The objective of this study is to find the temperature distribution of a slab as it moves through the pusher-type preheat furnaces. First, the imaginary planes method (IPM) as a new and applicable method for calculation of radiation heat transfer in industrial furnaces is studied, and the two-dimensional form of this method is used to calculate heat flux and temperature distribution in the furn...

The sideways heat equation is a one dimensional model of a problem, where one wants to determine the temperature on the surface of a body using interior measurements. More precisely, we consider a heat conduction problem, where temperature and heat–flux data are available along the line x=1 and the solution is sought in the interval 0≤x <1. The problem is ill–posed in the sense that the solutio...

People experiences heat propagation since ancient times. The mathematical foundations of this phenomenon were established nearly two centuries ago with the early works of Fourier [Fourier, 1952]. During this time the equations describing the conduction of heat in solids have proved to be powerful tools for analyzing not only the transfer of heat, but also an enormous array of diffusion-like pro...

Shocks are often simulated using the classical molecular dynamics (MD) method in which the electrons are not included explicitly and the interatomic interaction is described by an effective potential. As a result, the fast electronic heat conduction in metals and the coupling between the lattice vibrations and the electronic degrees of freedom can not be represented. Under conditions of steep t...

A nonlinear heat conduction equation is studied, and the maximal thermo-geometric parameter in the equation is analytically determined, above which thermal instability occurs. The first-order result yields an acceptable error, and the variational iteration method is recommended for a higher accurate prediction. 2010 Mathematics Subject Classification: 35K05, 35Q79, 80A20, 34B15

From the thermodynamics with internal variables we will derive the temperature equation for viscoelastic fluids. We consider the type of storage of mechanical energy, the dissipation of mechanical energy, the compressibility of the fluid, the non-equilibrium heat capacity and thermal expansion, and deformation induced anisotropy of the heat conduction. The wellknown stress differential models t...

Determination of the maximum temperature and its location is the matter of the greatest importance in many technological and scientific engineering applications. In terms of numerical calculations of the heat conduction equation by using uniform mesh increments in space, large computational cost is sometimes countered. However, adaptive grid refinement method could be computationally efficient ...

In this paper, a non-Fourier heat conduction problem is analyzed by employing newly developed theory. Application of conventional numerical schemes leads to strong oscillations of the results around discontinuities in solution domain. To overcome this difficulty the variational formulation of the Laplace-transformed hyperbolic heat conduction equation is developed. The results were used for eva...

We investigate picosecond laser ablation of metals using a hybrid simulation scheme. Laser energy input into the electron system and heat conduction within it are modeled using a finite-difference scheme for solving the heat conduction equation. Atom motion in the near-surface part ~72 nm! of the sample is modeled using molecular dynamics. Energy transfer between the electronic and atomic subsy...

in this research, the coupling between non-gray radiation and separation convection flow in a duct is investigated numerically. distributions of absorption coefficients across the spectrum  are obtained from the hitran2008 database. the full-spectrum k-distribution method is used to deal with the non-gray part of the problem, while the gray radiation calculations are performed using the planck ...