Solidification of circular Couette flow with viscous dissipation

A semi-analytic solution is presented for the solidification of laminar cir cular Couette flow within a one-dimensional annular region with a rotating outer cylinder and stationary inner cylinder. Viscous dissipation in the li quid is taken into account. Closed-form expressions for the dimensionless t emperature 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 pressu re distribution in the liquid are derived as a function of liquid-to-solid thermal conductivity ratio, Brinkman number, annulus radius ratio, and Stef an number, which is assumed to be small (<0.1) but non-vanishing. The insta ntaneous dimensionless solid-liquid interface location is determined using numerical integration. The results show that the power and torque requireme nts 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 wit hin the annular gap has a more controlling influence on the solidification rate at latter times (when the Brinkman number is small) while a Brinkman n umber of order unity has a dominant influence at earlier times. (C) 2001 El sevier Science Inc. All rights reserved.