Stability analysis of three-dimensional stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect in viscous fluid

This study presents the steady three-dimensional stagnation-point flow towards a permeable stretching/shrinking sheet in the presence of heat source effects. The governing equations in the form of partial differential equations are transformed into a system of ordinary differential equations by using similarity transformation, and then solved numerically using bvp4c function in Matlab software. The variations of the numerical solutions for the skin friction coefficient and the local Nusselt number as well as velocity and temperature profiles are obtained for several values of the governing parameters. It is found that the dual solutions exist for the stretching/shrinking case. Stability analysis is performed to determine which solution is stable and physically reliable. Results from the stability analysis show that the first solution is stable while the second solution is not.