**A mathematical
model for pulsatile flow of Herschel-Bulkley fluid through stenosed arteries**

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S. U. Siddiqui, N. K. Verma and R. S. Gupta^{*}

Department of Mathematics, Harcourt Butler Technological
Institute, Kanpur, India

^{*}Department
of Mathematics, Kamla Nehru Institute of Technology, Sultanpur, India

**Abstract**

Presented herein** **is the study of pulsatile
flow of blood through stenosed artery by modeling
blood as Herschel–Bulkley fluid.
The Herschel–Bulkley fluid has
two parameters, the yield stress *è* and the power index *n*.
Perturbation method is used to solve the resulting quasi-steady nonlinear
coupled implicit system of differential equations. The effects of pulsatility
and non-Newtonian nature of blood on velocity, flow rate, wall shear stress and
longitudinal impedance of the artery are discussed. The width of the plug core
region increases with increasing value of yield stress at any time. The velocity
and flow rate decrease, whereas wall shear stress and longitudinal impedance
increase for increasing value of yield stress with other parameters held fixed.
On the other hand, the velocity, flow rate and wall shear stress decrease but
resistance to flow increases as the radius of artery increases with other
parameters fixed. The results for power law fluid, Newtonian fluid and Bingham
fluid are obtained as special cases from this model.

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**Keywords. **
Pulsatile blood flow; Stenosed artery;
Herschel–Bulkley fluid; Yield stress; Wall shear stress; Longitudinal impedance.

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