Dual Solutions and Stability Analysis of Cu-H2O-Casson Nanofluid Convection past a Heated Stretching/Shrinking Slippery Sheet in a Porous Medium

Abstract

In this study, we examined the impact of Cu-H2O nanoparticles on two-dimensional Casson nanofluid flows past permeable stretching/shrinking sheet embedded in a Darcy-Forchheimer porous medium in the presence of slipperiness of surface, suction/injection, viscous dissipation, and convective heating. Using some realistic assumptions and appropriate similarity transformations, the governing nonlinear partial differential equations were formulated and transformed into a system of nonlinear ordinary differential equations and then numerically solved by using the shooting technique. Numerical results are displayed for dimensionless fluid velocity and temperature profiles, skin friction, and the local Nusselt number. The impacts of different governing physical parameters on these quantities are presented and discussed using graphs, tables, and a chart. For the specific range of shrinking sheet, the result shows that dual solutions exist, and temporal stability analysis is performed by introducing small disturbances to determine the stable solutions. It is detected that the upper branch solution is hydrodynamically stable and substantially realistic; however, the lower branch solution is unstable and physically unachievable. The fluid flow stability is obtained by enhancing the suction, surface slipperiness, and viscous dissipation parameters. However, augmenting the values of the Casson factor, Cu-H2O nanoparticle volume fraction, porous medium, porous medium inertia, and convective heating parameters increases the blow-up stability of the fluid flow. The rate of heat transfer enhances with the increment in the Casson factor, porous medium, porous medium inertia, suction, velocity ratio, nanoparticle volume fraction, and convective heating parameters, whereas it reduces as the slipperiness of the surface and viscous dissipation parameters rise. Increment of Cu-H2O nanoparticle volume fraction into the Casson fluid boosts the heat transfer enhancement rate higher for the shrinking sheet surface.