General solution for MHD-free convection flow over a vertical plate with ramped wall temperature and chemical reaction

The aim of the article is to study the unsteady magnetohydrodynamic-free convection flow of an electrically conducting incompressible viscous fluid over an infinite vertical plate with ramped temperature and constant concentration. The motion of the plate is a rectilinear translation with an arbitrary time-dependent velocity. Closed-form solutions for the temperature, concentration and velocity fields of the fluid are obtained. The influence of transverse magnetic field that is fixed relative either to fluid or plate is studied. Furthermore, the effects of system parameters on the fluid velocity are analyzed through numerical simulations and graphical illustrations.