Mixed Convection Flow Analysis of Carreau Fluid Over a Vertical Stretching/Shrinking Sheet

Abstract

The current investigation aspires to unravel the steady mixed convection flow of Carreau fluid over a permeable vertical stretching/shrinking sheet near a stagnation point. The system of governing equations is reduced into ODEs utilizing appropriate similarity transformations. The similarity transformations are obtained via the Lie scaling group of transformations. Dual similarity solutions are detected depending on the opposing flow parameter for stretching and shrinking cases. The effects of pertinent parameters on the skin friction coefficient, Nusselt number, velocity, and temperature fields are examined in detail. The influence of the suction parameter on the variations of skin friction coefficient for the stretching case shows various behavior than in the shrinking case. However, on the variations of the Nusselt number, a similar trend in both the stretching and shrinking cases is observed. The fluid velocity decreases, and the temperature rises with the increment of non-Newtonian parameter in the upper branch, whereas the lower branch depicts opposite trends. Due to the different characteristics of the lower branch than the upper branch, it is necessary to find a physically reliable solution branch. Thus, a linear temporal stability analysis is conducted based on the sign of the smallest eigenvalue. The smallest eigenvalues are determined numerically using the shooting technique, revealing that the upper branch is the only stable solution branch.