Flow of a Herschel-Bulkley Fluid in a Channel with Elastic Walls

  • Authors

    • S. Sreenadh
    • B. Sumalatha
    • A. N.S.Srinivas
    2018-10-02
    https://doi.org/10.14419/ijet.v7i4.10.21210
  • Poiseuille flow, Herschel-Bulkley fluid, elastic parameters

  • In order to model the blood flow through an artery in presence of catheter, we considered a steady, laminar, incompressible, Poiseuille flow of a Herschel-Bulkley fluid between two horizontal parallel elastic walls. The power law index ( ) and yield stress ( ) are the two parameters of the Herschel - Bulkley fluid. By giving different values for the above mentioned parameters, we get the Newtonian, Bingham and Power-law fluids as special cases. The exact solutions for the flow quantities such as velocity, plug flow velocity and flux are derived. The flux is determined as a function of inlet, outlet, external pressures and the elastic property of the channel. The effect of elastic parameters on flux variation is analyzed. Further when and our results qualitatively agree with those of Rubinow and Keller [2]. In addition, velocity of the Herschel- Bulkley fluid flow is expressed in terms of elastic parameters.

     

     

  • References

    1. [1] Roach, M. R., & Burton, A. C. “The reason for distensibility curves of arteriesâ€. Canadian Journal of Biochemistry and Physiology, Vol. 35(8) (1957) pp. 681-690. http://doi: 10.1139/o57-080.

      [2] Rubinow, S. I., & Keller, J. B.†Flow of a viscous fluid through an elastic tube with applications to blood flowâ€. Journal of Theoretical Biology, Vol. 35(2) (1972), pp. 299-313. https://doi.org/10.1016/0022-5193(72)90041-0.

      [3] Pedley, T. J., & Fung Y .C.â€The fluid mechanics of large blood vesselsâ€. Cambridge University press (1980).

      [4] Fung, Y. C., “Biodynamicsâ€, Springer-Verlag, Newyork, Berlin Hildelberd, Tokyo (1984).

      [5] Mazumdar, N. J., “Biofluid Mechanicsâ€. World Scientific publishing, Singapore (1992).

      [6] Taha Sochi, “The flow of Newtonian and Power-law fluids in elastic tubesâ€, Intern. Journal of Non-linear Mechanics, Vol.67 (2014), pp. 245 - 250. https://doi.org/10.1016/j.ijnonlinmec.2014.09.013.

      [7] Scott Blair G. W. S. “An equation for the flow of blood, Plasma and serum through glass Capillariesâ€. Nature, Vol. 183 (1959), pp. 613-614. http://dx.doi.org/10.1038/183613a0

      [8] Shankar, A & Jayaraman, G.,â€Non-linear analysis of oscillatory flow in the annulus of an elastic tube: Applications to catheterized arteryâ€. Physics of Fluids, Vol. 13(10) (2001), pp. 2901-2911. https://doi.org/10.1063/1.1389285.

      [9] Pedrizzetti, G., “Fluid flow in a tube with elastic membrane insertionâ€, Journal of Fluid Mechanics, Vol. 375, (1998) pp. 39-64. https://doi.org/10.1017/S0022112098002316

      [10] Vajravelu, K., Sreenadh, S., and Ramesh Babu, V., “Peristaltic pumping of a Herschel-Bulkley fluid in a channelâ€. Applied Mathematics and computation, Vol. 169 (1) (2005), pp. 726-735. http://doi.10.1016/j.amc.2004.09.063.

      [11] Vajravelu, K., Sreenadh, S., Devaki, P., and Prasad, K. V., (2014). “Mathematical model for aHerschel- Bulkley fluid flow in elastic tubeâ€. Central European Journal of Physics, 9(5), 1357-1365. https://doi.org/10.2478/s11534-011-0034-3

      [12] Ali Amini, Amir Saman Eghtesad and Kayvan Sadeghy, “Creeping flow of Herschel-Bulkley fluids in collapsible channels: A numerical studyâ€. Korea-Australia Rheology Journal, Vol. 28(4) (2016), pp. 255-265. https://doi.org/10.1007/s13367-016-0027-2.

      [13] Fusi, L., & Rosso, F., “Creeping flow of a Herschel–Bulkley fluid with pressure-dependent material moduliâ€. European Journal of Applied Mathematics, Vol. 29(2) (2017), pp. 352-368. http://doi. 10.1017/S0956792517000183.

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  • How to Cite

    Sreenadh, S., Sumalatha, B., & N.S.Srinivas, A. (2018). Flow of a Herschel-Bulkley Fluid in a Channel with Elastic Walls. International Journal of Engineering & Technology, 7(4.10), 491-496. https://doi.org/10.14419/ijet.v7i4.10.21210