A numerical study on steady laminar magnetohydrodynamics (MHD) mixed convection flow of an electrically conducting fluid in a vertical square duct under the action of transverse magnetic field has been investigated. The walls of the duct are electrically non-conducting. In this study both forced and free convection flows are considered. The viscous dissipation and Joule heat are also considered in the energy equation and moreover the walls of the duct are kept at constant temperature. The governing equations of momentum, induction and energy are first transformed into dimensionless equations by using dimensionless quantities, then these are solved employing finite difference method for velocity, induced magnetic field and temperature distribution. The computed results for velocity, induced magnetic field and temperature distribution are presented graphically for different dimensionless parameters Hartmann number , Prandtl number , Grashof number and magnetic Reynolds number .

Steady laminar magnetohydrodynamics flow and heat transfer of an electrically conducting fluid in a rectangular duct in the presence of oblique transverse magnetic field is considered. The walls of the duct are electrically insulated and kept at constant temperature( ). The fluid is kept in motion by a constant pressure gradient and the viscous and Joule dissipations are considered in the energy equation. The dimensionless coupled partial differential equations are solved numerically employing finite difference method for velocity, induced magnetic field and temperature distribution. The computed results for velocity, induced magnetic field and temperature are visualized in terms of graphics for different values of oblique angle( ), Hartmaan number , Prandtl number and the aspect ratio , the ratio of the length to the breadth. KeywordsMHD flow, electrically insulated walls, rectangular duct, heat transfer, finite difference method, aspect ratio.

Unsteady hydromagnetic Couette flow of a viscous, incompressible and electrically conducting fluid in a rotating system between two infinitely long parallel porous plates, taking Hall current into account, in the presence of a transverse magnetic field is studied numerically. Fluid flow within the channel is induced due to impulsive movement of the lower plate of the channel and fluid motion is subjected to a uniform suction and injection at upper and lower plates. Magnetic lines of force are assumed to be fixed relative to the fluid. Numerical solutions for primary and secondary velocities are obtained from the governing momentum equation by employing explicit finite difference method. The effects of various non-dimensional parameters: Hall current parameter , magnetic parameter , suction/injection parameter and time on primary and secondary velocities are presented graphically and discussed.

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In this paper, the steady fully developed MHD flow of a viscous incompressible electrically conducting fluid through a channel filled with a porous medium and bounded by two infinite walls is investigated numerically for the cases (i) Poiseuille flow and (ii) Couette--Poiseuille flow; with uniform suction and injection at the walls in the presence of an inclined magnetic field. The Brinkman equation is used for the flow in the porous channel and solved numerically using the finite difference method. Numerical results are obtained for velocity. The effects of various dimensionless parameters such as Hartmann number ( ), suction/ /injection parameter ( ), permeability parameter ( ) and angle of inclination ( ) on the flow are discussed and presented graphically.