An extended definition of the effective thermal diffusivity is posed via an analogy to acoustic and EM wave propagation in discretely inhomogeneous media. Specifically, the propagation of a periodic, plane thermal wave of frequency ω, through an inhomogeneous medium consisting of spherical particles embedded in a continuous matrix, is theoretically examined. An exact solution for the time–harmonic conduction equation, for the multiple sphere system, is developed by use of the scalar wave harmonic functions and the addition theorem for the harmonics. An effective medium model, which is based on the Quasi–Crystalline approximation (QCA) for acoustic and EM wave propagation, is developed, and a formulation for the frequency–dependent effective thermal diffusivity is derived. In the limit of x = Rω/α0→0, where R is the sphere radius and α0 the matrix thermal diffusivity, it is shown that formulation reduces to that derived from a static model.

This content is only available via PDF.
You do not currently have access to this content.