Analysis of Dual Solutions of Unsteady Micropolar Hybrid ‎Nanofluid Flow over a Stretching/Shrinking Sheet

An unsteady boundary layer flow of a micropolar hybrid nanofluid over a stretching/shrinking sheet is analyzed. The nonlinear ordinary differential equations of the problem have been solved using the efficient implicit Runge–Kutta–Butcher method along with Nachtsheim–Swigert iteration technique. For a certain set of parameters, numerical results expose dual solutions with the change of the velocity ratio parameter. The dual solutions are presented in a wide range of the physical parameters. Using a lot of numerical data, the critical values of the velocity ratio parameter, local friction factor, local couple-stress and local Nusselt number for the existence of dual solutions are expressed as a function of the physical parameters. These expressions might be useful for the development of new technology or for the future experimental investigation.