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

• Authors: Kuppalapalle Vajravelu , Sreedharamalle Sreenadh , Palluru Devaki , Kerehalli Prasad
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

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

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2011
• Volume: 9
• Issue: 5
• Pages: 1357-1365

Dates

published

1 - 10 - 2011

online

15 - 9 - 2011

Contributors

author

Kuppalapalle Vajravelu

• Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA

author

Sreedharamalle Sreenadh

• Department of Mathematics, Sri Venkateswara University, Tirupati, 517502, AP, India

author

Palluru Devaki

• Department of Mathematics, Sri Venkateswara University, Tirupati, 517502, AP, India

author

Kerehalli Prasad

• Department of Mathematics, Banaglore University, Bangalore, 560 001, Karnataka, India

References

• [1] T. Young, Philos. T. R. Soc. Lond. 98, 164 (1808) http://dx.doi.org/10.1098/rstl.1808.0014[Crossref]
• [2] S.I. Rubinow, J.B. Keller, J. Theor. Biol. 35, 299 (1972) http://dx.doi.org/10.1016/0022-5193(72)90041-0[Crossref]
• [3] A.C. Burton, Am. J. Physiol. 164, 319 (1951)
• [4] D.L. Fry, Comput. Biomed. Res. 2, 111 (1968) http://dx.doi.org/10.1016/0010-4809(68)90030-X[Crossref]
• [5] G.A. Brecher, Am. J. Physiol. 169, 423 (1952)
• [6] S. Rodbrad, Circulation 11, 280 (1955)
• [7] A.C. Guyton, In: W.F. Hamilton (Ed.), Handbook of Physiology Circulation II, Vol. 2 (American Physiologic Society, Washington DC, 1963) 1099
• [8] G.A. Brecher, Venos Return (Grune and Stratton, New York, 1956)
• [9] J. Bainster, R.W. Torrance, Q. J. Exp. Physiol. 45, 352 (1960)
• [10] S. Permutt, B. Bromberger-Barnea, H.N. Bane, Med. Thorac. 19, 239 (1962) [PubMed]
• [11] F.P. Knowlton, E.H. Starling, J. Physiol.-London 44, 206 (1912)
• [12] P. Chaturani, V.R. Ponnalagar, Biorheology 22, 521 (1985) [PubMed]
• [13] V.P. Srivastava, M. Sexena, J. Biomech. 27, 921 (1994) http://dx.doi.org/10.1016/0021-9290(94)90264-X[Crossref]
• [14] N. Iida, Jpn. J. Appl. Phys. 17, 203 (1978) http://dx.doi.org/10.1143/JJAP.17.203[Crossref]
• [15] G.W. Scott-Blair, D.C. Spanner, An Introduction to Biorheology (Elsevier Scientific Publishing Company, Amsterdam, 1974)
• [16] G.W. Scott-Blair, Rheol. Acta 5, 184 (1966) http://dx.doi.org/10.1007/BF01982424[Crossref]
• [17] A.G. Hoekstra, J. van’t-Hoff, A.M. Artoli, P.M.A. Sloot, Future Gener. Comp. Sy. 20, 917 (2004) http://dx.doi.org/10.1016/j.future.2003.12.003[Crossref]
• [18] D.S. Sankar, K. Hemalatha, Appl. Math. Model. 31, 1847 (2007) http://dx.doi.org/10.1016/j.apm.2006.06.009[Crossref]
• [19] K. Vajravelu, S. Sreenadh, V. Ramesh-Babu, Appl. Math. Comput. 169, 726 (2005) http://dx.doi.org/10.1016/j.amc.2004.09.063[Crossref]
• [20] C. Tu, M. Deville, J. Biomech. 29, 899 (1996) http://dx.doi.org/10.1016/0021-9290(95)00151-4[Crossref]
• [21] P. Chaturani, R.P. Swamy, Journal of Biorheology 22, 521 (1985)
• [22] D.S. Sankar, K. Hemalatha, Appl. Math. Comput. 188, 567 (2007) http://dx.doi.org/10.1016/j.amc.2006.10.013[Crossref]
• [23] K. Vajravelu, S. Sreenadh, V. Ramesh-Babu, Q. Appl. Math. 64, 593 (2005)
• [24] K. Vajravelu, S. Sreenadh, V. Ramesh-Babu, Int. J. Nonlin. Mech. 40, 83 (2005) http://dx.doi.org/10.1016/j.ijnonlinmec.2004.07.001[Crossref]
• [25] D.S. Snakar, U. Lee, Commun. Nonlinear Sci. 14, 2971 (2009) http://dx.doi.org/10.1016/j.cnsns.2008.10.015[Crossref]
• [26] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, 2nd ed. (Wiley, New York, 2007) 11
• [27] M.R. Roach, A.C. Burton, Can. J. Biochem. Phys. 37, 557 (1957) http://dx.doi.org/10.1139/o59-059[Crossref]

Identifiers

DOI

10.2478/s11534-011-0034-3