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

In this study, thermal wave method is applied to predict the non-steady effective thermal conductivity of composites with coated fibers, and the analytical solution of the problem is obtained. The Fourier heat conduction law is applied to analyze the propagation of thermal waves in the fibrous composite. The scattering and refraction of thermal waves by a cylindrical fiber with coating 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 layers are expressed by using the wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions of the layer. The theory of Waterman and Truell is employed to obtain the effective propagating wave number and non-steady effective thermal conductivity of composites. 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 thermal conductivity obtained from other methods are also presented.