Abstract
The flow of incompressible couple stress fluid in a circular tube with stenosis and dilatations has been investigated. The stenosis was assumed to be axially symmetric and mild. The flow equations have been linearized and the expressions for the resistance to the flow, velocity, pressure drop, wall shear stress have been derived. The effects of various parameters on these flow variables have been investigated. It is found that the resistance to the flow and pressure drop increase with height of the stenosis and decrease with post stenotic dilatation. Pressure drop decreases with couple stress fluid parameter for both stenosis and post stenotic dilatation. Further, the wall shear stress increases with height of the stenosis and couple stress parameter but decreases with post stenotic dilatation and couple stress fluid parameter.
Highlights
In the present world, diseases in the blood vessels and in the heart like heart attack and stroke are major health hazards causing a large number of deaths .The main reason for these deaths is stenosis
The wall shear stress increases with height of the stenosis and couple stress parameter but decreases with post stenotic dilatation and couple stress fluid parameter
It can be observed that, the pressure drop decreases with height of post stenotic dilatation (δ2 ) and couple stress fluid parameter (α ) but increases with volumetric flow rate (q)
Summary
Diseases in the blood vessels and in the heart like heart attack and stroke are major health hazards causing a large number of deaths .The main reason for these deaths is stenosis. Shukla et al [1] studied the effects of stenosis on Non-Newtonian flow of the blood in an artery. Sreenadh et al [8] developed a model and analyzed flow of a Casson fluid through an inclined tube of non-uniform cross section with multiple stenoses. Srikanth et al [16] have analyzed the mathematical problems of non-Newtonian fluid through multiple stenosis arteries in the presence of couple stress. Sanjeev Kumar et al [21] described blood flow resistance for a small artery with multiple stenosis and post stenotic dilatation. Motivated from the above studies a mathematical model was developed by considering blood as couple stress fluid, passing through an artery (tube) having stenosis and post stenotic dilatations. The variation of impedance and shear stress is analyzed for various values of couple stress fluid parameters and geometric parameters
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