A quasi-steady analytical solution to freezing planar laminar Couette flow with viscous heating effects is presented. Closed-form expressions for the dimensionless freeze-front location, interface Nusselt number, and dimensionless power density (or dimensionless shear stress) are derived as a function of various dimensionless parameters. Several classical results are obtained in the appropriate asymptotic limits.

1.
Cheung, F. B., and Epstein, M., 1984, “Solidification and Melting in Fluid Flow,” in Advances in Transport Processes, A. Mujumdar and R. A. Mashelkar, eds., Vol. 3, Wiley, New York, pp. 35–117.
2.
Slocum, A. H., 1992, Precision Machine Design, Prentice-Hall, Englewood Cliffs, NJ.
3.
Luelf
,
W. C.
, and
Burmeister
,
L. C.
,
1996
, “
Viscous Dissipation Effect on Pressure Gradient for Laminar Flow of a Non-Newtonian Liquid Through a Duct of Subfreezing Wall Temperature
,”
ASME J. Heat Transfer
,
118
, pp.
973
976
.
4.
Huang
,
T.
,
Liu
,
S.
,
Yang
,
Y.
,
Lu
,
D.
, and
Zhou
,
Y.
,
1993
, “
Coupling of Couette Flow and Crystal Morphologies in Directional Freezing
,”
J. Cryst. Growth
,
128
, pp.
167
172
.
5.
Huang
,
S. C.
,
1984
, “
Melting of Semi-Infinite Region with Viscous Heating
,”
Int. J. Heat Mass Transf.
,
27
, pp.
1337
1343
.
6.
Bird, R. B., Stewart, W. E., and Lightfoot, E. N., 1960, Transport Phenomena, Wiley, New York.
7.
Alexiades, V., and Solomon, A. D., 1993, Mathematical Modeling of Melting and Freezing Processes, Hemisphere, Washington, D.C.
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