# Nonlinear radiation effects on flow of nanofluid over a porous wedge in the presence of magnetic field

Umar Khan (Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan)
Naveed Ahmed (Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan)
Bandar Bin-Mohsen (Department of Mathematics, College of Sciences, King Saud University, Riyadh, Saudi Arabia)
Syed Tauseef Mohyud-Din (Department of Mathematics, Faculty of Sciences, HITEC University, Taxila Cantt, Pakistan)

ISSN: 0961-5539

Article publication date: 3 January 2017

## Abstract

### Purpose

The purpose of this paper is to assess the flow of a nanofluid over a porous moving wedge. The passive control model along with the magnetohydrodynamic (MHD) effects is used to formulate the problem. Furthermore, in energy equation, the non-linear thermal radiation has also been incorporated. The equations governing the flow are transformed into a set of ordinary differential equations by using suitable similarity transforms. The reduced system of equations is then solved numerically using a well-known Runge–Kutta–Fehlberg method coupled with a shooting technique. The influence of parameters involved on velocity, temperature and concentration profiles is highlighted with the help of a graphical aid. Expressions for skin-friction coefficient, local Nusselt number and Sherwood number are obtained and presented graphically.

### Design/methodology/approach

Numerical solution of the problem is obtained using the well-known Runge–Kutta–Fehlberg method.

### Findings

The analysis provided gives a clear description that the increase in m and magnetic parameter M results in an increased velocity profile. Both these parameters normalize the velocity field. Radiation parameter, Rd, increases the temperature and concentration of the system so does the temperature ratio θω reduces the heat transfer rate at the wall for both stretching and shrinking wedge.

### Originality/value

In the study presented, the flow of nanofluid over a moving permeable wedge is considered. The solution of the equations governing the flow is presented numerically. For the validity of results obtained, a comparison is also presented with already existing results. To the best of the authors’ knowledge, this investigation is the first of its kind on the said topic.

## Acknowledgements

Authors are thankful to the anonymous reviewers for the useful comments that helped in improving the quality of the presented work. The author Bandar Bin-Mohsin extends his appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group no. RG-1437-019.

## Citation

Khan, U., Ahmed, N., Bin-Mohsen, B. and Mohyud-Din, S.T. (2017), "Nonlinear radiation effects on flow of nanofluid over a porous wedge in the presence of magnetic field", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 1, pp. 48-63. https://doi.org/10.1108/HFF-10-2015-0433

## Publisher

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Emerald Publishing Limited