Scattering of Thermal Waves and Unsteady Effective Thermal Conductivity of Particular Composites with Functionally Graded Interface

Abstract

In this study, thermal wave method is applied to investigate the unsteady effective thermal conductivity of particular composites with a functionally graded interface, 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 particular composite. The scattering and refraction of thermal waves by a spherical particle with an inhomogeneous interface layer 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 employing spherical wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions of the layers. The theory of Waterman and Truell is applied to obtain the effective propagating wave number and the unsteady effective thermal conductivity of composites. Through the numerical examples, it is found that in different region of wave frequency, the effect of the thickness of the interface on the unsteady effective thermal conductivity of composites shows great difference. The effect of the thermal conductivity ratio of the particles and matrix on the unsteady effective thermal conductivity is closely related to the incident frequency of thermal waves. The variation of the interface properties between the particles and matrix also expresses great effect on the unsteady effective thermal conductivity of composites. Finally, comparison with the results obtained from other methods is made.