The Quasi-Static Approximation of Heat Waves in Anisotropic Thermo-Elastic Media

Shaohua Guo

doi:10.4236/am.2010.15054

Abstract

The equilibrium equations of anisotropic media, coupled to the heat conduction equations, are studied here based on the standard spaces of the physical presentation, in which an new thermo-elastic model based on the second law of thermodynamics is induced. The uncoupled heat wave equation for anisotropic media is deduced. The results show that the equation of heat wave is of the properties of dissipative waves. In final part of this paper, we discuss the propagation behaviour of heat waves for transversely isotropic media.

Highlights

In recent years, the considerable interests have been shown in the study of thermo-elastic wave propagations in anisotropic media
The idea of standard spaces [7,8,9,10] is used to deal with both the equilibrium equation and the heat conduction equation based on the quasi-static approximation of the propagation of heat wave, and by introducing an new thermo-elastic model that obeys the second law of thermo-dynamics, a uncoupled modal equations of heat wave are obtained, which shows that heat wave is of the properties of dissipative waves
Case 2 shows that heat wave propagates at an infinite speed when no dissipation exists in media, which is just the classical result of thermo-elasticity based on the conventional heat conduction equation

Summary

Introduction

The considerable interests have been shown in the study of thermo-elastic wave propagations in anisotropic media. The classical theory of thermoelasticity is based on Fourier’s law of heat conduction, which predicts an infinite speed of propagation of heat. This is physically absurd and some new theories have been proposed to eliminate this absurdity. Lord and Shulman [1] obtained a wave-type heat equation by modifying the Fourier’s law of heat conduction. Green and Lindsay [3] deduced another theory, known as temperature rate dependent theory of thermo-elasticity, including the rate of temperature in the constitutive equations This theory contains two constants that act as relaxation times and modifies all the equations of the coupled theory, the heat equation. Propagation direction and space pattern of heat wave can be completely determined by the modal equations

Modal Constitutive Equation of Anisotropic Thermo-Elastic Media

Heat Conduction and Thermo-Dynamic Equations

Application

Conclusions