Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 875754, 19 pages
http://dx.doi.org/10.1155/2011/875754
Research Article

Dual Solutions on Thermosolutal Marangoni Forced Convection Boundary Layer with Suction and Injection

R. A. Hamid,1 N. M. Arifin,1 R. Nazar,2 F. M. Ali,1 and I. Pop3

1Institute for Mathematical Research and Department of Mathematics, Universiti Putra Malaysia, UPM Serdang, Selangor 43400, Malaysia
2School of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, UKM Bangi, Selangor 43600, Malaysia
3Faculty of Mathematics, University of Cluj, CP 253 3400 Cluj, Romania

Received 30 September 2010; Accepted 15 January 2011

Academic Editor: Saad A. Ragab

Copyright © 2011 R. A. Hamid 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.

Abstract

This paper considers the extended problem of the thermosolutal Marangoni forced convection boundary layer by Pop et al. (2001) when the wall is permeable, namely, there is a suction or injection effect. The governing system of partial differential equations is transformed into a system of ordinary differential equations, and the transformed equations are solved numerically using the shooting method. The effects of suction or injection parameter 𝑓 0 on the velocity, temperature, and concentration profiles are illustrated and presented in tables and figures. It is shown that dual solutions exist for the similarity parameter 𝛽 less than 0.5.