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 couplestress 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.