Critical values in slip flow and heat transfer analysis of non-Newtonian nanofluid utilizing heat source/sink and variable magnetic field: Multiple solutions

•The multiple solutions are obtained for non-Newtonian nanofluid with heat source/sink.•The parametric critical values for power-law(nc), mass transfer(sc), shrinking(χc) are determined.•The revised no-flux boundary conditions are taken into consideration.•The local Nusselt number decreases with Nt and Q whereas increases with Pr.•In case of heat generation (Q > 0), the heat transfer changes dramatically for second solution.

Motivated by the various application of nanofluids, the present study deals with the numerical investigation of multiple solutions in MHD boundary layer flow and heat transfer of power-law nanofluid past a permeable nonlinear shrinking sheet with heat source/sink. The effect of Brownian motion, thermophoresis, viscous dissipation, suction/injection and surface slip are also considered with no nanoparticle flux at the sheet. The resulting conservation equations are transformed into dimensionless ordinary differential equations using suitable transformation and solved numerically by RKF45 method with shooting technique. The dual solutions are obtained in certain range of power-law index (nc, ∞), mass transfer parameter (sc, ∞)and shrinking parameter (χc, 0). The critical value nc lies in the domain of shear thinning nanofluid (0 < n < 1) for fixed values of other parameters. The rate of heat transfer improves due to heat sink, higher prandtl number and adequate suction for the both first and second solutions.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slide