A Thick Plate Problem in the Theory of Generalized Thermoelastic Diffusion

Abstract

In this work, the problem of a thermoelastic thick plate with a permeating substance in contact with one of the bounding planes is considered in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The bounding surface of the half-space is taken to be traction free and is subjected to a time-dependent thermal shock. The chemical potential is also assumed to be a known function of time on the bounding plane. Laplace transform techniques are used. The solution is obtained in the Laplace transform domain by using a direct approach. The solution of the problem in the physical domain is obtained numerically using a numerical method for the inversion of the Laplace transform based on Fourier expansion techniques. The temperature, displacement, stress, and concentration as well as the chemical potential are obtained. Numerical computations are carried out and represented graphically.

A two-dimensional generalized thermoelastic diffusion problem for a half-space

“…Aoudi (2007) examined the thermoelastic diffusion problem for an infinite elastic body with a spherical cavity. Sherief et al (2009) studied the problem of a thermoelastic thick plate with a permeating substance in contact with one of the bounding planes.…”

A Problem in Thermoelasticity with and without Energy Dissipation

“…Abd El-Latief and Khader [7] studied the fractional model of thermoelasticity for a half-space overlaid by a thick layer. Sherief and El-Maghraby [8] solved the problem of a thick plate in the theory of generalized thermoelastic diffusion.…”

A study of influence of diffusion inside a spherical shell under thermoelastic diffusion with relaxation times

“…These theories allow the finite speeds of propagation of waves inside the medium. Subsequently, a half-space problem and a problem of thick plate under the theory of generalized thermoelastic diffusion were discussed by Sherief and Saleh [15] and Sherief and El-Maghraby [16], respectively. Singh [17,18] studied the reflection phenomena of waves from the free surface of an elastic solid under theory of generalized thermodiffusion.…”