A Continuum Mixture Theory of Heat Conduction in Laminated Composites

Abstract

A continuum mixture theory with microstructure is developed for heat conduction in laminated wave guides. The theory leads to simple governing equations for the actual composite which retain the integrity of the diffusion process in each constituent but allow them to coexist under some defined interactions. The utility of the resulting equations is demonstrated by studying both harmonic and transient temperature pulses. In the case of harmonic loadings the results are found to correlate well with some existing exact solutions. For transient loadings, solutions are derived by means of Laplace transform techniques. Analytical inversion of the transforms is possible only for the limiting cases of “weak” and “strong” thermal coupling. The limit of strong interaction leads to the coalescence of both temperatures; in this case the composite behaves like a single but higher-order continuum. For the general coupling case, however, results are demonstrated by a direct numerical inversion of the transforms.