Heat Transfer in a Medium in Which Many Small Particles Are Embedded
A. G. Ramm · Mathematical Modelling of Natural Phenomena · 2013
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 field is derived when the characteristic size a of the small bodies tends to zero, their total number tends to infinity 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.