Homogenization of a two-component composite with interfacial thermal barrier

We study the homogenization of a diffusion equation in an ε−periodic two- component composite in which the heat flow through the interface is proportional, by a function of order εγ, to the jump of the temperature field. We give an homogenization result for γ ≤ −1. The two cases γ < −1 and γ = −1 are treated separately and they lead to different limit problems. In the first case, we obtain a classical composite without barrier resistance, while in the second one the interfacial thermal barrier contributes to the description of the effective thermal conductivity of the homogenized material.