A study is carried out for the two dimensional laminar flow of conducting fluid in presence of magnetic field. The governing non-linear equations of motion are transformed in to dimensionaless form. A solution is obtained by homotopy perturbation method and it is valid for moderately large Reynolds numbers for injection at the wall. Also an efficient algorithm based finite difference scheme is developed to solve the reduced coupled ordinary differential equations with necessary boundary conditions. The effects of Reynolds number, the magnetic parameter and the pradantle number on flow velocity and tempratare distribution is analysed by both the methods and results agree well with previous work for special cases. It is observed that overall effect of magnetic field is same as Hartmann flow. Further the analysis predicts that the heat transfer at the surface of the disks increases with increase in Reynolds number, magnetic parameter and Prandle number. The shear stress at the wall decreases with increase in injection, whearas increase with increase in magnetic parameter. The study of such phenomenon is beneficial in the industry for thermal control in polymeric processing.

The present work is connected with fluid dynamics aspects of circular slider. It is study about flow of Casson fluid through circular porous bearing. In this model Casson fluid is forced through the porous bottom of a circular slider which is moving laterally on a horizontal plane. The governing Navier Stokes equations are derived and reduced to nonlinear ordinary differential equations through transformations. The problem is analysed through Homotopy Perturbation Method (HPM) and Finite Difference Method (FDM). The effective terms in the HPM representing the physical parameters reveal the qualitative features of the flow. The results are presented for the velocity, wall gradients of vertical velocity functions and lateral velocity functions values in its absolute values with cross Reynolds number. The results are validated by two methods and are in good agreement. They show that they are increasing at one wall and decreasing at the other wall. It is clear that the efficiency of porous slider bearing increases in case of the Cason fluid. The model has application in hydrostatic thrust bearings and air cushioned vehicles. Further friction is greatly reduced in the present case. So it has importance in industry and technology.

The flow of viscous incompressible fluid through a tube is considered. The similarity transformation is used to reduce the governing equations into nonlinear ordinary differential equation. The solution procedure includes application of long series analysis with polynomial coefficients. The series representing physical parameters ( ,qualitative features which are comparable to pure numerical results. The analysis enables in extending region of validity. A complete description of the solutions is presented.

The present problem is considered as a coupled boundary value problem and is analyzed using a semi analytic method. A series method is used to obtain the solution and region of validity is extended by suitable techniques. In this case of series solution the results obtained are better than pure numerical findings up to moderately large Reynolds numbers. The variation of physical parameters is discussed in detail.

The steady flow of a viscous incompressible fluid between two coaxial discs, one rotating and other stationary with suction is analysed. We propose a semi-numerical method in which recurrence relations derived allow to generate large number of universal coefficients in small Reynolds number perturbation series of the solution function. The convergence of the series is restricted by a simple pole using some special techniques the region of validity of the series is increased. The results provided are in excellent agreement with pure numerical studies.