Heat transfer with interfacial barrier in a fine scale mixture of two highly different conductive materials

The paper deals with the asymptotic behavior of the heat transfer in a bounded domain formed by two -periodically interwoven components, of highly different conductivities. Both components might be connected. At the interface, the heat flux is continuous and the temperature subjects to a first-order jump condition. The homogeneous Dirichlet condition is imposed on the exterior boundary. We determine the macroscopic law when the order of magnitude of the jump transmission coefficient is ʳ, -1 r ≤ 1, using the two-scale convergence technique of the homogenization theory.