Parameter estimation for unsteady MHD oscillatory free convective flow of generalized second grade fluid with Hall effects and thermal radiation effects

Abstract

This work first establishes an unsteady magnetohydrodynamic (MHD) oscillatory free convection flow model of the generalized second grade fluid with Hall heat and mass transfer effect in a straight rectangular duct. A fast second-order spectral method with fractional backward difference formula (FBDF) is proposed to obtain the numerical solution of the established model. The distribution of the velocity and the temperature fields is discussed, and the effect of each parameter on the velocity and temperature fields is shown through graphical experiments. Moreover, in order to avoid the problems of slow computational speed and low accuracy of traditional numerical methods, new fractional physics-informed neural networks (PINNs) are proposed for the multi-parameter estimation of this model. At the same time, a comparative study of our method with the Bayesian method is presented. Experimental results show that fractional PINNs is more effective for multi-parameter estimation problems and get better accuracy at the same number of parameters.