MHD Flow Along a Vertical Plate with Heat and Mass Transfer under Ramped Plate Temperature

Abstract

Present study is carried out to examine the effects of Porosity, thermophoresis, and rotation on the unsteady natural convective flow of an incompressible, viscous and electrically conducting fluid past an impulsively started vertical plate in a porous medium under the influence of a magnetic field with ramped wall temperature condition. Analytical solution of partial differential equations of the model is obtained by the Laplace transform method with the help of the Heaviside step function; also the expression for the Sherwood Number, Nusselt Number and Shear stress at the plate is obtained. The obtained results are checked against previously published work for special cases of the problem and found to be in excellent agreement. The results obtained are shown by graphs. The effect of physical parameters such as M (Magnetic parameter), K (Darcy permeability), Sr (Soret number) and Ω (rotation parameter) on these fields are discussed in detail, and it has been observed that for both isothermal and ramped temperature plates; primary and secondary fluid velocity attain a different maximum value in the vicinity of the plate and then decrease gradually. The conclusions of the study have great applications in the field of science and engineering such as in rotating MHD induction machine energy generators, Magnetic field control of materials processing systems, planetary and solar plasma fluid dynamics systems, etc.