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

Abstract

In this work, we consider the two-dimensional problem of a thermoelastic half-space with a permeating substance in contact with the bounding plane 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 subjected to a time-dependent thermal shock. Laplace and Fourier transform techniques are used. The solution in the transformed domain is obtained by a direct approach. Numerical inversion techniques are used to obtain the inverse double transforms. Numerical results are represented graphically and discussed.

An Elastodiffusive Orthotropic Euler–Bernoulli Beam Considering Diffusion Flux Relaxation

“…An example of this is the interaction between mechanical and diffusion fields. Among the recent publications, it can be noted that [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] were devoted to this problem. In particular, [1][2][3][4][5][6][7][8][9][10][11] considered the thermal effects, while the electromagnetic effects were studied in [12][13][14][15].…”

“…Among the recent publications, it can be noted that [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] were devoted to this problem. In particular, [1][2][3][4][5][6][7][8][9][10][11] considered the thermal effects, while the electromagnetic effects were studied in [12][13][14][15]. In addition, the analysis of fast unsteady processes in relatively short time periods requires the relaxation of thermal and diffusion perturbations to be taken into account [1,2,[4][5][6]8,9,[11][12][13].…”

Thermoelastic Diffusion Multicomponent Half-Space under the Effect of Surface and Bulk Unsteady Perturbations

“…Most of the currently available work are devoted to solving static [6], quasistatic [7], and stationary [8] problems of thermomechanical diffusion. However, unsteady coupled one-dimensional [9] and two-dimensional problems [10,11] are the most interesting and difficult. In these articles, the solution of the unsteady problem has been reduced to the Laplace transform on time.…”

“…Their originals are found using well-known theorems and tables of operational calculus. Moreover, there is no need to develop new complex approaches for the numerical inversion of the Laplace transform, as it has been done in the above-mentioned works [9][10][11]. The inversion of the Fourier sine and cosine transforms, in general, can be done numerically, using such well-known approaches as the Filon's method or the inverse Discrete Fourier Transform (DFT).…”

A Two Dimensional Axisymmetric Thermoelastic Diffusion Problem of Micropolar Porous Circular Plate with Dual Phase Lag Model

“…El-Sayed [30] applied the theory of generalized thermoelastic diffusion with one relaxation time to study the two dimensional problem of a thermoelastic half space with a permitting substance and with the bounding plane. Abbas, Kumar and Kaushal [31] used finite element method to study the deformation in a micropolar thermoelastic diffusion medium subjected to thermal source within the context of Lord Shulman theory [32]. El-Karamany and Ezzat [33] derived the constitutive equations for thermoelastic diffusion in anisotropic and isotropic solids using generalized thermoelasticity theory with two time delays and kernel functions.…”