Abstract
The numerical solution of the entrance flow in a tube has been obtained for a Bingham fluid. The numerical procedure used is that of Patankar and Spalding [1]. The accuracy of the numerical results is demonstrated by comparing the fully-developed velocity profiles with analytical exact solutions. The results of the entrance flow in a tube for the case of a zero yield stress are compared with the entrance flow solution for a Newtonian fluid. Detailed results are presented for a wide range of yield numbers (=τ y D/ūμ).
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Abbreviations
- D :
-
diameter
- f x :
-
friction factor (eq. (5.1))
- f app :
-
total friction factor (eq. (5.2))
- p :
-
pressure
- r :
-
radius
- R :
-
radius of a tube
- R e :
-
Reynolds number (=ρūD/μ)
- u :
-
axial velocity
- ū :
-
average velocity
- v :
-
velocity in radial direction
- x :
-
axial co-ordinate
- Y :
-
yield number (=τ y D/ūμ)
- z :
-
dimensionless axial distance (=x/(D Re))
- z 1 :
-
1/z (=(D/x) Re)
- μ :
-
viscosity
- ρ :
-
density
- τ :
-
shear stress
- τ y :
-
yield stress
References
Patankar, S. V. and D. B. Spalding, Heat and Mass Transfer in Boundary Layers, Intertext Book, 2nd Ed., London, 1970.
Michiyoshi, L., K. Mizuno and Y. Hoshinai, Intern. Chem. Eng. 6 (1966) 373.
Chen, S. S., L. T. Fan and C. L. Hwang, AIChE J. 16 (1970) 293.
Campbell, W. D. and J. C. Slattery, Trans. Am. Soc. Mech. Engrs., J. Basic Eng. 95D (1963) 41.
Oldroyd, J. G., Proc. Cambridge Phil. Soc. 43 (1947) 383.
Shah, V. L. and K. Farnia, ASME 1973 Biomechanics Symposium AMD, Vol. 2 (1973).
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Shah, V.L., Soto, R.J. Entrance flow of a bingham fluid in a tube. Appl. Sci. Res. 30, 271–278 (1975). https://doi.org/10.1007/BF00386695
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DOI: https://doi.org/10.1007/BF00386695