STM Article Repository

Lord-Shulman theory is the first generalization of the coupled theory. The basis of the model proposed
by Lord and Shulman [79] was to modify Fourier’s law of the heat conduction equation by introducing
a new physical concept which called a relaxation time needed for acceleration of the heat flow. The
heat equation of this theory of the wave type, it automatically ensures finite speeds of propagation of
heat and elastic waves. The remaining governing equations for this theory, namely, the equations of
motions and constitutive relations, remain the same as those for the coupled and uncoupled theories.
This theory was extended by Dhaliwal and Sherief [80] to generalization isotropic media in the
presence of heat sources. Sherief and Dhaliwal [81] solved a thermal shock problem. These problems
are valid for short times. Lord-Shulman theory has been proved by many researchers such as
Ackerman et al. [82] and Ackerman and Overtone [83] experimentally for solid Helium that thermal
waves (second sound) propagation with a finite, though quite large speed. Nayfeh and Naser [84]
investigated the Maxwell’s surface waves propagate along a half-space consists of linearly elastic
materials that conduct heat. Puri [85] studied the properties of two dilatation motions in the context of
generalized thermo-elasticity. Sharma [86] studied the propagation of surface waves in a transversely
isotropic thermo-elastic half-space, taking into account the generalized form of heat conduction
equation. Sharma and Singh [87] investigated the propagation of plane harmonic waves in a cubic
crystal in the context of generalized thermo-elastic theories. Shreief [88] studied the stress and
temperature distributions with a continuous source of heat in an infinite elastic body governed by the
equations of generalized thermo-elasticity using Laplace transform technique. Inverse transforms
obtained in an approximate manner for small values of time. Youssef and Abbas [89] proposed a
general finite element model to analyze transient phenomena in a thermo-elastic model in the context
of the theory of generalized thermo-elasticity with one relaxation time and variable thermal
conductivity. Othman [90] derived the model of equations of generalized thermo-elasticity based on
the (L-S) theory in an isotropic elastic medium with the dependence of the modulus of elasticity on the
reference temperature. Othman and Lotfy [91] studied the plane waves of generalized thermo-micro
stretch elastic half-space under three theories, the normal mode (analytical method) was applied to
obtain the exact solutions of the problem using the general model of the heat conduction equation in
the context of the (L-S) theory as a special case. Othman [92] studied the effect of rotation on
generalized thermo-elasticity plane waves with thermal relaxation time under the temperature
dependent properties.