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Three-dimensional fundamental solution in transversely isotropic thermoelastic diffusion material. (English) Zbl 1299.80007
Summary: We study the fundamental solution for a three-dimensional problem in a 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 operator theory, we derive the general expression for the components of the displacement, the mass concentration, the temperature distribution, and the stress components. On the basis of the general solution, three-dimensional fundamental solutions for a point heat source in an infinite thermoelastic diffusion media are 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.
MSC:
80A20 Heat and mass transfer, heat flow (MSC2010)
80A17 Thermodynamics of continua
80M25 Other numerical methods (thermodynamics) (MSC2010)
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