Self-Similar Unsteady Flow of a Sisko Fluid in a Cylindrical Tube Undergoing Translation. - Khan, M.; Abelman, S.; Mahomed, F.M. (Hindawi Publishing Corporation, 2015)
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.
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