This paper presents the Jeffery Hamel flow of a NON-NEWTONIAN FLUID namely Casson FLUID. A suitable similaritytransform is applied to reduce governing NONlinear partial differential equations to a much simpler ordinarydifferential equation. The variation of Parameters Method (VPM) is then employed to solve the resulting equation. The same problem is solved numerically by using Runge-Kutta order 4 method. A comparison between bothsolutions is carried out to check the efficiency of VPM. The effects of emerging parameters are demonstrated forboth diverging and converging channels using graphical simulation.

The entropy generation analysis of NON-NEWTONIAN FLUID in rotational flow between two concentric cylinders is examined when the outer cylinder is fixed and the inner cylinder is revolved with a constant angular speed. The viscosity of NON-NEWTONIAN FLUID is considered at the same time interdependent on temperature and shear rate. The Nahme law and Carreau equation are used to modeling dependence of viscosity on temperature and shear rate, respectively. The viscous dissipation term is adding elaboration to the formerly highly associate set of governing motion and energy equations. The perturbation method has been applied for the highly NONlinear governing equations of base flow and found an approximate solution for narrowed gap limit. The effect of characteristic parameter such as Brinkman number and Deborah number on the entropy generation analysis is investigated. The overall entropy generation number decays in the radial direction from rotating inner cylinder to stationary outer cylinder. The results show that overall rate of entropy generation enhances within flow domain as increasing in Brinkman number. It, however, declines with enhancing Deborah number. The reason for this is very clear, the pseudo plastic FLUID between concentric cylinders is heated as Brinkman number increases due to frictional dissipation and it is cooled as Deborah number increases which is due to the elasticity behavior of the FLUID. Therefore, to minimize entropy need to be controlled Brinkman number and Deborah number.

The purpose of the present study is to investigate the boundary layer separation point in a magnetohydrodynamics diffuser. As an innovation, the Re value on the separation point is determined for the NON-NEWTONIAN FLUID flow under the influence of the NON-uniform magnetic field due to an electrical solenoid, in an empirical case. The governing equations including continuity and momentum are solved by applying the semi-analytical collocation method (C.M.). The analysis revealed that for specific values of De from 0.4 to 1.6, α from 20o to 2.5o and Ha from zero to 8, the Re value on the separation point is increased from 52.94 to 1862.78; thus, the boundary layer separation postponed. Furthermore, the impact of the magnetic field intensity on the separation point is analyzed from the physical point of view. It is observed the wall shear stress increases by increasing magnetic field intensity that leads to delaying the boundary layer separation.

The forced convection heat transfer in the circular couette flow of NON-NEWTONIAN FLUID is investigated when the inner cylinder is rotated at angular speed and the outer cylinder is fixed. The FLUID viscosity is considered concurrently to be dependent on the temperature and shear rate. The temperature dependency of viscosity is modeled exponentially according to the Nahme law and dependence of viscosity on shear is modeled with the Carreau equation. The Viscous dissipation term is adding intricacy to the already highly interdependent set of governing motion and energy equations. The highly NONlinear governing equations are derived for the steady state base flow in the narrow gap limit. The perturbation method has been applied to obtain an approximate solution for these equations. The effect of governing parameter such as Brinkman numbers and Deborah number on the thermal stability is examined. In addition, the analysis illustrated that the Nusselt number of the outer cylinder increases as the Deborah number increases. It, although, decreases by increasing Brinkman number. The pseudo plastic FLUID between concentric cylinders is heated as Brinkman number and increases due to frictional loss and it is cooled as Deborah number increases due to the FLUID elasticity behavior.

Two-dimensional, unsteady squeezed flow over a porous surface for a power-law NON-NEWTONIAN FLUID is considered. Continuity, momentum and energy equations are written and cast into a NON-dimensional form. Boundary conditions are selected in a general form. Lie Group theory is applied to the equations. Then, a partial differential system with three independent variables is converted into an ordinary differential system, via application of two successive symmetry generators. The ordinary differential equations are solved numerically. Effects of flow behavior index, Prandtl number, squeezing parameter, surface velocity parameter and suction/injection parameter on the flow are outlined in the figures.