Related papers: Implicit numerical schemes for generalized heat co…
We give a rigorous derivation of Fourier's law from a system of closure equations for a nonequilibrium stationary state of a Hamiltonian system of coupled oscillators subjected to heat baths on the boundary. The local heat flux is…
This paper aims at the transient heat transfer analysis on extended surfaces with temperature-dependent thermal conductivity, constant internal heat generation, and five different geometries. The governing equations developed in this work…
We present a new formulation and generalization of the classical theory of heat conduction with or without fading memory which includes the usual heat equation subject to a dynamic boundary condition as a special case. We investigate the…
Heat-flux boundary conditions are challenging to implement efficiently in rarefied gas flow simulations because the wall-reflected gas temperature and density must be determined dynamically during the computation. This paper aims to tackle…
We present an effective thermal open boundary condition for convective heat transfer problems on domains involving outflow/open boundaries. This boundary condition is energy-stable, and it ensures that the contribution of the open boundary…
Evaluation of effective or macroscopic coefficients of thermal conductivity under coupled heat and moisture transfer is presented. The paper first gives a detailed summary on the solution of a simple steady state heat conduction problem…
A stochastic inverse heat transfer problem is formulated to infer the transient heat flux, treated as an unknown Neumann boundary condition. Therefore, an Ensemble-based Simultaneous Input and State Filtering as a Data Assimilation…
The heat kernel method is extended to the case of finite temperature. Special emphasis is given to the study of gauge theories. Due to the compactness of space in the Euclidean time direction (inverse temperature) the field strength cannot…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
Integral equation based numerical methods are directly applicable to homogeneous elliptic PDEs, and offer the ability to solve these with high accuracy and speed on complex domains. In this paper, extensions to problems with inhomogeneous…
We analyze closed one-dimensional chains of weakly coupled many level systems, by means of the so-called Hilbert space average method (HAM). Subject to some concrete conditions on the Hamiltonian of the system, our theory predicts energy…
The main objective of this paper is to show that, within the present framework of the kinetic theoretical approach to irreversible thermodynamics, there is no evidence that provides a basis to modify the ordinary Fourier equation relating…
We present an adaptive wavelet Galerkin method for transient heat conduction in heterogeneous composite materials. The approach combines multiresolution wavelet bases with an implicit time discretization to efficiently resolve sharp…
We consider a general compressible, viscous, heat and magnetically conducting fluid described by the compressible Navier-Stokes-Fourier system coupled with induction equation. In particular, we do not assume conservative boundary conditions…
The effects of MHD boundary layer flow of non-linear thermal radiation with convective heat transfer and non-uniform heat source/sink in presence of thermophortic velocity and chemical reaction investigated in this study. Suitable…
We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions. We first show the…
In this work, we study the asymptotic behaviour of solutions to the heat equation in exterior domains, i.e., domains which are the complement of a smooth compact set in $\mathbb{R}^N$. Different homogeneous boundary conditions are…
In this work, we obtain the numerical temperature field to a thermally developing fluid flow inside parallel plates problem with a quantum computing method. The physical problem deals with the heat transfer of a steady state,…
A framework for studying the effect of the coupling to the heat bath in models exhibiting anomalous heat conduction is described. The framework is applied to the harmonic chain with momentum exchange model where the non-trivial temperature…
We study a time-reversed hyperbolic heat conduction problem based upon the Maxwell--Cattaneo model of non-Fourier heat law. This heat and mass diffusion problem is a hyperbolic type equation for thermodynamics systems with thermal memory or…