Dual-phase-lag heat conduction in the composites by introducing a new application of DQM

Abstract

The first application of the differential quadrature method (DQM) in solving the nonlinear dual-phase-lag (DPL) heat conduction equation is demonstrated here. To show the effect of DPL parameters, the temperature response of the medium was obtained from Fourier’s low, hyperbolic heat conduction and hyperbolic type DPL heat conduction model were compared. Furthermore, the transient temperature and resultant heat flux distributions have been found for various types of dynamic thermal loading. We show whether thermal waves exist or not in hyperbolic type DPL heat conduction by considering the time lag parameter in the microstructural interactions of fast transient heat conduction. Also, overshooting which is one of the hyperbolic heat conduction is investigated here. The numerical solution at each time level depends on the solutions at its previous levels. This means the temperature and heat flux obtained at the time nth are the initial conditions for the time (n + 1)th. After demonstrating the convergence and accuracy of the method, the effects of different parameters on the temperature and heat flux distribution of the medium are studied.