Title

Mathematical Model For A Herschel-Bulkley Fluid Flow In An Elastic Tube

Keywords

blood flow; elastic tube; fluid flux; Herschel-Bulkley fluid; non-Newtonian fluid

Abstract

The constitution of blood demands a yield stress fluid model, and among the available yield stress fluid models for blood flow, the Herschel-Bulkley model is preferred (because Bingham, Power-law and Newtonian models are its special cases). The Herschel-Bulkley fluid model has two parameters, namely the yield stress and the power law index. The expressions for velocity, plug flow velocity, wall shear stress, and the flux flow rate are derived. The flux is determined as a function of inlet, outlet and external pressures, yield stress, and the elastic property of the tube. Further when the power-law index n = 1 and the yield stress τ0 → 0, our results agree well with those of Rubinow and Keller [J. Theor. Biol. 35, 299 (1972)]. Furthermore, it is observed that, the yield stress and the elastic parameters (t1 and t2) have strong effects on the flux of the non-Newtonian fluid flow in the elastic tube. The results obtained for the flow characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the shear-thinning phenomena. Shear thinning reduces the wall shear stress. © 2011 Versita Warsaw and Springer-Verlag Wien.

Publication Date

10-1-2011

Publication Title

Central European Journal of Physics

Volume

9

Issue

5

Number of Pages

1357-1365

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.2478/s11534-011-0034-3

Socpus ID

80052739625 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/80052739625

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