Stability Analysis on Stagnation-Point Flow and Heat Transfer towards a Permeable Stretching/Shrinking Sheet with Heat Source in a Casson Fluid

Abstract

This paper deals with a stagnation-point boundary layer flow and heat transfer of a Casson fluid towards a stretching/shrinking sheet. The main objective of the present study is to analyse the effects of the injection parameter and heat source on the velocity and temperature profiles as well as the skin friction coefficient and the Nusselt number. It is vital to study the heat transfer and fluid flow problems in the presence of injection and heat source effects due to a wide variety of applications in engineering and industry. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations by using similarity transformation, before being solved numerically using the boundary value problem solver bvp4c routine in MATLAB. Dual solutions are found to exist for the shrinking sheet case, whereas the solution is unique for the stretching case. The stability analysis has been performed to determine the stable solution. It is shown that the first solutions are stable and physically reliable while the second solutions are not. Further, the present results have been compared with the previous published results for a particular case and the comparisons are found to be in good agreement. The local Nusselt number is decreases with an increase in heat source parameter. Rising values of the injection parameter has decreases both the skin friction coefficient and the local Nusselt number.