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The present paper, a theoretical analysis of steady fully developed flow and heat transfer of two immiscible magneto hydrodynamic and viscous fluid, partially filled with porous matrix and partially with clear fluid bounded by two vertical plates, has been discussed, when both the plates are moving in opposite directions. The plates are maintained at unequal temperatures. The Brink-man-extended Darcy model has described the momentum transfer in a porous medium. The effect of various parameters and Darcy number are discussed in the flow field and the temperature profiles numerically and are expressed by graphs. The non-dimensional governing momentum and energy equations are analytically solved by applying the homotopy perturbation technique and the method of ordinary differential equation. It is observed that magnetic parameter (M) has a retarding effect on the main flow velocity and is to enhance the temperature distribution, whereas the reversal phenomenon occurs for the Darcy dissipation parameter (Da). The skin-friction component has also been determined and is presented with the help of a table. The magnetic parameter (M) reduces the skin friction coefficient for clear fluid region and is to increase the skin friction coefficient for porous region. It is also evident from table that getting bigger the width of the clear fluid layer increases the skin friction. The skin friction coefficient on both the plates (comparing at y = 0 and at y = 1 for A or B) increases when those are heated.

Convective Effects on MHD Flow and Heat Transfer between Vertical Plates Moving in Opposite Direction and Partially Filled with a Porous Medium