Boundary Layer Equations and Lie Group Analysis of a Sisko Fluid

Gözde Sarı,Yiğit Aksoy,Mehmet Pakdemirli,Tasawar Hayat

doi:10.1155/2012/259608

Abstract

Boundary layer equations are derived for the Sisko fluid. Using Lie group theory, a symmetry analysis of the equations is performed. A partial differential system is transferred to an ordinary differential system via symmetries. Resulting equations are numerically solved. Effects of non‐Newtonian parameters on the solutions are discussed.

Highlights

Due to the inadequacy of Newtonian fluid model which predicts a linear relationship between the shear stress and velocity gradient, many non-Newtonian fluid models were proposed to explain the complex behavior
To the best of authors’ knowledge, boundary layer analysis and symmetry reductions of Sisko fluids do not exist in the literature
There is an additional infinite parameter Lie group symmetry represented by c x function

Summary

Introduction

Due to the inadequacy of Newtonian fluid model which predicts a linear relationship between the shear stress and velocity gradient, many non-Newtonian fluid models were proposed to explain the complex behavior. Since there are many non-Newtonian models and new models are being proposed continuously, boundary layer theory for each proposed model appears in the literature. Boundary layer theory is developed for the Sisko fluid, a non-Newtonian fluid model which combines the features of viscous and power law models. Some of the recent work on Sisko fluids is as follows: an analytical solution was presented using homotopy analysis method for the flow of a magnetohydrodynamic Sisko fluid through a porous medium. The equation modeling thin film flow of a Sisko fluid on a moving belt qualitatively was analyzed and a series solution was found using homotopy analysis method. A numerical study for the unsteady flow of a magnetohydrodynamic Sisko fluid in annular pipe was presented. To the best of authors’ knowledge, boundary layer analysis and symmetry reductions of Sisko fluids do not exist in the literature

Boundary Layer Equations

Lie Group Theory and Symmetry Reductions

The classifying relation for the outer velocity is

Numerical Results

Concluding Remarks