An analytical solution is reported for the temperature distribution in finite span thin-gap Couette devices which accounts for viscous dissipation. Taken in conjunction with an established solution for the stable velocity profile, this result describes the standard experimental configuration where no external heat fluxes are applied. We discuss physical aspects as well as conditions for which classical one-dimensional theory should be replaced by the present result.
Issue Section:
Technical Notes
Keywords:
Analytical,
Conduction,
Flow,
Heat Transfer,
Laminar,
Couette flow,
temperature distribution,
shear flow
1.
Taylor
, G. I.
, 1923
, “Stability of a Viscous Liquid Contained Between Two Rotating Cylinders
,” Philos. Trans. R. Soc. London, Ser. A
, 223
, pp. 289
–343
.2.
Kobayashi
, H.
, Nashima
, T.
, Okamoto
, Y.
, and Kaminaga
, F.
, 1991
, “End Effect in a Coaxial Cylindrical Viscometer
,” Rev. Sci. Instrum.
, 62
, pp. 2748
–2750
.3.
Ameer
, G. A.
, Barabino
, G.
, Sasisekharan
, R.
, Harmon
, W.
, Cooney
, C. L.
, and Langer
, R.
, 1999
, “Ex Vivo Evaluation of a Taylor–Couette Flow, Immobilized Heparinase I Device for Clinical Application
,” Proc. Natl. Acad. Sci. U.S.A.
, 96
, pp. 2350
–2355
.4.
Criminale
, W. O.
, Jackson
, T. L.
, Lasseigne
, D. G.
, and Joslin
, R. D.
, 1997
, “Perturbation Dynamics in Viscous Channel Flows
,” J. Fluid Mech.
, 339
, pp. 55
–75
.5.
Nagata
, M.
, 1997
, “Three-Dimensional Traveling-Wave Solutions in Plane Couette Flow
,” Phys. Rev. E
, 55
, pp. 2023
–2025
.6.
Waleffe
, F.
, 1997
, “On a Self-Sustaining Process in Shear Flows
,” Phys. Fluids
, 9
, pp. 883
–900
.7.
Yueh
, C.-S.
, and Weng
, C.-L.
, 1996
, “Linear Stability Analysis of Plane Couette Flow With Viscous Heating
,” Phys. Fluids
, 8
, pp. 1802
–1813
.8.
Davis
, S. H.
, Kreigsmann
, G. A.
, Laurence
, R. L.
, and Rosenblat
, S.
, 1983
, “Multiple Solutions and Hysteresis in Steady Parallel Viscous Flows
,” Phys. Fluids
, 26
, pp. 1177
–1182
.9.
Johns
, L. E.
, and Narayan
, R.
, 1997
, “Frictional Heating in Plane Couette Flow
,” Proc. R. Soc. London, Ser. A
, 453
, pp. 1653
–1670
.10.
Caridis
, K. A.
, Louwagie
, B.
, and Papathanasiou
, T. D.
, 1997
, “Viscous Heating in Planar Couette Flow: Series Solutions for Temperature-Sensitive Fluids
,” J. Chem. Eng. Jpn.
, 30
, pp. 123
–136
.11.
Bird, R. B., Armstrong, R. C., and Hassager, O., 1977, Dynamics of Polymeric Liquids, Wiley, New York.
12.
Benjamin
, T. B.
, 1978
, “Bifurcation Phenomena in Steady Flows of a Viscous Fluid II. Experiments
,” Proc. R. Soc. London, Ser. A
, 359
, pp. 27
–43
.13.
Benjamin
, T. B.
, and Mullin
, T.
, 1981
, “Anomalous Modes in the Taylor Experiment
,” Proc. R. Soc. London, Ser. A
, 377
, pp. 221
–249
.14.
Aitta
, A.
, Ahlers
, G.
, and Cannell
, D. S.
, 1985
, “Tricritical Phenomena in Rotating Couette-Taylor Flow
,” Phys. Rev. Lett.
, 54
, pp. 673
–676
.15.
Berker, R., 1963, “Inte´gration des e´quations du mouvement d’un fluide visqueux incompressible,” in Handbuch der Physik, Vol. VIII/2, S. Flu¨gge, ed., Springer-Verlag, Berlin, pp. 1–384.
16.
Schlichting, H., 1979, Boundary Layer Theory, McGraw-Hill, New York.
17.
Cotta, R. M., 1993, Integral Transforms in Computational Heat and Fluid Flow, CRC Press, Boca Raton.
18.
Wendl
, M. C.
, 1999
, “General Solution for the Couette Flow Profile
,” Phys. Rev. E
, 60
, pp. 6192
–6194
.19.
O¨zis¸ik, M. N., 1980, Heat Conduction, Wiley, New York.
20.
Sokolnikoff, I. S., and Sokolnikoff, E. S., 1941, Higher Mathematics for Engineers and Physicists, McGraw-Hill, New York.
21.
Roache
, P. J.
, 1997
, “Quantification of Uncertainty in Computational Fluid Dynamics
,” Annu. Rev. Fluid Mech.
, 29
, pp. 123
–160
.Copyright © 2002
by ASME
You do not currently have access to this content.
