Multiple Solutions for Stagnation-Point Flow of Unsteady Carreau Fluid along a Permeable Stretching/Shrinking Sheet with Non-Uniform Heat Generation

The aim of the present study was to explore the effect of a non-uniform heat source/sink on the unsteady stagnation point flow of Carreau fluid past a permeable stretching/shrinking sheet. The novelty of the flow model was enhanced with additional effects of magnetohydrodynamics, joule heating, and viscous dissipation. The nonlinear partial differential equations were converted into ordinary differential equations with the assistance of appropriate similarity relations and were then tackled by employing the Runge-Kutta-Fehlberg technique with the shooting method. The impacts of pertinent parameters on the dimensionless velocity and temperature profiles along with the friction factor and local Nusselt number were extensively discussed by means of graphical depictions and tables. The current results were compared to the previous findings under certain conditions to determine the precision and validity of the present study. The fluid flow velocity of Carreau fluid increased with the value of the magnetic parameter in the case of the first solution, and the opposite behavior was noticed for the second solution. It was seen that temperature of the Carreau fluid expanded with the higher values of unsteadiness and magnetic parameters. It was visualized from multiple branches that the local Nusselt number declined with the Eckert number parameter for both the upper and lower branch.