Disparate quasiballistic heat conduction regimes from periodic heat sources on a substrate
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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↗
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.↗
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↗
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↗
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↗
Determination of heat conductivity of waste glass feed and its applicability for modeling the batch-to-glass conversion
The heat conductivity of reacting melter feed affects the heat transfer and conversion process in the cold cap (the reacting feed floating on molten glass). To investigate it, we simulated the feed conditions and morphology in the cold-cap by preparing “fast-dried slurry blocks”, formed by rapidly evaporating water from feed slurry poured onto a 200°C surface. A heat conductivity meter was used to measure heat conductivity of samples cut from the fast-dried slurry blocks, samples of a cold cap retrieved from a laboratory-scale melter, and loose dry powder feed samples. Our study indicates that the heat conductivity of the feed in the cold cap is significantly higher than that of loose dry powder feed, resulting from the feed solidification during the water evaporation from the feed slurry. To assess the heat transfer at higher temperatures when feed turns into foam, we developed a theoretical model that predicts the foam heat conductivity based on morphology data from in-situ X-ray computed tomography. The implications for the mathematical modeling of the cold cap are discussed.
Hujova, Miroslava↗
Modeling Classical Heat Conduction in FLAG
The Los Alamos National Laboratory FLAG code contains both electron and ion heat conduction modules; these have been constructed to be directly relevant to user application problems. However, formal code verification of these modules requires quantitative comparison to exact solutions of the underlying mathematical models. A wide variety of exact solutions to the classical heat conduction equation are available for this purpose. This report summarizes efforts involving the representation of the classical heat conduction equation as following from the large electron-ion coupling limit of the electron and ion 3T temperature equations, subject to electron and ion conduction processes. In FLAG, this limiting behavior is quantitatively verified using a simple exact solution of the classical heat conduction equation. For this test problem, both heat conduction modules produce nearly identical spatial electron and ion temperature profiles that converge at slightly less than 2nd order to the corresponding exact solution.
97 MATHEMATICS AND COMPUTING↗
On heat conduction in an irregular magnetic field. Part 1
Anisotropic heat conduction in a plasma embedded in a magnetic field with irregular, possibly chaotic, field lines is discussed. If the collisional mean free path exceeds the electron gyroradius, the heat conductivity is much larger along the field lines than across them, and this enhances the transport across a domain where good flux surfaces do not exist. Recognising that anisotropic heat conduction may be cast in a variational form, and by constructing increasingly sophisticated trial functions that are based on invariant and almost-invariant structures under the magnetic field-line flow, bounds are derived on this enhancement and on the temperature variation along the magnetic field. In this way, remarkably accurate approximations for the temperature can be rapidly constructed without solving the diffusion equation, even in the small perpendicular-diffusion limit when the solution for the temperature is dominated by the fractal structure the magnetic field lines.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Time-domain theory of transient heat conduction in the local limit
Ultrafast and nanoscale heat conduction demands a unified theoretical framework that rigorously bridges macroscopic transport equations with microscopic material properties derived from statistical physics. Existing empirical generalizations of Fourier's law often lack a solid microscopic foundation, failing to connect observed non-Fourier behavior with underlying atomic-scale mechanisms. In this work, we present a time-domain theory of transient heat conduction rooted in Zwanzig's statistical theory of irreversible processes. Central to this framework is the time-domain transport function $\overleftrightarrow{𝑍}$(𝑡) defined through equilibrium time-correlation functions of heat fluxes. This function generalizes the conventional concept of steady-state thermal conductivity, governing the transition of conduction dynamics from onset second sound type wave propagation at finite speeds to diffusion-dominated behavior across broad temporal and spatial scales. Unlike phonon hydrodynamic models that rely on mesoscopic constructs such as phonon drift velocity, our approach provides a quantitative and microscopic description of intrinsic memory effects in transient heat fluxes and applies universally to bulk materials at any temperature or length scale. By integrating atomistic-scale first-principles calculations with continuum-level macroscopic equations, this framework offers a robust foundation for numerical simulations of transient temperature fields. Furthermore, it facilitates the interpretation and design of transient thermal grating experiments using nanometer-scale heat sources and ultrafast laser systems in the extreme ultraviolet and x-ray wavelength ranges, advancing our understanding of heat dissipation dynamics.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
The Role of Particle Interaction in the Cluster Model of Heat Conductivity of Nanofluids
Analytical dependences of the effective heat conductivity coefficient of an individual cluster and cluster nanofluid are obtained on the basis of classical equations of continuum mechanics with allowance for the interaction of temperature fields of spherical particles inside a cluster. The calculated dependences of the heat-conductivity coefficient of the cluster nanofluid agree with the corresponding experimental data.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Fourier heat conduction as a phenomenon described within the scope of the second law
