Inward solidification of Couette flow in an annulus with translating innercylinder

An analytical solution is presented for one-dimensional solidification of f ully developed, laminar Couette flow within an annular region with viscous dissipation. The solution is valid for small but non-vanishing Stefan numbe rs. A translating inner cylinder induces the shear-driven motion in the liq uid region. A closed-form expression for the instantaneous location of the solid-liquid interface is derived. In addition, expressions for the tempera ture distribution in the solidified region, temperature distribution in the liquid region, Nusselt number at the solid-liquid interface, and power per unit length are all derived as a function of pertinent dimensionless param eters. The analytical solution reduces to a classical result in the appropr iate asymptotic limits. (C) 2001 Elsevier Science Ltd.