Title

Numerical solution to a one-dimensional nonlinear problem of heat wave propagation in a rigid thermal conducting slab

Author's Department

Mathematics & Actuarial Science Department

All Authors

N.H. Sweilam, A.F. Ghaleb, M.S. Abdou-Dina, M.M. Abou Hasan

Document Type

Research Article

Publication Date

1-3-2021

Abstract

This work aims at presenting a new numerical solution to a nonlinear, one-dimensional problem of heat wave propagation in a thick slab of a rigid thermal conductor. The model predicts dependence of second sound velocity on temperature and heat flux. For this, an unconditionally stable numerical scheme is constructed using a kind of weighted average nonstandard finite difference discretization. Stability analysis of this scheme is studied by von Neumann technique, and its accuracy is proved. Numerical simulations are given for all quantities of physical interest to confirm the reliability of the proposed method. The model and the numerical results shed light on characteristics of heat wave propagation within the theory of extended thermodynamics.

First Page

223

Last Page

232

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