Numerical Solutions of Blood Flow in the Entrance of a Tube

  • V. L. Shah
  • R. Soto
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 191)


Hydrodynamic boundary layer predictions are obtained in the entrance region of a tube for non-Newtonian fluids like blood which obey Casson’s stress-strain relation. The numerical procedure used is that of Patankar and Spalding [2]. The mathematical accuracy of the numerical procedure is demonstrated by comparing the fully developed velocity profiles with the known analytical solutions. In addition the results of the numerical solution for the case of yield stress equal to zero are compared with the available entrance flow solution for Newtonian fluids. Detailed results are presented for a wide range of yield numbers.


Newtonian Fluid Entrance Region Total Pressure Drop Yield Number Develop Velocity Profile 
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  1. 1.
    Charm, S., and Kurland, G. S., “Viscometry of Human Blood for Shear Rates of 0–100,000 sec-1,” Nature (London), 206 (1965), p. 617.CrossRefGoogle Scholar
  2. 2.
    Patankar, S. V., and Spalding, D. B., “Heat and Mass Transfer in Boundary Layer,” Intertext Book, 2nd Edition, London (1970).Google Scholar
  3. 3.
    Shah, V. L. and Soto, R., “The Entry Flow for a Fluid Obeying Casson’s Stress-Strain Relation,” to be published.Google Scholar

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • V. L. Shah
    • 1
  • R. Soto
    • 1
  1. 1.College of Engineering and Applied Science, Medical College of WisconsinUniversity of Wisconsin-MilwaukeeUSA

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