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

In this study, the multiple scattering of thermal waves by dense coated fibers 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 fibrous composite. The scattered and refracted fields in different material zones are expressed by using wave functions expanded method. The addition theorem for Bessel functions is used to accomplish the translation between different coordinate systems. The theory of quasicrystalline approximation and the conditional probability density function are employed to treat the multiple scattering of thermal waves from the dense fibers in matrix. 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. With the increase of the volume fraction of fibers, the effect of the thickness of the coating on the non-steady effective thermal conductivity increases greatly. In different region of wave frequency, the effects of the thickness and properties of the coating and the volume fraction of fibers on the effective thermal conductivity show great difference. Comparisons with the steady thermal conductivity obtained from other methods are also presented.