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The problem of stagnation point flow over a stretching/shrinking sheet immersed in a micropolar fluid is analyzed numerically. The governing partial differential equations are transformed into a system of ordinary (similarity) differential equation and are then solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The effects of various parameters on the velocity and the angular velocity as well as the skin friction coefficient and the couple stress are shown in tables and graphs. The noticeable results are found that the micropolar and the slip parameters decrease the skin friction coefficient and the couple stress in the existence of magnetic field. Dual solutions appear for certain range of the shrinking strength. A stability analysis is performed to determine which one of the solutions is stable. Practical applications include polymer extrusion, where one deals with stretching of plastic sheets and in metallurgy that involves the cooling of continuous strips.

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This study is aimed to analyze the steady of stagnation point flow and radiative heat transfer of a non-Newtonian fluid which is Casson fluid passing over an exponentially permeable slippery Riga plate in presence of thermal radiation, magnetic field, velocity slip, thermal slip, and viscous dissipation effects. The governing partial differential equations are transformed into ordinary differential equations by using similarity transformation then solved numerically by boundary value problem solver (BVP4C) in MATLAB software package. The numerical results are evaluated with previous researches to reach an agreement with the parameters of the current study. This study is discussing the behavior of the velocity and temperature profiles as well as skin friction coefficient and local Nusselt number for various physical parameters such as magnetic field, radiation, suction, thermal slip, velocity slip, Prandtl number, Eckert number and modified Hartmann number. Numerical results are shown graphically for each parameter with different values. It is found that the momentum boundary layer thickness increases with increasing the values of Casson parameter. The temperature decreases when the velocity slip parameter and thermal slip parameter are increased.

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This study investigates the heat transfer dissipation on stagnation point flow over a slippery stretching/shrinking cylinder in a copper nanofluid by considering the effect of viscous dissipation. A system of nonlinear partial differential equations is modelled and transformed into ordinary differential equations using similarity transformations. The governing equations with the corresponding boundary conditions are analysed numerically using a bvp4c solver in MATLAB. The solutions are found to be dependent on the Eckert number and slip parameters. The results are represented by the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. Dual solutions are observed for the shrinking cylinder in the presence of Eckert number. Velocity profile and skin friction coefficient consistently increase while temperature profile increases initially and then decreases with the increase of slip parameter for both first and second solutions. Moreover, the presence of copper nanoparticles reduces the thermal boundary layer thickness. This research can be enhanced by using hybrid nanofluids to further improve the heat transfer.

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