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

摘要

We describe two methods for modeling the thermalconductivity and temperature profile in a graded composite film.The film consists of a random binary composite, whoseconcentration varies in the direction perpendicular to the filmsurface, and a fixed temperature difference is applied across thefilm. In the first method, the temperature profile is modeleddirectly, using a finite element technique in which the film isrepresented as a discrete network of thermal conductances,randomly distributed according to the assumed compositionprofile. The temperature at each node, and the effective thermalconductance, is then obtained by a transfer matrix technique. In thesecond approach, the film is treated by an effective-mediumapproximation, suitably generalized to account for thecomposition gradient. The methods are in rough agreement witheach other, and suggest that thermophysical properties of the filmcan be treated reasonably well by approaches generalized fromthose which succeed in conventional composites.