Solidification of circular Couette flow with viscous dissipation
A semi-analytic solution is presented for the solidification of laminar circular Couette flow within a one-dimensional annular region with a rotating outer cylinder and stationary inner cylinder. Viscous dissipation in the liquid is taken into account. Closed-form expressions for the dimensionless t...
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Published in | The International journal of heat and fluid flow Vol. 22; no. 4; pp. 473 - 479 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
New York, NY
Elsevier Inc
01.08.2001
Elsevier Science |
Subjects | |
Online Access | Get full text |
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Summary: | A semi-analytic solution is presented for the solidification of laminar circular Couette flow within a one-dimensional annular region with a rotating outer cylinder and stationary inner cylinder. Viscous dissipation in the liquid is taken into account. Closed-form expressions for the dimensionless temperature distribution in the solid and liquid regions, Nusselt number at the solid–liquid interface, dimensionless power and torque per unit length, dimensionless steady-state freeze front location, and dimensionless pressure distribution in the liquid are derived as a function of liquid-to-solid thermal conductivity ratio, Brinkman number, annulus radius ratio, and Stefan number, which is assumed to be small (<0.1) but non-vanishing. The instantaneous dimensionless solid–liquid interface location is determined using numerical integration. The results show that the power and torque requirements can increase by a factor of greater than seven for a thin-gap annulus (radius ratio >0.9). It is also shown that the size of the liquid region within the annular gap has a more controlling influence on the solidification rate at latter times (when the Brinkman number is small) while a Brinkman number of order unity has a dominant influence at earlier times. |
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Bibliography: | ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0142-727X 1879-2278 |
DOI: | 10.1016/S0142-727X(01)00108-4 |