Three-dimensional fundamental solution in transversely isotropic thermoelastic diffusion material

The aim of the present investigation is to study the fundamental solution for three dimensional problem in transversely isotropic thermoelastic diffusion medium. After applying the dimensionless quantities, two displacement functions are introduced to simplify the basic three-dimensional equations of thermoelastic diffusion with transverse isotropy for the steady state problem. Using the operator theory, we have derived the general expression for components of displacement, mass concentration, temperature distribution and stress components. On the basis of general solution, three dimensional fundamental solutions for a point heat source in an infinite thermoelastic diffusion media is obtained by introducing four new harmonic functions. From the present investigation, a special case of interest is also deduced to depict the effect of diffusion.