Nonsteady Effective Thermal Conductivity of Dense Fibrous Composites with Graded Interface

Abstract

The multiple scattering of thermal waves by dense fibers with a functionally graded interface in composites is considered, and the analytical solution of the nonsteady 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 scattering and refraction of thermal waves by cylindrical fibers with a nonhomogeneous interface layer in the matrix are expressed by using the wave function expansion method. The theory of quasi-crystalline approximation and the conditional probability density function are employed to treat the multiple scattering of thermal waves from the dense fibers. Through analysis, it is found that the nonsteady effective thermal conductivity under higher frequencies is quite different from the steady thermal conductivity. In different regions of wave frequency, the effects of the functional form of gradation and the properties and thickness of the functionally graded layers on the nonsteady effective thermal conductivity show great differences.