such traveling coherent phonon waves in superlattices lead to a linear increase in thermal conductivity as the number of periods increases. For applications such as thermal insulation or thermoelectrics, minimization of the phonon coherent effect is desirable. In this paper, we use molecular dynamics simulations to study how to control coherent heat conduction in superlattices (SLs). It is found that either aperiodic SLs or SLs with rough interfaces can significantly disrupt coherent heat conduction when the interface densities are high. For sample thickness less than 125 nm, aperiodic SLs with perfect interfaces are found to have the lowest thermal conductivity. We use the atomic Green’s function method to examine the phonon dynamics. The impact of either aperiodicity or interface roughness is attributed to reduced transmittance. Such impact diminishes as the interface density reduces.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Specially tailored transfinite-element formulations for hyperbolic heat conduction involving non-Fourier effects
The phenomenon of hyperbolic heat conduction in contrast to the classical (parabolic) form of Fourier heat conduction involves thermal energy transport that propagates only at finite speeds, as opposed to an infinite speed of thermal energy transport. To accommodate the finite speed of thermal wave propagation, a more precise form of heat flux law is involved, thereby modifying the heat flux originally postulated in the classical theory of heat conduction. As a consequence, for hyperbolic heat conduction problems, the thermal energy propagates with very sharp discontinuities at the wave front. Accurate solutions are found for a class of one-dimensional hyperbolic heat conduction problems involving non-Fourier effects that can be used effectively for representative benchmark tests and for validating alternate schemes. Modeling/analysis formulations via specially tailored hybrid computations are provided for accurately modeling the sharp discontinuities of the propagating thermal wave front. Comparative numerical test models are presented for various hyperbolic heat conduction models involving non-Fourier effects to demonstrate the present formulations.
Tamma, Kumar K.↗