Multiple scattering of thermal waves and non-steady effective thermal conductivity of composites with dense coated particles

In this study, the multiple scattering of thermal waves from dense coated particles in composites is considered, and the analytical solution of the non-steady effective thermal conductivity of composites is presented. The Fourier heat conduction law is applied to analyze the propagation of thermal waves in the particular composite. The scattered and refracted temperature fields in different material zones are expressed by using wave functions expanded method. The addition theorem for spherical Bessel functions is used to accomplish the translation between different coordinate systems. The theory of quasicrystalline approximation and conditional probability density function are employed to treat the multiple scattering of thermal waves from the dense particles. The effective propagating wave number and non-steady effective thermal conductivity of composites are obtained. As an example, the effects of the material properties of the coating on the effective thermal conductivity of composites are graphically illustrated and analyzed. Analysis shows that the non-steady effective thermal conductivity under higher frequencies is quite different from the steady thermal conductivity. 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.