Heat transfer in the boundary layer flow of a Casson fluid over a permeable shrinking sheet with viscous dissipation

In this paper the dual solutions in the flow of a Casson fluid over a porous shrinking surface are numerically discussed. Viscous dissipation in the heat transfer analysis is presented. Appropriate similarity transformations are used to convert governing nonlinear partial differential equations of flow and heat transfer into the system of nonlinear ordinary differential equations. The shooting technique with the Runge-Kutta method is employed to solve the resulting equations. Graphical results for dimensionless velocity and temperature are reported and examined very carefully. The study reveals that the existence of dual solutions is possible for some range of the suction parameter. For both solutions, the momentum boundary layer thickness decreases with the Casson fluid parameter. The thermal boundary layer thickness decreases with the Prandtl number and increases with the Eckert number (in both solutions). Further, the thermal boundary layer thickness decreases with increasing values of wall mass suction for the first solution, whereas it increases with increasing values of the mass suction parameter for the second solution.