Effects of Hall Current on Hydromagnetic Natural Convection Flow of a Heat Absorbing Fluid past an Impulsively Moving Vertical Plate with Ramped Temperature

Abstract

Effects of Hall current on unsteady MHD natural convection flow of a viscous, incompressible, electrically conducting and heat absorbing fluid past an impulsively moving vertical plate with ramped wall temperature in a porous medium, in the presence of thermal diffusion, is studied. The exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique for both ramped temperature and isothermal plates. Solution is also obtained in the case of unit Prandtl number for both ramped temperature and isothermal plates. The expressions for skin friction due to primary and secondary flows and Nusselt number for both ramped temperature and isothermal plates are also derived. Mathematical formulation of the problem, in non-dimensional form, contains six pertinent flow parameters viz. M^2 (magnetic parameter), m (Hall current parameter) Gr (Grashof number), K1 (permeability parameter), Pr (Prandtl number) and Phi (heat absorption coefficient). The numerical values of primary and secondary fluid velocities are displayed graphically versus boundary layer coordinate y for various values of m, Gr, K1, Phi and t while that of fluid temperature are presented in graphical form versus y for different values of Pr, Phi and t for both ramped temperature and isothermal plates. For both ramped temperature and isothermal plates, the numerical values of skin friction due to primary and secondary flows are presented in tabular form for various values of m, Gr, K1, Phi and t whereas that of Nusselt number are given in tables for different values of Pr, Phi and t.