Date of Publication : 07, Dec, 2019
Date Of Acceptance : 1 Dec, 2019
Author: KHADIJAH .K. LAWAL
Co Author: HARUNA .M. JIBRIL
Area of research / Subject: Mathematics
In this work, the unsteady free convection flow of a viscous, incompressible and electrically conducting fluid near a vertical porous plate with ramped temperature and ramped motion in the presence of uniform transverse magnetic field is studied. A unified closed form analytic solution have been obtained for the velocity field and skin friction coefficient corresponding to the case of a magnetic field fixed relative to the fluid or the porous plate. It is assumed that the bounding plate has ramped temperature profile and ramped motion subject to a uniform transverse magnetic field under the assumption of negligible induced magnetic field. Laplace transform technique has been used to find the solutions of the velocity and temperature in Laplace domain. While, the closed form semi-analytical solution has been obtained using the Riemann-sum approximation method. The effect of the flow parameters such as the Prandtl number , Hartmann number , Heat sink parameter and Suction/Injection on the fluid temperature, velocity, Nusselt Number as well as the skin friction co efficient are presented with the help of graph. It was observed that Suction/injection increases the velocity of the fluid. This is because injection increase thickens the boundary layer which eventually increases the fluid velocity while suction causes a thinning of the boundary layer which leads to the decreases in the fluid velocity.
Keywords : Ramped Temperature, Ramped Motion, Natural Convection, Magnetic field, Vertical porous plate heat generating or absorbing,
DOI (Digital Object Identifier) Number: http://doi.org/10.5281/zenodo.3566758