Title

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

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https://doi.org/10.1007/s12648-020-01952-8

Document Type

Research Article

Publication Title

Indian Journal of Physics

Publication Date

1-1-2021

doi

10.1007/s12648-020-01952-8

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.

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