Multiple solutions of MHD boundary layer flow and heat transfer behavior of nanofluids induced by a power-law stretching/shrinking permeable sheet with viscous dissipation

• The dual solutions exist in the case of shrinking sheet which are captured numerically.
• The critical values of mass transfer and stretching/shrinking parameter are determined.
• Rate of heat transfer can be controlled with power-law and thermophoresis parameter.
• Brownian motion has negligible effect on the rate of heat transfer with no mass flux.

In the present framework, magneto-hydrodynamic (MHD) boundary layer flow of nanofluid induced by a power-law stretching/shrinking permeable sheet has been investigated numerically using shooting method, taking the effects of viscous dissipation. The governing equations that incorporate the effects of Brownian motion and thermophoresis are reduced into the system of nonlinear ordinary differential equations. The study reveals the existence of dual solutions for various pertinent parameters in certain domain with the critical value of suction (0 < sc < s) and stretching/shrinking parameter (χc < χ). Even, the existence domain of heat transfer coefficient is found to have two unique solutions with β and χ. The viscous dissipation was found to be significant whereas the Brownian motion has negligible effect on the rate of heat transfer. Some of the numerical results are validated with earlier published results, available in the literature.

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