# MHD stagnation-point flow and heat transfer of a nanofluid over a stretching/shrinking sheet with melting, convective heat transfer and second-order slip

Ioan Pop (Department of Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania)
Natalia C. Roşca (Department of Mathematics, Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, Romania)
Alin V. Roşca (Department of Statistics-Forecasts-Mathematics, Faculty of Economics and Business Administration, Babeş-Bolyai University, Cluj-Napoca, Romania)

ISSN: 0961-5539

Article publication date: 4 October 2018

Issue publication date: 19 October 2018

## Abstract

### Purpose

The purpose of this paper is to study the effects of MHD, suction, second-order slip and melting on the stagnation-point and heat transfer of a nanofluid past a stretching/shrinking sheet.

### Design/methodology/approach

Using appropriate variables, the governing partial differential equations were transformed into ordinary (similarity) differential equations, which are then solved numerically using the function bvp4c from Matlab.

### Findings

It is found that dual (upper and lower branch) solutions exist for some values of the governing parameters. From the stability analysis, it is found that the upper branch solution is stable, while the lower branch solution is unstable. The sample velocity, temperature and concentration profiles along both solution branches are graphically presented.

### Originality/value

The results of the paper are new and original with many practical applications of nanofluids in the modern industry.

## Acknowledgements

The authors would like to acknowledge the financial support received from the grant PN-III-P4-ID-PCE-2016-0036, UEFISCDI of Romanian Ministry of Sciences. The authors also wish to thank the very competent reviewers for the valuable comments and suggestions.

## Citation

Pop, I., Roşca, N.C. and Roşca, A.V. (2018), "MHD stagnation-point flow and heat transfer of a nanofluid over a stretching/shrinking sheet with melting, convective heat transfer and second-order slip", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 9, pp. 2089-2110. https://doi.org/10.1108/HFF-12-2017-0488

## Publisher

:

Emerald Publishing Limited