# Dusty hybrid nanofluid flow over a shrinking sheet with magnetic field effects

Iskandar Waini (Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, Melaka, Malaysia)
Anuar Ishak (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia)
Ioan Pop (Department of Mathematics, Babeş-Bolyai University, Cluj-Napoca, Romania)
Roslinda Nazar (Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia)

ISSN: 0961-5539

Article publication date: 17 August 2021

Issue publication date: 20 January 2022

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## Abstract

### Purpose

This paper aims to examine the Cu-Al2O3/water hybrid nanofluid flow over a shrinking sheet in the presence of the magnetic field and dust particles.

### Design/methodology/approach

The governing partial differential equations for the two-phase flow of the hybrid nanofluid and the dust particles are reduced to ordinary differential equations using a similarity transformation. Then, these equations are solved using bvp4c in MATLAB software. The bvp4c solver is a finite-difference code that implements the three-stage Lobatto IIIa formula. The numerical results are gained for several values of the physical parameters. The effects of these parameters on the flow and the thermal characteristics of the hybrid nanofluid and the dust particles are analyzed and discussed. Later, the temporal stability analysis is used to determine the stability of the dual solutions obtained as time evolves.

### Findings

The outcome shows that the flow is unlikely to exist unless satisfactory suction strength is imposed on the shrinking sheet. Besides, the heat transfer rate on the shrinking sheet decreases with the increase of . However, the increase in and lead to enhance the heat transfer rate. Two solutions are found, where the domain of the solutions is expanded with the rising of, and. Consequently, the boundary layer separation on the surface is delayed in the presence of these parameters. Implementing the temporal stability analysis, it is found that only one of the solutions is stable as time evolves.

### Originality/value

The dusty fluid problem has been widely studied for the flow over a stretching sheet, but only limited findings can be found for the shrinking counterpart. Therefore, this study considers the problem of the dusty fluid flow over a shrinking sheet containing Cu-Al2O3/water hybrid nanofluid with the effect of the magnetic field. In fact, this is the first study to discover the dual solutions of the dusty hybrid nanofluid flow over a shrinking sheet. Also, further analysis shows that only one of the solutions is stable as time evolves.

## Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive 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., Ishak, A., Pop, I. and Nazar, R. (2022), "Dusty hybrid nanofluid flow over a shrinking sheet with magnetic field effects", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 32 No. 3, pp. 1067-1091. https://doi.org/10.1108/HFF-01-2021-0081

## Publisher

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Emerald Publishing Limited