The historical development of the Carnot cycle necessitated the construction of isothermal and adiabatic pathways within the cycle that were also mechanically 'reversible' which lead eventually to the Kelvin-Clausius development of the entropy function S where for any reversible closed path C, ∮{sub C} dS = 0 based on an infinite number of concatenated Carnot engines that approximated the said path and where for each engine ΔQ{sub 1}/T{sub 1}+ΔQ{sub 2}/T{sub 2} = 0 where the Q's and T's are the heat absorption increments and temperature respectively with the subscripts indicating the isothermal paths (1;2) where for the Carnot engine, the heat absorption is for the diathermal (isothermal) paths of the cycle only. Since 'heat' has been defined as that form of energy that is transferred as a result of a temperature difference and a corollary of the Clausius statement of the Second law is that it is impossible for heat to be transferred from a cold to a hot reservoir with no other effect on the environment, these statements suggested that the local mode of transfer of 'heat' in the isothermal segments of the pathway does imply a Fourier heat conduction mechanism (to conform to the definition of 'heat') albeit of a 'reversible' kind, but on the other hand, the Fourier mechanism is apparently irreversible, leading to an increase in entropy of the combined reservoirs at either end of the material involved in the conveyance of the heat energy. These and several other considerations lead Benofy and Quay (BQ) to postulate the Fourier heat conduction phenomenon to be an ancillary principle in thermodynamics, with this principle being strictly local in nature, where the global Second law statements could not be applied to this local process. Here we present equations that model heat conduction as a thermodynamically reversible but mechanically irreversible process where due to the belief in mechanical time reversible symmetry, thermodynamical reversibility has been unfortunately linked to mechanical reversibility, that has discouraged such an association. The modeling is based on an application of a 'recoverable transition', defined and developed earlier on ideas derived from thermal desorption of particles from a surface where the Fourier heat conduction process is approximated as a series of such desorption processes. We recall that the original Carnot engine required both adiabatic and isothermal steps to complete the zero entropy cycle, and this construct lead to the consequent deduction that any Second law statement that refers to heat-work conversion processes are only globally relevant. Here, on the other hand, we examine Fourier heat conduction from MD simulation and model this process as a zero-entropy forward scattering process relative to each of the atoms in the lattice chain being treated as a system where the Carnot cycle can be applied individually. The equations developed predicts the 'work' done to be equal to the energy transfer rate. The MD simulations conducted shows excellent agreement with the theory. Such views and results as these, if developed to a successful conclusion could imply that the Carnot cycle be viewed as describing a local process of energy-work conversion and that irreversible local processes might be brought within the scope of this cycle, implying a unified treatment of thermodynamically (i) irreversible, (ii) reversible, (iii) isothermal and (iv) adiabatic processes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Atomistic insights into the heat conductance across the interfaces between erythritol and different metals: A non-equilibrium molecular dynamics study
The heat conductance across the interface between a phase change material (PCM) and the metal shell is important for thermal design of latent heat storage systems. Non-equilibrium molecular dynamics simulations were carried out in this work to unravel, at the atomistic level, the interfacial heat conductance mechanisms between erythritol (the most promising medium-temperature polyol PCM) and two different metals (i.e., copper and aluminum). The interfacial contact ratio was introduced as a parameter to represent different contact conditions at the interfaces, for example, different surface roughness levels of the metals. It was found that with the increase of interfacial contact ratio, the temperature difference between the erythritol/metal interfaces decreases, whereas the interfacial heat transfer coefficient increases gradually. At the perfect contact condition, i.e., the interfacial contact ratio reaches 100%, the interfacial heat transfer coefficients across the erythritol/Cu and erythritol/Al interfaces were predicted to be 398 ± 26 MW/m 2 K and 544 ± 11 MW/m 2 K, respectively. The interfacial heat conductance of erythritol/Al is better than that of erythritol/Cu. The mismatch of atomic spectral density across the interfaces between erythritol and the two metals was analyzed and distinguished. These results could guide the selection of packaging materials and the thermal design of erythritol-based latent heat storage systems.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
Quantum bath augmented stochastic nonequilibrium atomistic simulations for molecular heat conduction
Classical molecular dynamics (MD) has been shown to be effective in simulating heat conduction in certain molecular junctions since it inherently takes into account some essential methodological components which are lacking in the quantum Landauer-type transport model, such as many-body full force-field interactions, anharmonicity effects and nonlinear responses for large temperature biases. However, the classical MD reaches its limit in the environments where the quantum effects are significant (e.g. with low-temperatures substrates, presence of extremely high frequency molecular modes). Here, we present an atomistic simulation methodology for molecular heat conduction that incorporates the quantum Bose–Einstein statistics into an “effective temperature” in the form of a modified Langevin equation. We show that the results from such a quasi-classical effective temperature MD method deviates drastically when the baths temperature approaches zero from classical MD simulations and the results converge to the classical ones when the bath approaches the high-temperature limit, which makes the method suitable for full temperature range. In addition, we show that our quasi-classical thermal transport method can be used to model the conducting substrate layout and molecular composition (e.g. anharmonicities, high-frequency modes). Anharmonic models are explicitly simulated via the Morse potential and compared to pure harmonic interactions to show the effects of anharmonicities under quantum colored bath setups. Finally, the chain length dependence of heat conduction is examined for one-dimensional polymer chains placed in between quantum augmented baths.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Anisotropy of heat conduction in Mo/Si multilayers
This paper reports on the studies of anisotropic heat conduction phenomena in Mo/Si multilayers with individual layer thicknesses selected to be smaller than the mean free path of heat carriers. We applied the frequency-domain thermoreflectance technique to characterize the thermal conductivity tensor. While the mechanisms of the cross-plane heat conduction were studied in detail previously, here we focus on the in-plane heat conduction. To analyze the relative contribution of electron transport to the in-plane heat conduction, we applied sheet-resistance measurements. Results of Mo/Si multilayers with variable thickness of the Mo layers indicate that the net in-plane thermal conductivity depends on the microstructure of the Mo layers.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