Series expansion for the effective conductivity of a periodic dilute composite with thermal resistance at the two-phase interface

. We study the asymptotic behavior of the effective thermal conductivity of a periodic two-phase dilute composite obtained by introducing into an infinite homogeneous matrix a periodic set of inclusions of a different material, each of them of size proportional to a positive parameter (cid:2) . We assume that the normal component of the heat flux is continuous at the two-phase interface, while we impose that the temperature field displays a jump proportional to the normal heat flux. For (cid:2) small, we prove that the effective conductivity can be represented as a convergent power series in (cid:2) and we determine the coefficients in terms of the solutions of explicit systems of integral equations.