Dual solutions and linear temporal stability analysis of mixed convection flow of non-Newtonian special third grade fluid with thermal radiation

The present study aims to investigate the steady mixed convection stagnation-point flow of a special third grade fluid over a vertical stretching/shrinking sheet with the inclusion of suction and thermal radiation effects. The governing momentum and energy equations are transformed into a system of ordinary differential equations (ODEs) using the Lie scaling group of transformations. The resulting system of highly nonlinear boundary value problems (BVPs) is solved numerically with the help of Matlab solver 'bvp4c'. Dual similarity solutions are found for the opposing flow case within the range lambda(c) <= lambda < 0, where lambda is the buoyancy parameter. Emphasis has been given to conducting a temporal stability analysis to determine the practically reliable solution. The analysis reveals that the primary (upper) solution branch is stable while the other solution branch is unstable. It has been observed that the range of dual solutions and the magnitude of the critical point increase with the increasing value of the suction parameter. The increment of the thermal radiation parameter enhances fluid temperature in the upper solution branch, whereas temperature diminishes far away from the sheet in the lower solution branch.