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The effects of radiation on MHD free convection flow of a viscous incompressible electrically conducting fluid past a moving infinite vertical plate with ramped wall temperature have been studied. The Laplace transform technique has been applied to obtain an exact solution in a closed form, when the plate is moving impulsively with a velocity 0 U . It is examined that two different solutions for the fluid velocities, one valid for fluids of Prandtl number ( Pr ) different from 1 and the other for which the Prandtl number equal to1. The variations of velocity and fluid temperature are presented graphically. It is observed that the velocity decreases with an increase in Prandtl number for ramped temperature as well as for constant wall temperature. An increase in Grashof number leads to a rise in the values of velocity due to enhancement in buoyancy force. The velocity decreases with an increase in Hartmann number which implies that magnetic field has an retarding influence on the flow. The effect of the Prandtl number is very important in the temperature field. A fall in temperature occurs due to an increasing value of the Prandtl number. It is seen that the temperature decreases as the radiation parameter increases for ramped temperature as well as for constant wall temperature.

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The unsteady MHD Couette flow of an incompressible viscous electrically conducting fluid between two infinite nonconducting horizontal porous plates under the boundary layer approximations has been studied with the consideration of both Hall currents and ion-slip. An analytical solution of the governing equations describing the flow is obtained by the Laplace transform method. It is seen that the primary velocity decreases while the magnitude of secondary velocity increases with increase in Hall parameter. It is also seen that both the primary velocity and the magnitude of secondary velocity decrease with increase in ion-slip parameter. It is observed that a thin boundary layer is formed near the stationary plate for large values of squared Hartmann number and Reynolds number. The thickness of this boundary layer increases with increase in either Hall parameter or ion-slip parameter. N. GHARA ET AL. 2 rameter. It also is found that both the primary velocity and the magnitude of secondary velocity decrease with increase in ion-slip parameter. Asymptotic behavior of the solution has been analyzed for large values of squared Hartmann number and Reynolds number. It is observed that a thin boundary layer is formed near the stationary plate for large values of the magnetic parameter and Reynolds number. The thickness of this boundary layer increases with increases in either Hall parameter or ion-slip parameter. Further, it is seen that the shear stress components 0 x  and 0 z  due to the primary and secondary flows at the stationary plate 0   increase with increase in Hall parameter for fixed value of squared Hartmann number and ion slip parameter. It is also seen that for fixed value of both squared Hartmann number and Hall parameter, 0 x  increases while 0 z  decreases with increase in ion-slip parameter. N. GHARA ET AL. Copyright © 2012 SciRes. OJFD 3 N. GHARA ET AL. 8 Figure 8. Velocity profiles for general solution and small time solution when M 2 = 5, Re = 5, β e = 0.5 and β i = 0.5. for β e when Re = 5, β i = 0.5 and τ = 0.02. Figure 9. Shear stresses and z 0  x 0  Copyright © 2012 SciRes. OJFD N. GHARA ET AL. 9 for β i when Re = 5, β e = 0.5 and τ = 0.02. Figure 10. Shear stresses and z x   0 0 for Re when β e = 0.5, β i = 0.5 and τ = 0.02. Figure 11. Shear stresses and z 0  x 0 

Hydrodynamic viscous incompressible fluid flow through a porous medium between two disks rotating with same angular velocity  about two non-coincident axes has been studied. An exact solution of the governing equations has been obtained in a closed form. It is found that the primary velocity decreases and the secondary velocity increases with increase in porosity parameter to the left of the z-axis and the result is reversed to the right of the z-axis. It is also found that the torque on the disks increases with increase in either rotation parameter or porosity parameter. For large rotation, there exist a thin boundary layer near the disks and the thickness of this boundary layer decreases with increase in porosity parameter.

In this paper, an analysis is made on the unsteady flow of an incompressible electrically conducting viscous fluid bounded by an infinite porous flat plate. The plate executes harmonic oscillations at a frequency n in its own plane. A uniform magnetic field H0 is imposed perpendicular to the direction of the flow. It is found that the solution also exists for blowing at the plate. The temperature distribution is also obtained by taking viscous and Joule dissipation into account. The mean wall temperature θ0(0) decreases with the increase in the Hall parameter m. It is found that no temperature distribution exists for the blowing at the plate.

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The unsteady hydromagnetic flow due to torsional oscillations of a rotating disc in a viscous incompressible electrically conducting fluid which is also rotating is studied taking the effects of the Hall current and ion-slip into consideration. The governing equations are solved analytically. The results show that the inclusion of the Hall current and ion slip have important effects on the velocity distributions as well as shear stresses at the disc. The flow is characterized by two opposite circularly polarized waves, travelling with different velocities. It is found that there is a formation of two-deck boundary layers, thicknesses of which increase with increase in either Hall parameter or ion-slip parameter. The radial velocity increases with an increase in Hall parameter and the azimuthal velocity increases with an increase in either Hall parameter or ion-slip parameter. Further, it is found that the amplitude of the transverse shear stress at the disc decreases with an increase in either Hall parameter or ion-slip parameter.