Study the flow of a non-Newtonian viscoelastic fluid in a converging channel with suction and injection at the walls: an analytical approach

An analysis has been performed to study the steady flow of an incompressible viscoelastic fluid in a converging channel with porous walls. It is assumed that the fluid isinjected into the channel through one wall and sucked from the channel through the other wall at the same velocity. It is also assumed that this velocity magnitude varies in inverse proportion to distance along the wall from the origin of the channel. The equations ofcontinuity and momentum will reduce to a singlenonlinear ordinary differential equation that we call it the similarity equation. This equation will then besolved with its appropriate boundary conditions by a new analytical approach called homotopy perturbation method. The obtained solutions in comparison with thenumerical solutions admit a remarkable accuracy. The perturbation method depends on small parameter assumption and the obtained results in most cases arenon-physical. Also when nonlinear term is more effective it gives inaccurate results. The numerical methods lead to inaccurate results when the equation is intensively depends on time. The analytical method called homotopy perturbation method does not dependon small parameter and it gives nearly exact solutions. In this paper the effects of different parameters such as Reynolds number on fluid flow and velocity field will be investigated. We also study how the elasticity of fluid characterized by elastic number affect the velocity distribution for different values of Reynolds number and cross-flow Reynolds number.

Keywords:

Homotopy perturbation method , Nonlinear equation , Viscoelastic fluid , Porous walls