2D Problem for a Half-Space under the Theory of Fractional Thermoelastic Diffusion

In this work, we apply the fractional order thermoelasticity diffusion theory to a problem for a halfspace. The surface is taken to be traction free and subjected to a time dependent thermal shock. The chemical potential is assumed to be a known function of time on the bounding plane. Laplace and exponential Fourier transform techniques are used to obtain the solution by a direct approach. The solution of the problem in the physical domain is obtained by using a numerical method for the inversion of the Laplace transforms based on Fourier series expansions. The predictions of the theory are discussed and compared with those for the generalized theory of thermoelastic diffusion. We also study the effect of the fractional derivative parameter on the behavior of the solution. Numerical results are computed and represented graphically for the temperature, displacement, stress, concentration and chemical potential distributions.