New fractional model for 2 dimensional half space problem with in the theory of generalized thermoelastic diffusion

Abstract

AbstractIn this manuscript, the generalized thermoelastic diffusion theory is modified by using fractional derivatives. The revised equation is employed to study a two‐dimensional problem of the axisymmetric temperature distribution during a half space with a permeating substance in touch with the bounding plane. The surface of the half space is taken into account to be traction‐free and subject to an axisymmetric temperature distribution. Laplace and Hankel transformation techniques are used. The analytical solution within the transform domain is obtained by an immediate method. By employing a numerical method supported the Fourier expansion technique, the inverse of the double transforms is often obtained. Numerical results for the temperature, displacement, stress, concentration, and chemical potential are administered and represented graphically. The figures show some comparisons to estimate the impact of fractional parameter on all research areas.