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Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube

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Central European Journal of Physics

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 τ 0 → 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 (t 1 and t 2) 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.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

    Kuppalapalle Vajravelu

  2. Department of Mathematics, Sri Venkateswara University, Tirupati, 517502, AP, India

    Sreedharamalle Sreenadh & Palluru Devaki

  3. Department of Mathematics, Banaglore University, Bangalore, 560 001, Karnataka, India

    Kerehalli V. Prasad

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  1. Kuppalapalle Vajravelu
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  2. Sreedharamalle Sreenadh
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  3. Palluru Devaki
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  4. Kerehalli V. Prasad
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Correspondence to Kuppalapalle Vajravelu.

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Vajravelu, K., Sreenadh, S., Devaki, P. et al. Mathematical model for a Herschel-Bulkley fluid flow in an elastic tube. centr.eur.j.phys. 9, 1357–1365 (2011). https://doi.org/10.2478/s11534-011-0034-3

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

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