%0 Journal Article
%T A Note on the Unsteady Incompressible MHD Fluid Flow with Slip Conditions and Porous Walls
%A H. Zaman
%A Z. Ahmad
%A M. Ayub
%J ISRN Mathematical Physics
%D 2013
%R 10.1155/2013/705296
%X This work is concerned with the influence of uniform suction or injection on flow and heat transfer analysis of unsteady incompressible magnetohydrodynamic (MHD) fluid with slip conditions. The resulting unsteady problem for velocity and heat transfer is solved by means of Laplace transform. The characteristics of the transient velocity, overall transient velocity, steady state velocity and heat transfer at the walls are analyzed and discussed. Graphical results reveal that the magnetic field, slip parameter, and suction (injection) have significant influences on the velocity, and temperature distributions, which also changes the heat transfer behaviors at the two plates. The results of Fang (2004) are also recovered by keeping magnetic field and slip parameter absent. 1. Introduction Navier-Stokes equations are the basic equations of fluid mechanics. Exact solutions of Navier-Stokes equations are rare due to their inherent nonlinearity. Exact solutions are important because they serve as accuracy checks for numerical solutions. Complete integration of these equations is done by computer techniques, but the accuracy of the results can be established only by comparison with exact solutions. In the literature, there are a large number of Newtonian fluid flows for which exact solutions are possible [1¨C6]. The effects of transverse magnetic field on the flow of an electrically conducting viscous fluid have been studied extensively in view of numerous applications to astrophysical, geophysical, and engineering problems [7¨C15]. If the working fluid contains concentrated suspensions, then the wall slip can occur [16]. Khaled and Vafai [3] studied the effect of the slip on Stokes and Couette flows due to an oscillating wall. However, the literature lacks studies that take into account the possibility of fluid slippage at the walls. Applications of these problems appear in microchannels or nanochannels and in applications where a thin film of light oil is attached to the moving plates or when the surface is coated with special coating such as a thick monolayer of hydrophobic octadecyltrichlorosilane [17]. Yu and Ameel [18] imposed nonlinear slip boundary conditions on flow in rectangular microchannels. Erdogan [6] studied deeply the solution to the Stokes problem under nonslip conditions at the wall. Ayub and Zaman [19] studied the effects of suction and blowing for orthogonal flow impinging on a wall. Khan et al. [20] discussed the flow of Sisko fluid through a porous medium. Ariel et al. [21] considered the flow of elasticoviscous fluid with partial slip.
%U http://www.hindawi.com/journals/isrn.mathematical.physics/2013/705296/