Eur. Phys. J. Plus (2017) 132: 265
https://doi.org/10.1140/epjp/i2017-11519-4

Regular Article

Melting heat transfer in the MHD flow of a third-grade fluid over a variable-thickness surface

¹ Department of Mathematics, Quaid-I-Azam University, 45320, 44000, Islamabad, Pakistan
² Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589, Jeddah, Saudi Arabia
³ Department of Mathematics, University of Wah, 47040, Wah Cantt, Pakistan

^* e-mail: mi_qau@yahoo.com

Received: 15 February 2017
Accepted: 27 April 2017
Published online: 14 June 2017

Abstract

The present study addresses the magnetohydrodynamic (MHD) flow of a third-grade fluid over a nonlinear stretched surface with variable thickness. The heat transfer phenomenon is discussed through melting. The system of nonlinear ordinary differential equations is attained by considering proper transformations. Convergent series solutions of velocity and temperature are developed. Fluid flow, temperature, skin friction coefficient and Nusselt number are examined through graphs for different parameters. It is noted that velocity and temperature decrease with decreasing the wall thickness parameter. It is also revealed that the temperature distribution enhances for increasing values of the Prandtl number. Here the velocity field reduces for increasing values of the melting parameter.