Thermal Diffusivity of Heterogeneous Materials. II. Limits of the Steady-State Approximation

Abstract

In the first paper of this series, the concept of the thermal diffusivity as a characteristic constant of a heterogeneous material was examined by considering the derivation of the heat conduction equation. In this second paper, a specific transient thermal problem with periodic boundary conditions is treated for two model heterogeneous materials: spheres imbedded in a matrix, and a two-phase material composed of roughly spherical particles with neither phase continuous. In the steady-state limit (low frequency or small particle size), it is shown that the material may be considered homogeneous and the proper value of thermal conductivity and heat capacity are those developed from a steady-state development of thermal conductivity and the equilibrium heat capacity. A criterion for determining when a material of this type may be treated as homogeneous for a given transient thermal problem is also developed.