Santhosh Nallapu This email address is being protected from spambots. You need JavaScript enabled to view it.1 and G. Radhakrishnamacharya1

1Department of Mathematics, National Institute of Technology, Warangal, India


Received: October 2, 2015
Accepted: May 5, 2016
Publication Date: September 1, 2016

Download Citation: ||  


A two-fluid model of Herschel-Bulkley fluid flow through tubes of small diameters is studied. It is assumed that the core region consists of Herschel-Bulkley fluid and Newtonian fluid in the peripheral region. The analytical solutions for velocity, flow flux, effective viscosity, core hematocrit and mean hematocrit have been derived and the effects of various relevant parameters on these flow variables have been studied. It is found that the effective viscosity, core hematrocit and mean hematrocit for Newtonian fluid is less than that for Bingham fluid, power-law fluid and Herschel Bulkley fluid. It has been observed that the effective viscosity and mean hematocrit increase with yield stress, power-law index, hematocrit and tube radius but the core hematocrit decreases with hematocrit and tube radius. Further, it is also noticed that the flow exhibits the anomalous Fahraeus-Lindqvist effect.

Keywords: Effective Viscosity, Herschel-Bulkley Fluid, Hematocrit, Fahraeus-Lindqvist Effect, Yield Stress


  1. [1] Haynes, R. H. and Burton, A. C., “Role of Non-Newtonian Behaviour of Blood in Hemodynamics,” Am. J. Physiol., Vol. 197, p. 943 (1959).
  2. [2] Srivastava, V. P. and Saxena, M., “ATwo-Fluid Model of Non-Newtonian Blood Flow Induced by Peristaltic Waves,” Rheol.Acta,Vol.34,No.4,pp.406414(1995). doi: 10.1007/BF00367155
  3. [3] Haynes, R. H., “Physical Basis of the Dependence of Blood Viscosityon Tube Radius,” Am. J. Physiol., Vol. 198, pp. 11931200 (1960).
  4. [4] Bugliarello, G. and Sevilla, J., “Velocity Distribution and other Characteristics of Steady and Pulsatile Blood Flow in Fine Glass Tubes,” Biorheology, Vol. 7, pp. 85107 (1970).
  5. [5] Sharan, M. and Popel, A. S., “ATwo-phase Model for Flow of Blood in Narrow Tubes with Increased Effective Viscosity near the Wall,” Biorheology, Vol. 38, pp. 415428 (2001).
  6. [6] Srivastava, V. P., “A Theoretical Model for Blood Flow in Small Vessels,” Appl. Appl. Math., Vol. 2, pp. 5165 (2007).
  7. [7] Haldar, K. and Andersson, H. I., “Two-layered Model of Blood Flow through Stenosed Arteries,” Acta Mech., Vol. 117, No. 1, pp. 221228 (1996). doi: 10.1007/BF 01181050
  8. [8] Chaturani, P. and Ponalagusamy, R.,“Pulsatile Flow of Casson’s Fluid through Stenosed Arteries with Applicationsto Blood Flow,” Biorheology, Vol. 23, pp. 499 511 (1986).
  9. [9] Chaturani, P. and Upadhya, V. S., “On Micropolar Fluid Model for Blood Flow through Narrow Tubes,” Biorheology, Vol. 16, pp. 419428 (1979).
  10. [10] Chaturani, P. and Upadhya, V. S., “ATwo-Fluid Model for Blood Flow through Small Diameter Tubes,” Biorheology, Vol. 18, pp. 245253 (1981).
  11. [11] Shukla, J. B., Parihar, R. S. and Gupta, S. P., “Effects of Peripheral Layer Viscosity on Blood Flow through the Artery with Mild Stenosis,” Bull. Math. Biol., Vol. 42, pp. 797805 (1980). doi: 10.1016/S0092-8240 (80)80003-6
  12. [12] Blair, G. W. S. and Spanner, D. C., “An Introduction to Biorheology,” Elsevier, Amsterdam. (1974).
  13. [13] Maruthi Prasad, K. and Radhakrishnamacharya, G., “Flow of Herschel-Bulkley Fluid through an Inclined tube of Non-uniform Cross-section with Multiple Stenoses,” Arch. Mech., Vol. 60, No. 2, pp. 161172 (2008).
  14. [14] Vajravelu, K., Sreenadh, S., Devaki, P. and Prasad K. V., “Mathematical Model for a Herschel-Bulkley Fluid Flow in an Elastic Tube,” Cent. Eur. J. Phys., Vol. 9, No. 5, pp. 13571365 (2011). doi: 10.2478/s11534011-0034-3
  15. [15] Sankar, D. S. and Lee, U., “Two-fluid Herschel-Bulkley Model for Blood Flow in Catheterized Arteries,” J. Mech. Sci. Tech., Vol. 22, pp. 10081018 (2008). doi: 10.1007/s12206-008-0123-4
  16. [16] Vajravelu, K., Sreenadh, S. and RameshBabu, V., “Peristaltic Transport of a Herschel-Bulkley Fluid in an Inclined Tube,” Int. J. Non-Linear Mech., Vol. 40, No. 1, pp. 8390 (2005). doi: 10.1016/j.ijnonlinmec.2004. 07.001
  17. [17] Santhosh, N., Radhakrishnamacharya, G. and Chamkha, A. J., “Flow of a Jeffrey Fluid Through a Porous Medium in Narrow Tubes,” J. Por. Media., Vol. 18, No. 1, pp. 7178 (2015). doi: 10.1615/JPorMedia.v18.i1.60