Related papers: Mathematical Modeling of Heat Conduction
We use the multidimensional heat conduction and heat transfer equations to model the temperature distribution of water in a bathtub by solving partial differential equations. We address optimal water addition and bathtub design. First, we…
A non-Fourier thermal transport regime characterizes the heat conduction in solids with internal structure. Several thermodynamic theories attempt to explain the separation from the Fourier regime in such kind of systems. Here we develop a…
We construct a solution of a pure conduction problem in ice and bedrock. This solution is suitable for, and is used in this paper for, verifying a numerical scheme for conservation of energy. This exact solution forms one of a suite of…
Many computational studies on hotspot microfluidic cooling devices found in the literature rely on simplified assumptions and conventions that do not capture the full complexity of the conjugate thermal problem, such as constant…
We study temperature distribution in a heat conducting problem, for a system of p-Laplace equation, giving rise to a free boundary.
We study heat conduction in a one-dimensional chain of particles with longitudinal as well as transverse motions. The particles are connected by two-dimensional harmonic springs together with bending angle interactions. The problem is…
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…
In this article we present a parallel algorithm for simulation of the heat conduction process inside the so-called pulse cryogenic cell. This simulation is important for designing the device for portion injection of working gases into…
The method consists in the monitoring of the temperature variation of a superconductor tape subjected to a trapezoidal current pulse. Simulations of the experiment were performed using the lumped capacitance model and also the finite…
We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…
With the objective to understand microscopic principles governing thermal energy flow in nanojunctions, we study phononic heat transport through metal-molecule-metal junctions using classical molecular dynamics (MD) simulations. Considering…
In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly…
This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…
Understanding and controlling heat transport in molecular junctions would provide new routes to design nanoscale coupled electronic and phononic devices. Using first principles full quantum calculations, we tune thermal conductance of a…
To determine the electron heat flux density on macroscopic scales, the most widely used approach is to solve a diffusion equation through a multi-group technique. This method is however restricted to transport induced by temperature…
This work presents an efficient numerical method based on spectral expansions for simulation of heat and moisture diffusive transfers through multilayered porous materials. Traditionally, by using the finite-difference approach, the problem…
We study the transfer of heat in the non-equilibrium spin-boson model with an Ohmic dissipation. In the non-adiabatic limit we derive a formula for the thermal conductance based on a rate equation formalism at the level of the…
The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have…
Understanding and quantifying the fundamental physical property of coherence of thermal excitations is a long-standing and general problem in physics. The conventional theory, i.e. the phonon gas model, fails to describe coherence and its…
In this paper the Lorentz transformation for temperature is derived and discussed. Considering the hyperbolic heat transport equation it is shown that T(prim) = gamma T, where gamma is the Lorentz factor, T denotes the temperature in the…