Numerical calculation and fast method for the magnetohydrodynamic flow and heat transfer of fractional Jeffrey fluid on a two-dimensional irregular convex domain

Abstract

In this paper, we study the magnetohydrodynamic (MHD) flow and heat transfer of the fractional Jeffrey fluid in a straight channel, of which the cross section is a two-dimensional irregular convex domain. We consider a spatial fractional operator to modify the classical Fourier's law of thermal conduction, and obtain the time-space fractional coupled model. The fractional coupled model is solved numerically by the L2−1σ method in the temporal direction and the unstructured mesh finite element method in the spatial direction. Besides, we prove the stability and convergence of the numerical scheme. In order to reduce the computational time, a fast method is proposed. Finally, a numerical example is given to verify the theoretical analysis and the efficiency of the fast method. Furthermore, an example is considered to discuss the effects of the fractional parameters on the MHD flow and heat transfer of the fractional Jeffrey fluid.