Analytical solution of unsteady heat conduction in a two-layered material in imperfect contact subjected to a moving heat source

An analytical approach of transient heat conduction in two-layered material, of finite depth, with an imperfect thermal contact, subjected to a moving gaussian laser beam was developed.The method consists of deriving the solution of the homogeneous part of the heat equation by using the well known separation of variables method and expressing the source term in series form. The porous aspect of granular coating layer on substrate was also taken into account earlier in this modelling work. This model has been successfully applied on a practical system; laser cladding of electronic copper tracks on alumina substrates. This analytical model can be used also for estimation of the thermal contact resistance between layers.