Mathematical Modelling of Magnetohydrodynamic Transient Free and Forced Convective Flow with Induced Magnetic Field Effects

摘要

An exact solution for the unsteady mixed convective MHD flow of an incompressible viscous electrically-conducting fluid over an infinite vertical isothermal plate impulsively held fixed in a uniform stream is presented here. A uniform magnetic field is assumed to be applied transversely to the direction of the flow, taking into account the induced magnetic field. The governing equations are solved in close form by the Laplace Transform technique. The expressions for the velocity field, induced magnetic field and skin friction at the plate are obtained and solutions are presented graphically for the various governing dimensionless parameters. The effects of Hartmann (magnetohydrodynamic body force) number, M, Prandtl number, Pr, magnetic Prandtl number, Pm, induced to applied magnetic field strength ratio, H and Grashof number, Gr, on the velocity, induced magnetic field and skin friction distributions at the plate are discussed. It is observed that the velocity field, skin friction and induced magnetic field are significantly affected by the applied magnetic field as well as magnetic Prandtl number. Induced magnetic field is found to decrease with a rise in Hartmann number. Velocity is enhanced with positive Grashof number and reduced with negative Grashof number. Induced magnetic field is strongly reduced with increasing magnetic field ratio parameter but enhanced with magnetic Prandtl number. The flow is accelerated i.e. shear stress accentuated with increasing Hartmann number and Prandtl number but decelerated with elapse of time.