Solidification of circular Couette flow with viscous dissipation

• Published in: The International journal of heat and fluid flow Vol. 22; no. 4; pp. 473 - 479
• Main Authors: Mackie, Calvin, Hall, Carsie A., Perkins, Judy A.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01.08.2001; Elsevier Science
• Subjects: Circular Couette flow; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Heat flow in porous media; Heat transfer; Heat transfer in inhomogeneous media, in porous media, and through interfaces; Laminar flows; Low-reynolds-number (creeping) flows; Physics; Solidification; Viscous dissipation; Circular Couette flow; Viscous dissipation; Solidification; Temperature distribution; Liquid solid interface; Nusselt number; Annular space; Pressure distribution; Velocity distribution; Heat transfer coefficient; Laminar flow; Couette flow; Coaxial cylinders; Rotating cylinder; Analytical solution; Heat transfer
• ISSN: 0142-727X; 1879-2278
• DOI: 10.1016/S0142-727X(01)00108-4

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.