Thermal conductivity of graded composites : Numerical simulations and an effective medium approximation

We describe two methods for modeling the thermal conductivity and temperature profile in a graded composite film. The film consists of a random binary composite, whose concentration varies in the direction perpendicular to the film surface, and a fixed temperature difference is applied across the film. In the first method, the temperature profile is modeled directly, using a finite element technique in which the film is represented as a discrete network of thermal conductances, randomly distributed according to the assumed composition profile. The temperature at each node, and the effective thermal conductance, is then obtained by a transfer matrix technique. In the second approach, the film is treated by an effective-medium approximation, suitably generalized to account for the composition gradient. The methods are in rough agreement with each other, and suggest that thermophysical properties of the film can be treated reasonably well by approaches generalized from those which succeed in conventional composites.