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Slip effects on MHD Hiemenz stagnation point nanofluid flow and heat transfer along a nonlinearly shrinking sheet with induced magnetic field: multiple solutions

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Abstract

The present investigation deals with two-dimensional boundary layer flow of an incompressible electrically conducting nanofluid induced by a nonlinearly (power-law) shrinking flat surface in the presence of passively controlled nanoparticle boundary condition along with induced magnetic field effect. The similarity transformations developed by Lie group method are used which transforms the set of governing equations into a set of coupled similarity equations. This system of nonlinear ordinary differential equation is solved to obtain multiple solutions using a Runge–Kutta–Fehlberg fourth–fifth-order method (RKF45) with shooting method. This study claims the existence of multiple solutions of velocity and temperature profiles as function of suction (\(s\)) and shrinking parameter (\(\chi\)). The critical points (turning points) have also been reported for suction (\(0 < s_{c} < s\)) and shrinking parameter (\(\chi_{c} < \chi < 0\)) for the default set of other parameters. The temporal stability analysis has been performed to confirm the uniqueness of stable solution.

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Acknowledgements

The authors acknowledge financial support from Universiti Sains Malaysia, RU Grant 1001/PMATHS/811252.

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Authors and Affiliations

  1. Department of Mathematics, Jaypee Institute of Information Technology, Noida, Uttar Pradesh, India

    Puneet Rana & Yogesh Gupta

  2. School of Mathematical Sciences, Universiti Sains Malaysia, 11800, Penang, Malaysia

    M. J. Uddin & A. I. Md. Ismail

  3. American International University-Bangladesh, Banani, Dhaka, 1213, Bangladesh

    M. J. Uddin

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  1. Puneet Rana
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Correspondence to Puneet Rana.

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Technical Editor: Jader Barbosa Jr..

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Rana, P., Uddin, M.J., Gupta, Y. et al. Slip effects on MHD Hiemenz stagnation point nanofluid flow and heat transfer along a nonlinearly shrinking sheet with induced magnetic field: multiple solutions. J Braz. Soc. Mech. Sci. Eng. 39, 3363–3374 (2017). https://doi.org/10.1007/s40430-017-0730-z

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