e-Περιοδικό Επιστήμης & Τεχνολογίας

e-Journal of Science & Technology, (e-JST)

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

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 θ 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.

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

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