Unsteady magnetohydrodynamic flow, heat, and mass transfer of the fractional Oldroyd-B fluid along a moving infinite vertical plate

In this study, we develop a novel magnetohydrodynamic (MHD) model to characterize the coupled flow, heat, and mass transfer of the fractional Oldroyd-B fluid along a moving infinite vertical plate. This coupled model consists of a fractional momentum equation, a fractional dual-phase-lag heat conduction equation with thermal radiation effects, and a mass transfer equation governed by a generalized Fick's first law. To compute the numerical solutions of this model, we employ the double-parameter shifted convolution quadrature formula combined with the BDF2-θ for time discretization and the finite difference method for space discretization. We present a numerical experiment to confirm that the proposed method is effective and achieves second-order convergence in both time and space. Finally, we numerically simulate the fractional MHD model and provide detailed graphical analyses about the influences of various parameters on the velocity, temperature, and concentration fields.