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Journal of Applied Mathematics
Volume 2013, Article ID 219486, 7 pages
Research Article

New Analytical and Numerical Solutions for Mixed Convection Boundary-Layer Nanofluid Flow along an Inclined Plate Embedded in a Porous Medium

1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
2Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt
3Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia

Received 17 July 2013; Accepted 23 August 2013

Academic Editor: Mohamed Fathy El-Amin

Copyright © 2013 Emad H. Aly and Abdelhalim Ebaid. 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.


Two different analytical and numerical methods have been applied to solve the system describing the mixed convection boundary-layer nanofluids flow along an inclined plate embedded in a porous medium, namely, homotopy perturbation method (HPM) and Chebyshev pseudospectral differentiation matrix (ChPDM), respectively. Further, ChPDM is used as a control method to check the accuracy of the results obtained by HPM. The analytical method is applied using a new way for the deformed equations, and the resulted solution was expressed in terms of a well-known entire error function. In addition, using only two terms of the homotopy series, the approximate analytical solution is compared with the numerical solution obtained by the accurate ChPDM approach. The results reveal that good agreements have been achieved between the two approaches for various values of the investigated physical parameters.