Transient conduction and convection heat transfer across a multi-layer floor subjected to multiple heat sources

This paper analyses the transient heat transfer across multi-layer floors subjected to multiple heat sources. The formulation that is proposed to solve this problem uses analytical expressions handling both conduction and convection phenomena. The Greenʹs functions (analytical expressions) for the layered formation are established by imposing the continuity of temperatures and heat fluxes at the medium interfaces between the various layers. The heat field inside a layer is obtained by adding the contribution of the direct heat incident field, generated as in an unbounded medium, to the heat produced by a set of virtual surface heat sources, that take into account the presence of the interfaces. The technique used to deal with the unsteady state conditions consists of first computing the solution in the frequency domain and then applying (fast) inverse Fourier transforms into space-time.