Abstract:
An investigation has been made on an unsteady Couette flow of a viscous incompressible fluid through a porous me- dium in a rotating system. The solution of the governing equations has been obtained by the use of Laplace transform technique. It is found that the primary velocity decreases and the magnitude of the secondary velocity increases with an increase in rotation parameter. The fluid velocity components are decelerated by an increase of Reynolds number. An increase in porosity parameter leads to increase the primary velocity and the magnitude of the secondary velocity. It is also found that the solution for small time converges more rapidly than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of rotation parameter and Reynolds number. It is observed that a thin boundary layer is formed near the moving plate of the channel and the thicknesses of the boundary layer increases with an increase in porosity parameter.

Abstract:
The combined influences of Hall currents and rotation on the MHD Couette flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel porous plates channel in a rotating system in the presence of a uniform transverse magnetic field have been carried out. The solutions for the velocity field as well as shear stresses have been obtained for small time as well as for large times by Laplace transform technique. It is found that for large times the Hall currents accelerates primary flow whereas it retards secondary flow while the rotation retards the primary flow whereas it accelerates the secondary flow. It is also found that the velocity components converge more rapidly for small time solution than the general solution. The asymptotic behavior of the solution is analyzed for small as well as large values of magnetic parameter M^{2}, rotation parameter K^{2} and Reynolds number R_{e}. It is observed that a thin boundary layer is formed near the moving plate of the channel and the thicknesses of the layer increases with increase in either Hall parameter m or Reynolds number R_{e} while it decreases with increase in Hartmann number M. It is interesting to note that for large values of M^{2} , the boundary layer thickness is independent of the rotation parameter.

Abstract:
The free convection flow of radiating gas between two vertical thermally conducting walls through porous medium in the presence of a uniform gravitational field has been studied. Closed form solutions for the velocity and temperature have been obtained in the optically thin limit case when the wall temperatures are varying linearly with the vertical distance. It is observed that the fluid velocity increases and the temperature difference between the walls and the fluid decreases with an increase in the radiation parameter. It is also observed that both the fluid velocity and temperature in the flow field increase with an increase in the porosity parameter. It is found that the fluid velocity decreases while the temperature increases with an increase in the thermal conductance of the walls. Further, it is found that radiation causes to decrease the rate of heat transfer to the fluid, thereby reducing the effect of natural convection.

Abstract:
Radiation effects on free convection MHD Couette flow started exponentially with variable wall temperature in the presence of heat generation have been studied. The governing equations are solved analytically using the Laplace transform technique. The variations of velocity and fluid temperature are presented graphically. It is observed that the velocity decreases with an increase in either magnetic parameter or radiation parameter or Prandtl number. It is also observed that the velocity increases with an increase in either heat generation parameter or Grashof number or accelerated parameter or time. An increase in either radiation parameter or Prandtl number leads to fall in the fluid temperature. It is seen that the fluid temperature increases with an increase in either heat generation parameter or time. Further, it is seen that the shear stress at the moving plate decreases with an increase in either magnetic parameter or radiation parameter while it increases with an increase in either heat generation parameter or Prandtl number. The rate of heat transfer increases with an increase in either Prandtl number or time whereas it decreases with an increase in heat generation parameter.

Abstract:
The combined effects of Hall current and radiation on an unsteady MHD free convective flow of a viscous incompressible electrically conducting fluid in a vertical channel with an oscillatory wall temperature have been studied. We have considered two different cases 1) flow due to the impulsive motion of one of the channel walls and 2) flow due to the accelerated motion of one of the channel walls. The governing equations are solved analytically using the Laplace transform technique. It is found that the primary velocity and the magnitude of the secondary velocity increase with an increase in Hall parameter for both the impulsive as well as the accelerated motions of one of the channel walls. An increase in either radiation parameter or frequency parameter leads to decrease in the primary velocity and the magnitude of the secondary velocity for both the impulsive as well as accelerated motions of one of the channel walls. The fluid temperature decreases with an increase in radiation parameter. Further, the shear stresses at the left wall reduce with an increase in either radiation parameter or frequency parameter for both the impulsive as well as the accelerated motions of one of the channel wall.

Abstract:
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 govern-ing equations has been obtained in a closed form. It is found that the primary velocity decreases and the sec-ondary velocity increases with increase in porosity parameter to the left of the z-axis and the result is re-versed 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.

Abstract:
The unsteady MHD Couette flow of an incompressible viscous electrically conducting fluid between two infinite non- conducting 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.

Abstract:
The effects of radiation on the MHD flow past a vertical plate with oscillatory ramped plate temperature in the presence of a uniform transverse applied magnetic field have been investigated. An analytical solution of the governing equations has been obtained by employing Laplace transform technique. The numerical results for fluid velocity and temperature are presented graphically. It is found that an increase in radiation parameter leads to decrease the fluid velocity and temperature. It is also found that both the velocity as well as the temperature of the fluid decrease with an increase in Prandtl number. It is found that the shear stress due to the flow decreases with an increase in magnetic parameter while it increases with an increase in radiation parameter. Further, the rate of heat transfer at the plate increases with an increase in radiation parameter.

Abstract:
The unsteady free convective flow past a vertical porous plate with Newtonian heating has been studied. The governing equations have been solved numerically by Crank-Nicolson implicit finite-difference scheme. The variations of velocity and fluid temperature are presented graphically. It is found that the fluid velocity decreases with an increase in Prandtl number. Both the fluid velocity and the fluid temperature increase with an increase in suction parameter. An increase in Grashof number leads to rise in the fluid velocity. Further, it is observed that the shear stress and the rate of heat transfer at the plate increase with an increase in either Prandtlnumber or suction parameter or time.

Abstract:
We study a steady hydromagnetic Couette flow of a viscous incompressible electrically conducting fluid in a rotating system between two infinitely long parallel plates in the presence of a uniform transverse magnetic field on taking Hall Current into account. The governing equations describing the flow are solved analytically. It is observed that the Hall currents accelerate the primary velocity whereas they retard the secondary velocity. The induced magnetic field is significantly affected by the Hall currents. An increase in Hall currents leads to fall in the fluid temperature. The heat transfer characteristics have also been studied. The rate of heat transfer at the lower plate decreases whereas the rate of heat transfer at the upper plate increases with an increase in Hall parameter. The asymptotic behavior of the solutions are discussed for small and large values of magnetic parameter and rotation parameter. It is interesting to note that either for strong magnetic field or for large rotation there exists a single-deck boundary layer in the region near the stationary plate. The thickness of this boundary layer first decreases, reaches a minimum and then increases with an increase in Hall parameter.