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Stagnation point flow toward an exponentially shrinking sheet in a hybrid nanofluid

Iskandar Waini (Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Durian Tunggal, Melaka, Malaysia)
Ioan Pop (Universitatea Babes Bolyai Facultatea de Matematica si Informatica, Cluj-Napoca, Romania)
Sakhinah Abu Bakar (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia)
Anuar Ishak (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 3 July 2021

Issue publication date: 20 January 2022

57

Abstract

Purpose

This paper aims to investigate the radiation and magnetohydrodynamic effect on the flow toward a stagnation point of an exponentially shrinking sheet in a hybrid nanofluid.

Design/methodology/approach

The governing partial differential equations are transformed into a set of similarity equations and are then solved numerically using the boundary value problem solver, bvp4c, available in MATLAB software. The effects of several physical parameters on the flow and the thermal characteristics of the hybrid nanofluid are analyzed and discussed.

Findings

Numerical results clarify that the dual solutions arise for the shrinking case (λ < 0). The critical values expand for the stronger magnetic field. Besides, the skin friction and the heat transfer coefficients enhance with the rise of the magnetic field and the hybrid nanoparticles. The heat transfer rate increases by 10.11% for the nanofluid and 28.69% for the hybrid nanofluid compared to the regular fluid. In addition, the presence of radiation gives a higher heat transfer rate. Using the stability analysis, it is found that the first solution is stable, and the second solution is unstable, over time.

Originality/value

The stagnation point flow problem has been widely studied for the flow over a stretching sheet, but only limited findings can be found for the flow over a shrinking sheet. Therefore, the present study considers the problem of the stagnation point flow over a shrinking sheet in a Cu-Al2O3/water hybrid nanofluid with the effects of magnetic field and thermal radiation. The dual solutions of the hybrid nanofluid flow over a shrinking sheet are obtained. Further analysis shows that only one of the solutions is stable and thus physically reliable as time evolves.

Keywords

Acknowledgements

The authors wish to express their thanks to the anonymous reviewers for their valuable comments and suggestions. The financial supports received from the Universiti Kebangsaan Malaysia (Project Code: DIP-2020–001) and the Universiti Teknikal Malaysia Melaka are gratefully acknowledged.

Competing interests: The authors declare no competing interests.

Citation

Waini, I., Pop, I., Abu Bakar, S. and Ishak, A. (2022), "Stagnation point flow toward an exponentially shrinking sheet in a hybrid nanofluid", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 3, pp. 1012-1024. https://doi.org/10.1108/HFF-01-2021-0039

Publisher

:

Emerald Publishing Limited

Copyright © 2021, Emerald Publishing Limited

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