# MHD mixed convection boundary layer stagnation-point flow on a vertical surface with induced magnetic field: A stability analysis

Fadzilah Md Ali (Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, Serdang, Malaysia)
Kohilavani Naganthran (School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia)
Roslinda Nazar (School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi, Malaysia)
Ioan Pop (Department of Applied Mathematics, Babeş-Bolyai University, Cluj-Napoca, Romania)

ISSN: 0961-5539

Article publication date: 29 July 2019

Issue publication date: 15 October 2020

134

## Abstract

### Purpose

This study aims to perform a stability analysis on a steady magnetohydrodynamic (MHD) mixed convection boundary-layer stagnation-point flow of an incompressible, viscous and electrically conducting fluid over a vertical flat plate. The effect of induced magnetic field is also considered.

### Design/methodology/approach

The governing boundary layer equations are transformed into a system of ordinary differential equations using the similarity transformations. The system is then solved numerically using the “bvp4c” function in MATLAB.

### Findings

Dual solutions are found to exist for a certain range of the buoyancy parameter for both the assisting and opposing flows. The results from the stability analysis showed that the first solution (upper branch) is stable and valid physically, while the second solution (lower branch) is unstable.

### Practical implications

This problem is important in many metallurgical processes, namely, drawing, annealing and tinning of copper wires. The results obtained are very useful for researchers to determine which solution is physically stable, whereby mathematically more than one solution exists for the skin friction coefficient and the heat transfer characteristics.

### Originality/value

The present results of the stability analysis are original and new for the problem of MHD mixed convection stagnation-point flow of viscous conducting fluid over a vertical flat plate, with the effect of induced magnetic field.

## Acknowledgements

The work of Fadzilah Md Ali has been supported by the research university grant (FRGS-5524295) received from Universiti Putra Malaysia. The work of Kohilavani Naganthran and Roslinda Nazar has been supported by the research university grant (DIP-2017-009) from Universiti Kebangsaan Malaysia. The work of Ioan Pop was supported from the grant PN-III-P4-ID-PCE-2016-0036, UEFISCDI, Romania.

## Citation

Md Ali, F., Naganthran, K., Nazar, R. and Pop, I. (2020), "MHD mixed convection boundary layer stagnation-point flow on a vertical surface with induced magnetic field: A stability analysis", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 30 No. 11, pp. 4697-4710. https://doi.org/10.1108/HFF-11-2016-0436

## Publisher

:

Emerald Publishing Limited