Stability Analysis of Dual Solutions of Convective Flow of Casson Nanofluid past a Shrinking/Stretching Slippery Sheet with Thermophoresis and Brownian Motion in Porous Media

Abstract

This article considered the steady two-dimensional boundary layer flow of incompressible viscous Casson nanofluids over a permeable, convectively heated, shrinking/stretching slippery sheet surface. The achievements of this work are extremely relevant, both theoretically with respect to the mathematical modeling of non-Newtonian nanofluid flow with heat transfer in engineering systems and with respect to engineering cooling applications. The combined impacts of suction/injection, viscous dissipation, convective heating, and chemical reactions were considered. The governing modeled partial differential equations with boundary conditions are transformed into nonlinear ordinary differential equations using similarity transformations and finally converted to the first-order initial value problem. Then, the technique of the fourth-fifth order Runge–Kutta–Fehlberg with the shooting method is used to obtain numerical solutions. Moreover, the effects of different involving parameters on the dimensionless temperature, velocity, and concentration, as well as, from an engineering viewpoint, local Nusselt number, the skin friction, and local Sherwood number are illustrated and presented in graphs and tabular forms. For critical shrinking parameter ${\lambda }_c$ , the existence of a dual solution within the interval ${\lambda }_c<\lambda <0$ is revealed, and this range escalates with the suction and slipperiness parameters; hence, both control the flow stability. The increment in the values of the porous media, Casson, Forchheimer, slipperiness, and convective heating parameters reduces the local skin friction and intensifies the rates of mass and heat transfer. For the Newtonian flow (that is, as the Casson parameter $\beta$ gets to infinity $\infty$ ), the thermal boundary layer thickness, temperature profile, and skin friction diminish, whereas the concentration profile, mass, and heat transfer rates increase compared to the non-Newtonian Casson nanofluid. These results excellently agree with the existing ones.