Fractional Dual-Phase-Lag Non-Fourier Heat Transfer in a Bimaterial with a Circular Interface Insulator

Abstract

The transient temperature response of a bimaterial with a circular insulated interface region is studied under sudden heating or cooling. The time-fractional dual-phase-lag heat conduction model is adopted to simulate the non-Fourier effect. The problem is reduced to an initial-boundary value problem. The Laplace transform is applied to convert the problem to a mixed boundary value problem, and then the Hankel transform reduces it to a Fredholm integral equation. Special situations for asymptotic thermal behavior near the insulated circular edge and for the steady-state cases are discussed, respectively. The dynamic intensity factors of heat flux and temperature gradient near the insulated circular edge are computed numerically through Stehfest’s Laplace inversion transform technique. The influences of fractional order and relaxation times on the instantaneous temperature change are analyzed. The exact solution of temperature fields for the steady-state case is derived and displayed graphically. The wave-like diffusion behavior of the fractional dual-phase-lag model is interpreted.