Scattering of thermal waves and non-steady effective thermal conductivity of composites with coated particles

Abstract

In this study, thermal wave method is proposed to predict the non-steady effective thermal conductivity of composites with coated particles, and the analytical solution of this problem is obtained. The Fourier heat conduction law is introduced to analyze the propagation of thermal waves in the particular composite. The scattering and refraction of thermal waves by a coated particle in the matrix are analyzed, and the results of the single scattering problem are applied to the composite medium. The wave fields in different material zones are expanded by using the spherical wave functions and Legendre polynomial, and the expanded mode coefficients are determined by satisfying the boundary conditions of the coating layer. The theory of Waterman and Truell is employed to obtain the effective propagating wave number and the non-steady effective thermal conductivity of composites. As an example, the effects of the material properties of the particles, coating and matrix on the effective thermal conductivity of composites under different wave frequencies are graphically illustrated and analyzed. Analysis shows that the non-steady effective thermal conductivity under higher frequencies is quite different from the effective thermal conductivity under lower frequencies. In the region of lower frequency, the effect of the properties of the coating on the effective thermal conductivity is greater. Comparisons with the steady effective thermal conductivity obtained from other methods are also presented.