Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl

PL EN


Preferences help
enabled [disable] Abstract
Number of results

Journal

2011 | 9 | 5 | 1357-1365

Article title

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

Content

Title variants

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.

Publisher

Journal

Year

Volume

9

Issue

5

Pages

1357-1365

Physical description

Dates

published
1 - 10 - 2011
online
15 - 9 - 2011

Contributors

  • Department of Mathematics, University of Central Florida, Orlando, FL, 32816, USA
  • Department of Mathematics, Sri Venkateswara University, Tirupati, 517502, AP, India
  • Department of Mathematics, Sri Venkateswara University, Tirupati, 517502, AP, India
  • 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]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-011-0034-3
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.