Mathematical approach of demarcation of dual solutions for a flow over a shrinking surface

An extensive investigation is performed to reveal the flow and heat transfer characteristics of a thermomicropolar hybrid nanofluid over a shrinking surface. For a wide range of physical parameters, the dual solutions of the shear stress, gradient of microrotation and heat transfer are presented. When the dual solutions fail to occur beyond a critical value of the shrinking parameter, the boundary layer separation takes place. However, this causes mechanical damages to a system. The critical values of the shrinking parameter, shear stress, gradient of microrotation and heat transfer are expressed in explicit functions of the physical parameters. Results show that these functions can predict the solutions with a good accuracy. Since these expressions can easily be used in order to identify the drawbacks of a system with a wide range of flow parameters, it might play an important role for the development of technologies.