Variational iteration method for flow of non-Newtonian fluid on a moving belt and in a collector

Abstract

In this paper, the thin film of a non-Newtonian fluid namely, a Sisko fluid on a vertical moving belt and this fluid in a collector is investigated. Sisko fluid’s behavior is expressed by non-linear equation. At the first problem, we consider a container having a non-Newtonian fluid in it. A wide moving belt passes through this container and moves vertically upward with constant velocity. The graphical representation of the velocity v against the horizontal distance x shows that the velocity increases as the non-Newtonian effect increases. Physics of the second problem includes a moving flat plate with constant velocity. The flat plate is cooled with a kind of oil through which its properties follow the Sisko fluid model. We obtain the velocity gradient with difference values of b and k coefficient, in Collector. By the use of velocity gradient, the pressure gradient can be predicted. Predicting the pressure can help to analyze the extra stresses in the collector. The variational iteration method (VIM) is used to solve this non-linear equation analytically. Comparison of the result obtained by the present method with numerical solution shows the accuracy, reliable and fast convergence of this method for nonlinear problems.

Keywords

• Variation iteration method (VIM)
• Thin film
• Non-Newtonian fluids
• Sisko fluid