Eur. Phys. J. Plus (2015) 130: 57
https://doi.org/10.1140/epjp/i2015-15057-9

Regular Article

Exact solutions for free convection flow of nanofluids with ramped wall temperature

¹ Department of Mathematics, SBK Women’s University, 87300, Quetta, Pakistan
² Basic Sciences Department, College of Engineering, Majmaah University, 11952, Majmaah, Saudi Arabia
³ Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310, UTM Skudai, Malaysia

^* e-mail: awaisiasma@gmail.com

Received: 10 October 2014
Revised: 31 January 2015
Accepted: 10 February 2015
Published online: 1 April 2015

Abstract

This article aims to study the unsteady convection flow of nanofluids induced by free convection and the oscillating plate condition. The fluid is confined to the region over an infinite vertical flat plate with ramped wall temperature. Five different types of water-based nanofluids containing copper (Cu), silver (Ag), copper oxide (CuO), alumina ( Al₂O₃ and titanium oxide (TiO₂ are chosen for this analysis. The Laplace transform technique is applied to obtain exact solutions of velocity and temperature for both cases of ramp and isothermal plate conditions. Ramp and isothermal solutions are compared graphically and it is found that the ramp velocity and the temperature are smaller in magnitude than isothermal velocity and temperature. Corresponding expressions for skin-friction and Nusselt number are also evaluated. The results are plotted for various physical parameters contained in the governing equations and discussed in details. Comparison with earlier results provides an excellent agreement.