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MHD flow and heat transfer over a permeable stretching/shrinking sheet in a hybrid nanofluid with a convective boundary condition

Emad H. Aly (Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia and Department of Mathematics, Faculty of Education, Ain Shams University, Cairo, Egypt)
Ioan Pop (Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca, Romania)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 15 August 2019

Issue publication date: 11 September 2019

Abstract

Purpose

The purpose of this study is to present both effective analytic and numerical solutions to MHD flow and heat transfer past a permeable stretching/shrinking sheet in a hybrid nanofluid with suction/injection and convective boundary conditions. Water (base fluid) nanoparticles of alumina and copper were considered as a hybrid nanofluid.

Design/methodology/approach

Proper-similarity variables were applied to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. Exact analytical solutions were then presented for the dimensionless stream and temperature functions. Further, the authors introduce a very nice analytic and numerical solutions for both small and large values of the magnetic parameter.

Findings

It was found that no/unique/two equal/dual physical solutions exist for the investigated boundary value problem. The physically realizable practice of these solutions depends on the range of the governing parameters. For a stretching/shrinking sheet, it was deduced that a hybrid nanofluid works as a cooler on increasing some of the investigated parameters. Moreover, in the case of a shrinking sheet, the first solutions of hybrid nanofluid are stable and physically realizable rather than the nanofluid, while those of the second solutions are not for both hybrid nanofluid and nanofluid.

Originality/value

The present results for the hybrid nanofluids are new and original, as they successfully extend (generalize) the problems previously considered by different authors for the case of nanofluids.

Keywords

Acknowledgements

The work of I. Pop was supported from the grant PN-III-P4-ID-PCE-2016-0036, UEFISCDI, Romania. The authors also wish to express their thanks to the very competent referees for the valuable comments and suggestions.

Citation

Aly, E.H. and Pop, I. (2019), "MHD flow and heat transfer over a permeable stretching/shrinking sheet in a hybrid nanofluid with a convective boundary condition", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 29 No. 9, pp. 3012-3038. https://doi.org/10.1108/HFF-12-2018-0794

Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited