Related papers: Mathematical Modeling of Heat Conduction
We perform non-equilibrium simulations to study heat conduction in two-dimensional strongly coupled dusty plasmas. Temperature gradients are established by heating one part of the otherwise equilibrium system to a higher temperature. Heat…
We develop a one-dimensional mathematical model for the loading process of hydrogen in a metal hydride tank. The model describes the evolution of the density and pressure of the hydrogen gas, the temperature of the tank, the averaged…
Considering high-temperature heating, the equations of transient heat conduction model require an adaptation, i.e. the dependence of thermophysical parameters of the model on the temperature is to be identified for each specific material to…
We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial…
A new quasilinear mathematical model of heat conduction with finite velocity of heat front movement is offered.
It has recently been shown theoretically that the time-dependent heat conduction equation is form-invariant under curvilinear coordinate transformations. Thus, in analogy to transformation optics, fictitious transformed space can be mapped…
An equation based reduced order model applicable to generalized heat equation and thermal simulations of power electronics systems developed in commercial CFD tools, is presented in this work. The model considers the physics of heat…
In this paper, we study the heat equation with an irregular spatially dependent thermal conductivity coefficient. We prove that it has a solution in an appropriate very weak sense. Moreover, the uniqueness result and consistency with the…
We present a new method for motion planning for control systems. The method aims to provide a natural computational framework in which a broad class of motion planning problems can be cast; including problems with holonomic and…
An innovative and accurate dynamic Compact Thermal Model extraction method is proposed for multi-chip power electronics systems. It accounts for thermal coupling between multiple heat sources. Transient electro-thermal coupling can easily…
Motivated by the classical picture of heat flow we construct a stationary temperature gradient in a relativistic microscopic transport model. Employing the relativistic Navier-Stokes ansatz we extract the heat conductivity {\kappa} for a…
We present a new explicit and stable numerical algorithm to solve the homogeneous heat equation. We illustrate the performance of the new method in the cases of two 2D systems with highly inhomogeneous random parameters. Spatial…
A new formulation of physical thermal models for variable plug flow through a pipe is proposed. The derived model is based on a commonly used one-dimensional distributed parameter model, which explicitly takes into account the heat capacity…
By combining ab initio quantum mechanics calculation and Drude model, electron temperature and lattice temperature dependent electron thermal conductivity is calculated and implemented into a multiscale model of laser material interaction,…
When the variations of surface temperature are measured both spatially and temporally, analytical expressions that correctly account for multi-dimensional transient conduction can be applied. To enhance the accessibility of these accurate…
This paper focuses on the numerical solution of a dual-phase-lag heat conduction equation on a space unbounded domain. First, based on the Laplace transform and the Pad\'e approximation, a high-order local artificial boundary condition is…
We study anomalous transport in a one-dimensional system with two conserved quantities in presence of thermal baths. In this system we derive exact expressions of the temperature profile and the two point correlations in steady state as…
We derive and analyze the linearized hyperbolic equations describing a relativistic heat-conducting elastic rod. We construct a decreasing energy integral for these equations, compute the associated characteristic propagation speeds, and…
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…
Laser irradiation of materials is most commonly modeled with the two-temperature model (TTM), or its combination with molecular dynamics, TTM-MD. For such modeling, the electronic transport coefficients are required. Here, we calculate the…