Numerical Simulation of Dual-Phase-Lag Model and Inverse Fractional Single-Phase-Lag Problem for the Non-Fourier Heat Conduction in a Straight Fin

In recent years, many studies have been done on heat transfer in the fin under unsteady boundary conditions using Fourier and non-Fourier models. In this paper, unsteady non-Fourier heat transfer in a straight fin having an internal heat source under periodic temperature at the base was investigated by solving numerically Dual-Phase-Lag and Fractional Single-Phase-Lag models. In this way, the governing equations of these models were presented for heat conduction analysis in the fin, and their results of the temperature distribution were validated using the theoretical results of Single and Dual-Phase-Lag models. After that, for the first time the order of fractional derivation and heat flux relaxation time of the fractional model were obtained for the straight fin problem under periodic temperature at the base using Levenberg-Marquardt parameter estimation method. To solve the inverse fractional heat conduction problem, the numerical results of Dual-Phase-Lag model were used as the inputs. The results obtained from Fractional Single-Phase-Lag model could predict the fin temperature distribution at unsteady boundary condition at the base as well as the Dual-Phase-Lag model could.