Non-steady effective thermal conductivity of matrix composite materials with high volume concentration of particles

A new approach is proposed to investigate the non-steady effective thermal conductivity resulting from thermal waves in matrix composite materials with randomly distributed particles, and the interactions between the dense particles are considered. The theory of quasicrystalline approximation and Waterman’s T matrix formalism are employed to treat the multiple scattering of thermal waves from the particles in composites. The addition theorem for spherical Bessel functions is used to accomplish the translation between different coordinate systems. The Percus–Yevick correlation function widely applied in the molecular theory of liquids is applied to analyze the interaction between the densely distributed particles. The analytical expression of the Percus–Yevick correlation function is also given. Closed form solution of the effective propagation constants is obtained in the low frequency limit. Only numerical solutions are obtained at higher frequencies. Numerical examples show that the non-steady effective thermal conductivity of composite materials shows great difference when the frequency of thermal waves is different. Under different region of wave frequency, the effects of the volume fraction of particles and the material properties (thermal conductivity, specific heat and density) of the particles and matrix on the non-steady effective thermal conductivity are also examined.