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 ϵ. 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 ϵ small, we prove that the effective conductivity can be represented as a convergent power series in ϵ and we determine the coefficients in terms of the solutions of explicit systems of integral equations.
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