Research on macroscopic and microscopic heat transfer mechanisms based on non-Fourier constitutive model

Based on the Cattaneo-Christov model and dual-phase-lag model, a novel constitutive model is proposed to study macroscopic and microscopic heat transfer mechanisms in the moving media. Formulated governing equation contains relaxation parameters and time fractional derivative with the highest order of 1 + α (0 < α ≤ 1) which possesses both the relaxation characteristic and memory characteristic. With the help of L1-scheme, solutions are obtained by numerical difference method. Two applications with the new proposed model are given. One is to analyze the heat conduction in processed meat which analyzes the effects of convection velocity on the temperature distribution. The other is to study the thermal behavior of a biological tissue that the spatial evolution of the temperature distribution with the effects of involved parameters, such as fractional parameter, convection velocity parameter, macroscopic relaxation parameter and microscopic one is spotlighted by graphical illustrations. An interesting result is found that the temperature transports faster at the smaller x while slower at the larger x for a larger fractional parameter α, a smaller β or a larger microscopic relaxation parameter. For a larger macroscopic relaxation parameter or convection velocity parameter, the temperature transports slower.