Multiple solutions in MHD flow and heat transfer of Sisko fluid containing nanoparticles migration with a convective boundary condition: Critical points

The motivation behind the present analysis is to focus on magneto-hydrodynamic flow and heat transfer characteristics of non-Newtonian fluid (Sisko fluid) past a permeable nonlinear shrinking sheet utilizing nanoparticles involving convective boundary condition. The non-homogenous nanofluid transport model considering the effect of Brownian motion, thermophoresis, suction/injection and no nanoparticle flux at the sheet with convective boundary condition has been solved numerically by the RKF45 method with shooting technique. Critical points for various pertinent parameters are evaluated in this study. The dual solutions ( both first and second solutions) are captured in certain range of material constant (-infinity < A < A(c)), power-law index (n(c) < n < infinity), mass transfer parameter (s(c) < s < infinity) and shrinking parameter (chi(c) < chi < 0). For both the branches (upper and lower branch), the rate of heat transfer is an increasing function of the power-law index, Prandtl number and Biot number, whereas it is a decreasing function of the material constant and thermophoresis parameter.