Unsteady MHD Free Convection in a Radiating Fluid Flow past a Vertically Time-Dependent Moving Plate with Ramped Double-Diffusive Condition

An unsteady MHD-free convection heat-mass transfer from a viscous, incompressible fluid flow past an infinite vertical moving plate is studied here. The fluid is considered to be electrically conducting and chemically reacting. We consider three types of plate movements: uniform velocity, uniform acceleration, and periodic acceleration. Ramped as well as constant conditions at the plate for both temperature and concentration are considered. We obtain the exact solutions of the governing equations using the method of the Laplace transform technique. The impact of the type of thermal and concentration boundary condition (constant/ramped) at the plate as well as the kind of plate movement on the flow, heat and mass transfer characteristics, are presented and analyzed here. While doing so, we also consider the variation of our governing parameters: thermal and solutal Grashof numbers, magnetic field intensity, radiation ( \(R\) ), chemical reaction ( \(Kc\) ), Prandtl number and Schmidt numbers. It is observed that the presence of buoyancy and other forces close to the plate can be almost nullified due to the imposition of a strong transverse magnetic field. The viscous drag at the plate diminishes (and increases) with the increase of the strength of the applied magnetic field (and  \(R\)  and \(Kc\) ). The rate of increment of skin friction with respect to time is more for the case of periodic oscillating plate movement. The magnitude of viscous drag is reported as more significant for the constant case compared to the ramped case.