Convergence, stability, and numerical solution of unsteady free convection magnetohydrodynamical flow between two slipping plates

In this study, the unsteady free convection magnetohydrodynamical flow of a viscous, incompressible, and electrically conducting fluid between two horizontally directed slipping plates is considered. The external magnetic filed is applied uniformly in the y-direction and the fluid is assumed to be of low conductivity so that the induced magnetic field is negligible. So the relevant variables, that is, the velocity and the temperature, depend only on one coordinate, the y-axis. The governing equations of velocity and temperature fields are obtained from the continuity, momentum, and energy equations. The boundary conditions for the velocity are taken in the most general form as Robins type which contain slipping parameter. Moreover, the upper plate is heated exponentially and the lower plate is adiabatic. Finite difference method (FDM) is used to simulate the numerical solutions of the problem in which the explicit forward difference in time variable t and central difference in space variable y is used. Hartmann number, Prandtl number, decay factor, and slipping parameter influences on the flow and temperature are shown graphically. It is seen that as the Hartmann number increases, the velocity magnitude drops, which is the well-known flattening tendency of the MHD flow. Also, the increase in decay factor causes an increase in both the velocity and temperature magnitudes at increasing time levels, but it does not change further close to the steady-state. Furthermore, the convergence and stability conditions of the considered scheme are obtained in terms of Hartmann number, Prandtl number, and the slip length.