Numerical Simulation and Parameter Estimation of the Space-Fractional Magnetohydrodynamic Flow and Heat Transfer Coupled Model

In this paper, a coupled model is built to research the space-fractional magnetohydrodynamic (MHD) flow and heat transfer problem. The fractional coupled model is solved numerically by combining the matrix function vector products method in the temporal direction with the spectral method in the spatial direction. A fast method based on the numerical scheme is established to reduce the computational time. With the help of the Bayesian method, the space-fractional orders of the coupled model are estimated, and the problem of multi-parameter estimation in the coupled model is solved. Finally, a numerical example is carried out to verify the stability of the numerical methods and the effectiveness of the parameter estimation method. Results show that the numerical method is stable, which converges with an accuracy of O(τ2+N−r). The fast method is efficient in reducing the computational time, and the parameter estimation method can effectively estimate parameters in the space-fractional coupled model. The numerical solutions are discussed to describe the effects of several important parameters on the velocity and the temperature. Results indicate that the Lorentz force produced by the MHD flow blocks the movement of the fluid and prolongs the time for the fluid to reach a stable state. But the Hall parameter m weakens this hindrance. The Joule heating effects play a negative role in heat transfer.