FRACTIONAL MODEL IN THE THEORY OF GENERALIZED THERMOELASTIC DIFFUSION

Abstract

A problem for thermoelastic thick plate of infinite extension and finite thickness is considered, where a permeating substance is in contact with one of the bounding planes in the context of generalized thermoelastic diffusion theory with fractional parameter. The upper surface is assumed to be traction-free, subject to time-dependent thermal shock, and the chemical potential is also assumed to be a known function of time. The lower surface of the plate is laid on an insulated rigid foundation. Laplace and Hankel transform techniques are used. Analytical solutions in the transform domain are obtained using direct methods. The inverse of the double transform is obtained using a numerical method based on the Fourier expansion technique. A general solution to the cylindrical region problem is obtained. The solution can calculate under any boundary conditions. All numerical results are in perfect agreement with earlier work in various thermoelastic theories. Numerical calculations are performed for two different time values and for three distinct fraction parameter values. Temperature, stress, displacement, concentration, and chemical potential are displayed graphically. Comparisons are made with the results of the previous theory.