相关论文: Heat equation on a network using the Fokas method
We propose a numerical approach for solving conjugate heat transfer problems using the finite volume method. This approach combines a semi-implicit scheme for fluid flow, governed by the incompressible Navier-Stokes equations, with an…
We derive Fourier's law for a completely coherent quasi one--dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show…
Analytic solutions for cylindrical thermal waves in solid medium is given based on the nonlinear hyperbolic system of heat flux relaxation and energy conservation equations. The Fourier-Cattaneo phenomenological law is generalized where the…
We derive two different generalized heat-transport equations: The most general one, of the first order in time and second order in space, encompasses some well known heat equations and describes the hyperbolic regime in the absence of…
Thermal convection stands out as an exceptionally efficient thermal transport mechanism, distinctly separate from conduction and radiation. Yet, the inherently elusive nature of fluid motion poses challenges in accurately controlling…
In this paper, we establish the well-posedness of stochastic heat equations on moving domains, which amounts to a study of infinite dimensional interacting systems. The main difficulty is to deal with the problems caused by the time-varying…
Convection on geophysical and astrophysical scales is subject to rapid rotation and strong heating from within the domain. In studying the long-time behaviour of the solutions for such a system, energy identities fail to capture the effects…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
A general formulation is developed to study heat conduction in disordered harmonic chains with arbitrary heat baths that satisfy the fluctuation-dissipation theorem. A simple formal expression for the heat current J is obtained, from which…
We analyze the heat current traversing a quantum dot sandwiched between a ferromagnetic and a superconducting electrode. The heat flow generated in response to a voltage bias presents rectification as a function of the gate potential…
We present a family of integral equation-based solvers for the linear or semilinear heat equation in complicated moving (or stationary) geometries. This approach has significant advantages over more standard finite element or finite…
We study the problem of heat conduction in general relativity by using Carter's variational formulation. We write the creation rates of the entropy and the particle as combinations of the vorticities of temperature and chemical potential.…
Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic…
The second law of thermodynamics is a useful and universal tool to derive the generalizations of the Fourier's law. In many cases, only linear relations are considered between the thermodynamic fluxes and forces, i.e., the conduction…
We show the unique reconstruction of the heat-reflection coefficients in a phonon transport equation. This is a mathematical model used to characterize the dynamics of heat-conducting phonons in multiple layers of media, commonly composed…
We are investigating the effective heat transfer in complex systems involving porous media and surrounding fluid layers in the context of mathematical homogenization. We differentiate between two fundamentally different cases: Case (a),…
We present a theoretical study of the heat dissipation in single-molecule junctions. In order to investigate the heat dissipation in the electrodes and the relationship between the transmission spectra and the electronic structures, we…
We derive a macroscopic heat equation for the temperature of a pinned harmonic chain subject to a periodic force at its right side and in contact with a heat bath at its left side. The microscopic dynamics in the bulk is given by the…
Using nonequilibrium molecular dynamics simulations, we study the heat conduction in graphene flakes composed by two regions. One region is mass-loaded and the other one is intact. It is found that the mass interface between the two regions…
This paper presents a multiscale methodology for efficient unsteady conjugate heat transfer simulations. The solid domain is modelled by coupling a global representation of the temperature field, based on the eigenfunctions of the unsteady…