HOMOGENIZATION OF TWO HEAT CONDUCTORS WITH AN INTERFACIAL CONTACT RESISTANCE

Abstract

In this paper we describe the asymptotic behavior of a problem depending on a small parameter ε>0 and modelling the stationary heat diffusion in a two-component conductor. The flow of heat is proportional to the jump of the temperature field, due to a contact resistance on the interface. More precisely, we give an homogenization result for the stationary heat equation with oscillating coefficients in a domain [Formula: see text] of ℝ n , where [Formula: see text] is connected and [Formula: see text] is union of ε-periodic disconnected inclusions of size ε. These two sub-domains of Ω are separated by a contact surface Γ ε , on which we prescribe the continuity of the conormal derivatives and a jump of the solution proportional to the conormal derivative, by means of a function of order ε γ . We describe the limit problem for γ>-1. The two cases -1<γ≤1 (Theorem 2.1) and γ>1 (Theorem 2.2) need to be treated separately, because of different a priori estimates.