A semi-analytic solution is presented for the solidi®cation of laminar circular Couette ¯ow within a one-dimensional annular region with a rotating outer cylinder and stationary inner cylinder. Viscous dissipation in the liquid is taken into account. Closedform 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 in¯uence on the solidi®cation rate at latter times (when the Brinkman number is small) while a Brinkman number of order unity has a dominant in¯uence at earlier times.