This study offers the numerical solutions for the problem of mixed convection stagnation-point flow along a permeable
vertical flat plate in an Oldroyd-B fluid. The present investigation considers the effects of thermal radiation and heat
generation/absorption in the fluid flow. The similarity transformation simplifies the complex model and the bvp4c function
generates the numerical solutions according to the variations in the governing parameters. A higher degree of shrinking
hastens flow separations. The dual solutions are visible in the range of buoyancy opposing flow. The results from this study
may be useful for the scientist to understand the behaviour of the dilute polymer solutions in the industrial applications,
for example, the drag reduction in pipe flows.
In this study, the effects of suction and injection on the mixed convection flow of a nanofluid, over a moving permeable
vertical plate were discussed. A similarity variable was used to transform the governing equations to the ordinary
differential equations, which were then solved numerically using the bvp4c programme from MATLAB. Dual solutions
(upper and lower branches) were found within a certain range of the mixed convection parameter in assisting and
opposing flow regions. A stability analysis was implemented to confirm that the upper branch solution was stable, while
the lower branch solution was unstable.
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.