Three-dimensional fundamental solution of wave propagation and transient heat transfer in non-homogenous media

The main purpose of this paper is developing fundamental solutions of three-dimensional wave and transient heat conduction in non-homogenous media. A variable transformation method is used to change the basic equations into a simple standard Helmholtz form. First, two different ways, i.e. harmonic excitation method and Laplace transform are used to eliminate time expression, and final solutions are expressed in the time-space domain. In addition, FE approach is applied to solve transient heat conduction in functionally graded material (FGM) domain. Different numerical examples are used to validate the proposed methodology by comparing the results with others and FE method. Fundamental solutions are found for both homogenous and non-homogenous media separately. For each example, appropriate graphs are provided to show the differences between the results of homogenous and non-homogenous media.