The flow of blood through a narrow artery with bell-shaped stenosis is investigated, treating blood as Casson fluid. Present results are compared with the results of the Herschel-Bulkley fluid model obtained by Misra and Shit (2006) for the same geometry. Resistance to flow and skin friction are normalized in two different ways such as (i) with respect to the same non-Newtonian fluid in a normal artery which gives the effect of a stenosis and (ii) with respect to the Newtonian fluid in the stenosed artery which spells out the non-Newtonian effects of the fluid. It is found that the resistance to flow and skin friction increase with the increase of maximum depth of the stenosis, but these flow quantities (when normalized with non-Newtonian fluid in normal artery) decrease with the increase of the yield stress, as obtained by Misra and Shit (2006). It is also noticed that the resistance to flow and skin friction increase (when normalized with Newtonian fluid in stenosed artery) with the increase of the yield stress.
A computational model is developed to analyze the effects of magnetic field in a pulsatile flow of blood through narrow arteries with mild stenosis, treating blood as Casson fluid model. Finite difference method is employed to solve the simplified nonlinear partial differential equation and an explicit finite difference scheme is obtained for velocity and subsequently the finite difference formula for the flow rate, skin friction and longitudinal impedance are also derived. The effects of various parameters associated with this flow problem such as stenosis height, yield stress, magnetic field and amplitude of the pressure gradient on the physiologically important flow quantities namely velocity distribution, flow rate, skin friction and longitudinal impedance to flow are analyzed by plotting the graphs for the variation of these flow quantities for different values of the aforesaid parameters. It is found that the velocity and flow rate decrease with the increase of the Hartmann number and the reverse behavior is noticed for the wall shear stress and longitudinal impedance of the flow. It is noted that flow rate increases and skin friction decreases with the increase of the pressure gradient. It is also observed that the skin friction and longitudinal impedance increase with the increase of the amplitude parameter of the artery radius. It is also found that the skin friction and longitudinal impedance increases with the increase of the stenosis depth. It is recorded that the estimates of the increase in the skin friction and longitudinal impedance to flow increase considerably with the increase of the Hartmann number.
The steady flow of blood through a catheterized artery is analyzed, assuming the blood as a two-fluid model with the core region of suspension of all the erythrocytes as a Herschel-Bulkley fluid and the peripheral region of plasma as a Newtonian fluid. The expressions for velocity, flow rate, wall shear stress and frictional resistance are obtained. The variations of these flow quantities with yield stress, catheter radius ratio and peripheral layer thickness are discussed. It is observed that the velocity and flow rate decrease while the wall shear stress and resistance to flow increase when the yield stress or the catheter radius ratio increases when all the other parameters held constant. It is noticed that the velocity and flow rate increase while the wall shear stress and frictional resistance decrease with the increase of the peripheral layer thickness. The estimates of the increase in the frictional resistance are significantly much smaller for the present two-fluid model than those of the single-fluid model.
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