Related papers: Implicit numerical schemes for generalized heat co…
We obtained a new representation of a solution of the heat conduction equation with boundary condition of the third kind for a layer. The result is presented as a superposition of fundamental solutions for an unbounded system with variable…
Heat transfer in semiconductor devices is dominated by chip and substrate assemblies, where heat generated within a finite chip layer dissipates into a semi-infinite substrate with much higher thermophysical properties. This mismatch…
We consider a time-stepping scheme of Crank-Nicolson type for the heat equation on a moving domain in Eulerian coordinates. As the spatial domain varies between subsequent time steps, an extension of the solution from the previous time step…
We study classical heat conduction in a dissipative open system composed of interacting oscillators. By exactly solving a twisted Fokker-Planck equation which describes the full counting statistics of heat flux flowing through the system,…
Hamiltonian mechanics can be used to constrain temperature simultaneously with energy. We illustrate the interesting situations that develop when two different temperatures are imposed within a composite Hamiltonian system. The model…
Many challenges faced in today's semiconductor devices are related to self-heating phenomena. The optimization of device designs can be assisted by numerical simulations using the non-isothermal drift-diffusion system, where the magnitude…
In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each iteration a linear initial-value problem has to be solved.…
This work deals with the problem of determining a non-homogeneous heat conductivity profile in a steady-state heat conduction boundary-value problem with mixed Dirichlet-Neumann boundary conditions over a bounded domain in $\mathbb{R}^n$,…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
We prove new bounds on the heat flux out of the bottom boundary, $\mathcal{F}_B$, for a fluid at infinite Prandtl number, heated internally between isothermal parallel plates under two kinematic boundary conditions. In uniform internally…
Nonequilibrium statistical mechanics close to equilibrium is a physically satisfactory theory centered on the linear response formula of Green-Kubo. This formula results from a formal first order perturbation calculation without rigorous…
Nonlinear heat transfer can be exploited to reveal novel transport phenomena and thus enhance peo-ple's ability to manipulate heat flux at will. However, there hasn't been a mature discipline called nonlinear thermotics like its counterpart…
The work presents integral solutions of the fractional subdiffusion equation by an integral method, as an alternative approach to the solutions employing hypergeometric functions. The integral solution suggests a preliminary defined profile…
We describe a fluctuating surface-current formulation of radiative heat transfer, applicable to arbitrary geometries, that directly exploits standard, efficient, and sophisticated techniques from the boundary-element method. We validate as…
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…
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…
For heat flux $q$ and temperature $T$ we introduce a modified Fourier--Cattaneo law $q_t+ l \frac{q}{t}= - kT_x .$ The consequence of it is a non-autonomous telegraph-type equation. % $\epsilon S_{tt} + \frac{a}{t} S_t = S_{xx}$ . This…
The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but…
The problem of a steady forced convection thermal boundary-layer past a flat plate with a prescribed surface heat flux is investigated both analytically and numerically. In view of the present formulation, the governing equations reduce to…
Understanding the generation mechanism of the heating flux is essential for the design of hypersonic vehicles. We proposed a novel formula to decompose the heat flux coefficient into the contributions of different terms by integrating the…