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

Abstract EN

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.

The reduction 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.