Dual Solutions in MHD Boundary Layer Nanofluid Flow and Heat Transfer with Heat Source/Sink Considering Viscous Dissipation

In this present analysis, the numerical investigation of steady, magneto-hydrodynamic boundary-layer nanofluid past a permeable shrinking sheet has been discussed considering Brownian motion and thermophoresis. The effect of viscous dissipation, heat source/sink and suction/injection are taken into account and controlled by the non-dimensional parameters. After using appropriate similarity transformation, the final system of ordinary differential equation is solved numerically by shooting technique. The dual solutions exist for whereas unique solution is obtained at critical values and solution does not exist for for other fixed parameters. The current study shows that the effect of nonlinear parameter, Hartmann number and heat source/sink on skin friction and rate of heat transfer. The results are validated for the limiting cases.