Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation.

Date
2015
Authors
Khan, M.
Abelman, S.
Mahomed, F.M.
Journal Title
Journal ISSN
Volume Title
Publisher
Hindawi Publishing Corporation
Abstract
The governing nonlinear equation for unidirectional flow of a Sisko fluid in a cylindrical tube due to translation of the tube wall is modelled in cylindrical polar coordinates.The exact steady-state solution for the nonlinear problem is obtained.Thereduction of the nonlinear initial value problem is carried out by using a similarity transformation.The partial differential equation is transformed into an ordinary differential equation, which is integrated numerically taking into account the influence of the exponent n and the material parameter b of the Sisko fluid. The initial approximation for the fluid velocity on the axis of the cylinder is obtained by matching inner and outer expansions for the fluid velocity. A comparison of the velocity, vorticity, and shear stress of Newtonian and Sisko fluids is presented.
Description
Keywords
Initial value problems , Mathematical transformation , Nonlinear equations , Ordinary differential equations , Shear stress Cylindrical tube , Initial approximation , Material parameter , Nonlinear initial-value problem , Similarity transformation , Steady state solution , Unidirectional flow , Nonlinear problems
Citation
Khan, M., Abelman, S., and Mason, D.P., Mahomed, F.M. 2015. Mathematical Problems in Engineering.