Inward solidification of Couette flow in an annulus with translating inner cylinder

• Published in: International communications in heat and mass transfer Vol. 28; no. 6; pp. 857 - 866
• Main Authors: Hall, Carsie A., Russo, Edwin P., Mackie, Calvin
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Ltd 01.08.2001; Elsevier
• Subjects: Cylinders (shapes); Exact sciences and technology; Fundamental areas of phenomenology (including applications); Heat flow in porous media; Heat transfer; Heat transfer in inhomogeneous media, in porous media, and through interfaces; Interfaces (materials); Nusselt number; Physics; Solidification; Temperature distribution; Temperature distribution; Liquid solid interface; Nusselt number; Annular space; Shear flow; Heat transfer coefficient; Moving wall; Solidification; Laminar flow; Couette flow; Viscous dissipation; Analytical solution; Heat transfer
• ISSN: 0735-1933; 1879-0178
• DOI: 10.1016/S0735-1933(01)00289-5

An analytical solution is presented for one-dimensional solidification of fully developed, laminar Couette flow within an annular region with viscous dissipation. The solution is valid for small but non-vanishing Stefan numbers. A translating inner cylinder induces the shear-driven motion in the liquid region. A closed-form expression for the instantaneous location of the solid-liquid interface is derived. In addition, expressions for the temperature 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 parameters. The analytical solution reduces to a classical result in the appropriate asymptotic limits.