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In the present study, an analysis for steady hydromagnetic mixed convective generalised Couette flow between two infinite parallel plates of arbitrary electrical conductivities and finite thicknesses filled with a porous medium in the presence of a uniform transverse magnetic field in a rotating system with the Hall effect is presented. The heat transfer characteristics of the fluid flows are also investigated, taking viscous and Joule dissipations into account. Exact solutions of the resulting simultaneous ordinary differential equations governing the fluid flows are obtained in a closed form. The closed form analytical solutions for shear stress and mass flow rate are also obtained. To examine the physical consequences and flow characteristics, the numerical results for velocity, induced magnetic field, temperature field, shear stress, mass flow rate, and rate of heat transfer are computed for different values of various system parameters and are displayed in graphical and tabular forms. An interesting observation recorded that there arises flow reversal in the secondary flow direction when the permeability parameter is very small, i.e., when Darcian drag force is very large.

An investigation on an unsteady MHD natural convection flow with radiative heat transfer of a viscous, incompressible, electrically conducting and optically thick fluid past an impulsively moving vertical plate with ramped temperature in a porous medium in the presence of a Hall current and thermal diffusion is carried out. An exact solution of momentum and energy equations, under Boussinesq and Rosseland approximations, is obtained in a closed form by the Laplace transform technique for both ramped temperature and isothermal plates. Expressions for the skin friction and Nusselt number for both ramped temperature and isothermal plates are also derived. The numerical values of fluid velocity and fluid temperature are displayed graphically versus the boundary layer coordinate y for various values of pertinent flow parameters for both ramped temperature and isothermal plates. The numerical values of the skin friction due to primary and secondary flows are presented in tabular form for various values of pertinent flow parameters.

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In this study, a mathematical analysis is presented for the hydromagnetic convective flow of an incompressible, chemically reacting, and electrically and thermally conducting viscoelastic fluid through a vertical channel bounded by the porous regime under the action of an applied magnetic field with Hall current and induced magnetic field effects. The left wall of the channel is considered to be nonmagnetic, whereas the right wall of the channel is periodically magnetized. The flow within the channel is induced due to the nonuniform wall temperature and concentration, periodic pressure gradient, and periodic movement of the right wall. The method of separation of variable is used to convert the flow governing coupled partial differential equations into the ordinary differential equations that are solved analytically, and the solution for fluid velocity, induced magnetic field, temperature, and concentration is presented in a closed form. Numerical computation has been performed to demonstrate the impact of various system parameters on the fluid flow behavior. It is observed that oscillations increase the primary flow and primary induced magnetic field. Buoyancy forces have a tendency to lessen the secondary induced magnetic field. Furthermore, it is examined that magnetic diffusivity increases the primary flow, whereas it decreases the secondary flow and primary induced magnetic field.