Abstract
The paper deals with the asymptotic behavior of the heat transfer in a bounded domain formed by two $\eps$-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 $\eps^r, -1 r \leq 1$, using the two-scale convergence technique of the homogenization theory.