Abstract
This paper provides an investigation regarding the modeling and analysis of a thin film flow of an Oldroyd 8-constant fluid on a vertically moving belt. The governing nonlinear problem is solved by using Variational Iteration Method (VIM). The results of the present method are then compared with those obtained by Adomian Decomposition Method (ADM) and an excellent agreement is observed. This comparison reveals that VIM may be considered as an efficient alternative method for solving nonlinear problems arising in non-Newtonian fluid mechanics. Expressions for some important physical quantities such as volume flux, average velocity, the belt speed for the lifting of the non-Newtonian fluid are also derived.
Highlights
In the recent years, the studies of thin film flows of non-Newtonian fluids have received considerable attention by many researchers, see for instance [1,2,3,4], and the references therein
The governing nonlinear equation is solved by using Variational Iteration Method (VIM)
In order to verify the efficiency of this method, the same problem is solved by Adomian Decomposition Method (ADM)
Summary
The studies of thin film flows of non-Newtonian fluids have received considerable attention by many researchers, see for instance [1,2,3,4], and the references therein This is perhaps due to their several applications in nonlinear sciences and engineering industries. The basic motivation of this paper is to apply the VIM and the ADM to find the approximate analytical solution of a highly nonlinear differential equation that arises in the thin film flow problems of a non-Newtonian Oldroyd 8-constant fluid lifting on a moving belt. The VIM as a powerful analytical technique was first introduced by He and has been used by many mathematicians to solve various nonlinear equations [10,11,12,13,14] This method gives rapidly convergent successive approximations of the exact solutions if such solution exists. For the convergence criteria and error estimation of VIM, see [13, 14]
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