PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
2011 | 9 | 5 | 1357-1365
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
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.
Wydawca

Czasopismo
Rocznik
Tom
9
Numer
5
Strony
1357-1365
Opis fizyczny
Daty
wydano
2011-10-01
online
2011-09-15
Twórcy
  • 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
Bibliografia
  • [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]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-011-0034-3
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.