The unsteady free convection flow of rotating MHD second grade fluid in porous medium with effect of ramped wall temperature

In this paper, the unsteady free convection flow of an incompressible second grade fluid in a vertical plate with ramped wall temperature is investigated. The fluid in magnetohydrodynamics (MHD) flows through a porous medium is also considered. The fluid is electrically conducting under the assumption of a small magnetic Reynolds number applied in a vertically inward direction to the flow. The governing equations are modeled in a rotating plate such that both the fluid and plate in unison with angular velocity. The exact solutions of velocity and temperature are obtained in closed form by using Laplace transform method. These solutions are presented graphically and discussed for second grade parameter ? , rotation parameter ? , porosity parameter K , magnetic parameter M , Prandtl number Pr , and Grashof number Gr