Heat transfer in a medium in which many small particles are embedded

Abstract

The heat equation is considered in the complex system consisting of many small bodies (particles) embedded in a given material. On the surfaces of the small bodies a Newton-type boundary condition is imposed. An equation for the limiting eld is derived when the characteristic size a of the small bodies tends to zero, their total number N(a) tends to in nity at a suitable rate, and the distance d = d(a) between neighboring small bodies tends to zero a << d. No periodicity is assumed about the distribution of the small bodies.