A method of recursive images to solve transient heat diffusion in multilayer materials

An innovative method of recursive images is presented to obtain solutions to the transient diffusion equation in a N-layered material based on the superposition of Green functions for a semi-infinite material. Through a sequential sum of image reflected functions a temperature solution is initially built for a structure of one layer over a substrate. These functions are chosen in order to satisfy in sequence the boundary conditions, first at the front interface then at the back interface then again at the front interface and so on until the magnitude of the added functions becomes negligible. Based on this so-called 1-layer algorithm, a 2-layer algorithm is obtained. This is accomplished through a sequential application of the 1-layer algorithm first to layer 1 then to layer 2 then again to layer 1 and so on. After that it is suggested how the sequential application of the N − 1 algorithm leads to the N-layer algorithm. This present scheme is valid for boundary conditions of the first and second kind but it will not applicable neither to the case where there is a contact resistance between layers or to the case of convective heat transfer at the end interfaces.