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Advances in Mathematical Physics
Volume 2014, Article ID 538950, 9 pages
Research Article

Effect of Velocity Slip Boundary Condition on the Flow and Heat Transfer of Cu-Water and TiO2-Water Nanofluids in the Presence of a Magnetic Field

1Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia
2Department of Chemical Engineering, Faculty of Engineering, University of Tabuk, Tabuk, Saudi Arabia
3Department of Mathematics, Faculty of Sciences, Helwan University, Cairo, Egypt
4Department of Studies and Basic Sciences, Faculty of Community, University of Tabuk, Tabuk, Saudi Arabia

Received 24 April 2014; Revised 21 May 2014; Accepted 26 June 2014; Published 5 August 2014

Academic Editor: Ricardo Weder

Copyright © 2014 Abdelhalim Ebaid et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In nanofluid mechanics, it has been proven recently that the no slip condition at the boundary is no longer valid which is the reason that we consider the effect of such slip condition on the flow and heat transfer of two types of nanofluids. The present paper considers the effect of the velocity slip condition on the flow and heat transfer of the Cu-water and the TiO2-water nanofluids over stretching/shrinking sheets in the presence of a magnetic field. The exact expression for the fluid velocity is obtained in terms of the exponential function, while an effective analytical procedure is suggested and successfully applied to obtain the exact temperature in terms of the generalized incomplete gamma function. It is found in this paper that the Cu-water nanofluid is slower than the TiO2-water nanofluid for both cases of the stretching/shrinking sheets. However, the temperature of the Cu-water nanofluid is always higher than the temperature of the TiO2-water nanofluid. In the case of shrinking sheet the dual solutions have been obtained at particular values of the physical parameters. In addition, the effect of various physical parameters on such dual solutions is discussed through the graphs.