Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation.
Hindawi Publishing Corporation
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.
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
Khan, M., Abelman, S., and Mason, D.P., Mahomed, F.M. 2015. Mathematical Problems in Engineering.