Two dimensional spherical regions problem in the context of the theory of generalized thermoelastic diffusion
Eman M. Hussein
Abstract
In this work a spherical thermoelastic region problem with a permeating substance in contact of the bounding plane is considered in the context of the theory of generalized thermoelastic diffusion with one relaxation time. The general solution is obtained in the Laplace transform domain by using a direct approach without the use of potential functions. The resulting formulation is used to solve problem of a solid sphere. The surface is taken to be traction free, subjected to a given axisymmetric temperature distribution and the chemical potential also assumed to be a known function of time. The inversion of the Laplace transform is carried out using the inversion formula of the transform together with Fourier expansion techniques. Numerical methods are used to accelerate the convergence of the resulting series to obtain the temperature, displacement, concentration, stress distributions as well as the chemical potential in the physical domain. Numerical results are represented graphically and discussed.