Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 359297, 11 pages
A Note on Improved Homotopy Analysis Method for Solving the Jeffery-Hamel Flow
1Department of Mathematics, University of Swaziland, Private Bag 4, Kwaluseni M201, Swaziland
2School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01 Scottsville 3209, Pietermaritzburg, South Africa
3Department of Mathematics, University of Venda, P Bag X5050, Thohoyandou 0950, South Africa
Received 13 September 2010; Revised 19 November 2010; Accepted 16 December 2010
Academic Editor: Oded Gottlieb
Copyright © 2010 Sandile Sydney Motsa 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.
This paper presents the solution of the nonlinear equation that governs the flow of a viscous, incompressible fluid between two converging-diverging rigid walls using an improved homotopy
analysis method. The results obtained by this new technique show that the improved homotopy
analysis method converges much faster than both the homotopy analysis method and the optimal
homotopy asymptotic method. This improved technique is observed to be much more accurate
than these traditional homotopy methods.