%0 Journal Article
%T Flow of an Eyring-Powell Model Fluid between Coaxial Cylinders with Variable Viscosity
%A Azad Hussain
%A M. Y. Malik
%A Farzana Khan
%J Chinese Journal of Engineering
%D 2013
%R 10.1155/2013/808342
%X We consider the flow of Eyring-Powell model fluid in the annulus between two cylinders whose viscosity depends upon the temperature. We consider the steady flow in the annulus due to the motion of inner cylinder and constant pressure gradient. In the problem considered the flow is found to be remarkedly different from that for the incompressible Navier-Stokes fluid with constant viscosity. An analytical solution of the nonlinear problem is obtained using homotopy analysis method. The behavior of pertinent parameters is analyzed and depicted through graphs. 1. Introduction The analysis of the behaviour of the fluid motion of the non-Newtonian fluids becomes much complicated and subtle as compared to Newtonian fluids due to the fact that non-Newtonian fluids do not exhibit the linear relationship between stress and strain. Rivlin and Ericksen [1] and Truesdell and Noll [2] classified viscoelastic fluids with the help of constitutive relations for the stress tensor as a function of the symmetric part of the velocity gradient and its higher (total) derivatives. In recent years, there have been several studies [3¨C12] on flows of non-Newtonian fluids. It is a well-known fact that it is not possible to obtain a single constitutive equation exhibiting all properties of all non-Newtonian fluids from the available literature. That is why several models of non-Newtonian fluids have been proposed in the literature. Eyring-Powell model fluid is one of these models. Eyring-Powell model was first introduced by Powell and Eyring in 1944. However, the literature survey indicates that very low energy has been devoted to the flows of Eyring-Powell model fluid with variable viscosity. Massoudi and Christie [13] have considered the effects of variable viscosity and viscous dissipation on the flow of a third grade fluid in a uniform pipe. Massoudi and Christie [13] found the numerical solutions with the help of straight forward finite difference method. They also discussed that the flow of a fluid-solid mixture is very complicated and may depend on many variables such as physical properties of each phase and size and shape of solid particles. Later on, the influence of constant and space dependent viscosity on the flow of a third grade fluid in a pipe has been discussed analytically by Hayat et al. [14]. The approximate and analytical solution of non-Newtonian fluid with variable viscosity has been analyzed by Y¨ır¨ısoy and Pakdermirli [15] and Pakdemirli and Yilbas [16]. The pipe flow of non-Newtonian fluid with variable viscosity keeping no slip and partial slip has been
%U http://www.hindawi.com/journals/cje/2013/808342/