Eur. Phys. J. Plus (2018) 133: 154
https://doi.org/10.1140/epjp/i2018-11991-2

Regular Article

Numerical study of unsteady Williamson fluid flow and heat transfer in the presence of MHD through a permeable stretching surface

¹ Department of Mathematics, Quaid-i-Azam University, 44000, Islamabad, Pakistan
² Department of Mathematics, Faculty of Science, King Abdulaziz University, PO Box-80203, 21589, Jeddah, Saudi Arabia
³ Department of Mathematics, Faculty of Basic Sciences, HITEC University, Taxila, Pakistan

^* e-mail: krehman@math.qau.edu.pk

Received: 5 May 2017
Accepted: 12 March 2018
Published online: 20 April 2018

Abstract

In the present article, unsteady flow field characteristics of the Williamson fluid model are explored. The nanosized particles are suspended in the flow regime having the interaction of a magnetic field. The fluid flow is induced due to a stretching permeable surface. The flow model is controlled through coupled partial differential equations to the used shooting method for a numerical solution. The obtained partial differential equations are converted into ordinary differential equations as an initial value problem. The shooting method is used to find a numerical solution. The mathematical modeling yields physical parameters, namely the Weissenberg number, the Prandtl number, the unsteadiness parameter, the magnetic parameter, the mass transfer parameter, the Lewis number, the thermophoresis parameter and Brownian parameters. It is found that the Williamson fluid velocity, temperature and nanoparticles concentration are a decreasing function of the unsteadiness parameter.