Dual solutions of a nanofluid flow past a convectively heated nonlinearly shrinking sheet

Effects of magnetic field, convective heating and thermal radiation on the dual solutions and boundary layer separations of nanofluid flow over a nonlinearly shrinking sheet are investigated. Shrinking sheet problems may have applications in polymer technology where one deals with stretching/shrinking of plastic sheets and in metallurgy that involves the cooling of continuous strips. The new type of shrinking sheet flow is essentially a backward flow and it shows physical phenomena quite distinct from the stretching flow case. Governing equations of the problem are reduced to a system of dimensionless equations using similarity transformations. The resulting equations are solved using the well-known shooting method. A comparison between the present solutions and the available data shows a good agreement. Higher volume fraction of nanoparticles causes a decrease in skin friction coefficient and local Nusselt number. The converse is observed for increasing suction parameter. Local Nusselt number is substantially increased by larger shrinking index parameter and Biot number. An increase in suction parameter and magnetic parameter leads to diminish the boundary layer separation and the domain of existence of dual solutions. But the reverse is observed with higher volume fraction of nanoparticles and shrinking index parameter. For increasing nanoparticle volume fraction and decreasing suction parameter the velocity decreases and the temperature increases.