The problem of the transient thermal response of two semi-infinite solids not making perfect contact, is treated analytically by modeling the interface to be a series of equally spaced strips making perfect contact. The remaining area is assumed to perfectly insulated, and a criterion is established for the validity of this assumption, taking radiation into consideration. The mixed interface conditions present a considerable difficulty and a long-time perturbation scheme is therefore used to obtain approximate expressions for the transient temperature distributions, average heat flux and the thermal contact resistance. The method is applicable to a large class of problems with mixed boundary conditions for which the existing techniques give exact solutions only for the steady state.

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