Abstract
This article examines the slip effect on the creeping flow of an incompressible second grade fluid in an axisymmetric channel having varying width. We have used three different methods depending upon the geometrical configuration to find out the solution. The results obtained are applied to study the flow of a second grade fluid through a smooth stenosis. To understand the flow behavior near stenosis, resistance to the flow and shear stress at the wall are calculated. The results obtained are graphically evaluated for different values of dimensionless non-Newtonian parameters, maximum height of the stenosis and slip parameter. It is observed that the resistance to the flow and wall shear stress increase with increasing value of non-Newtonian parameter and maximum height of the stenosis and decrease as the value of slip parameter increases.
Highlights
Stenosis is formed due to deposition of fatty substance on the inner sides of arteries
In this study an attempt has been made to study the effects of slip at the stenotic wall for the creeping flow of an incompressible second grade fluid in an axisymmetric channel having varying width. we have used three different methods depending upon the geometrical configuration to find out the solution
In addition to the no-slip boundary condition (18) we need one more boundary condition. This boundary condition is obtained by calculating the net flux Q across the channel, which has to be constant at all cross-sections of the channel for an incompressible second grade fluid
Summary
Stenosis is formed due to deposition of fatty substance on the inner sides of arteries. The rheological properties of blood being very important from the point of view of basic understanding of arterial stenosis many researchers have studied blood flow through stenosed arteries both theoretically and experimentally. The flow of a fluid in an elastic tube, without considering slip effects, was first approximated by Rashkevsky [10] and later by Morgan [11] This problem was further investigated by Langlois [12] under several approximations on the geometry of the gap for a Newtonian fluid. Siddique et al [13] have extended the work of Langlois for a non-Newtonian fluid of second grade with application to stenosed artery. They did not take into account slip effects in their work. The problem is formulated, solved and the obtained results are discussed
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