Thin film flow of non-Newtonian fluids on a moving belt A.M. Siddiqui a , M. Ahmed b, * , Q.K. Ghori b a Department of Mathematics, Pennsylvania State University, York Campus, 1031 Edgecomb Avenue, York, PA 17403, United States b Department of Mathematics, COMSATS Institute of Information Technology, H-8/I- Islamabad, Pakistan Accepted 9 January 2006 Abstract In this paper, the thin film flow of two non-Newtonian fluids namely, a Sisko fluid and an Oldroyd 6-constant fluid on a vertical moving belt is considered. The nonlinear equations governing the flow problems are formulated and ana- lyzed, using homotopy perturbation method due to He. Explicit expressions for velocity field are obtained and graph- ically sketched. Volume flux and average velocity are also calculated. Ó 2006 Elsevier Ltd. All rights reserved. 1. Introduction In recent years, there has appeared an ever increasing interest of scientists and engineers in analytical techniques for studying nonlinear problems. Such techniques have been dominated by the perturbation methods and have found many applications in science, engineering and technology. However, like other analytical techniques, perturbation methods have their own limitations. For example, all perturbation methods require the presence of a small parameter in the non- linear equation and the approximate solutions of equation containing this parameter are expressed as series expansions in the small parameter. Selection of small parameter requires a special skill. A proper choice of small parameter gives acceptable results, while an improper choice may result in incorrect solutions. Therefore, an analytical method is wel- come which does not require a small parameter in the equation modeling the phenomena. In 1998, He [2–6,8] proposed such a technique which is a coupling of the traditional perturbation method and homotopy. This is homotopy pertur- bation method (HPM) and has been successfully employed by He [7,9–12] and others [1,13–18] to discuss important and practically significant nonlinear problems in different areas of science and engineering. Recently, Abbasbandy [14–16], Cveticanin [13], He [11,12] and others have discussed the effectiveness and reliability of this method over other methods by solving interesting problems of current importance. The equations modeling non-Newtonian incompressible fluid flow give rise to highly nonlinear differential equations. Such non-Newtonian fluids find wide applications in commerce, industry and have now become the focus of extensive study. For example, plastics and polymers are handled extensively by chemical industries whereas biological and bio- medical devices like homodialyser make use of the rheological behavior. 0960-0779/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2006.01.101 * Corresponding author. E-mail addresses: ams5@psu.edu (A.M. Siddiqui), manshoor_post@yahoo.com (M. Ahmed), ghori@comsats.edu.pk (Q.K. Ghori). Chaos, Solitons and Fractals 33 (2007) 1006–1016 www.elsevier.com/locate/chaos