Derivations of transient thermal Green's functions in three-dimensional general anisotropic media

In this paper, three-dimensional transient thermal Green's functions in general anisotropic media are derived in relatively concise forms via the Radon transform. Both situations in full-space and half-space are provided. For the case in full-space, the governing equation of heat conduction problem in three-dimension is reduced to a similar one in one-dimension whose solution is existent. For the case in half-space, both Dirichlet and flux-free boundary conditions are considered, and the solutions are derived by an image method. Applying the inverse Radon transform to solutions in transform domain, Green's functions in physical domain are subsequently expressed as an integral over a unit sphere. If written in terms of usual spherical coordinate, moreover, these solutions are regular integrals over finite intervals and can be evaluated easily and effectively. Numerical examples are presented to verify the accuracy and applicability of the present derivations, and to demonstrate the effects of distinguishing boundary conditions.