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International audience; 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.

An analytical approach of transient heat conduction in a two layered material, in finite dimensions within imperfect thermal contact, subjected to a moving Gaussian laser beam was achieved. The result of this study allows on the one hand an easy access to the distribution and the evolution of the temperature in both layers of the workpiece; on the other hand permits to clarify the influence of the contact quality on the temperature gap at the interface. The effect of a porous grannular deposit layer was also considered in this study. A design of electronic tracks by laser cladding was studied as an application example in the surface treatment area; this model can be also used to estimate the thermal contact resistance between layers.