Axisymmetric convection in a cylinder
Abstract
The geometrical properties of axisymmetric convection in a Boussinesq fluid contained in a cylindrical cell with free boundaries are investigated. The range of unsteady behavior requiring a full three-dimensional solution of the governing equations is not considered. The solution near the critical Reynolds number is obtained from a perturbation expansion. For values of the Nusselt number not greater than 2, solutions are obtained from an expansion in a finite number of vertical modes. For Prandtl numbers less than unity the solution becomes independent of the Prandtl number at large Reynolds numbers. As the Prandtl number approaches 0 the Nusselt number is a function of the Rayleigh number only and there is an effective critical Rayleigh number equal to 1.32 times the critical Rayleigh number. Numerical results obtained for Rayleigh numbers up to 100 times the critical Rayleigh number and Prandtl numbers not in excess of 0.01 are similar to those for two-dimensional rolls. For Prandtl numbers greater than unity there is a viscous regime. At high Rayleigh numbers a large isothermal region develops in which the ratio of vorticity to distance from the axis is almost constant.
- Publication:
-
Journal of Fluid Mechanics
- Pub Date:
- January 1976
- DOI:
- 10.1017/S0022112076001407
- Bibcode:
- 1976JFM....73..353J
- Keywords:
-
- Axisymmetric Flow;
- Benard Cells;
- Boussinesq Approximation;
- Convective Flow;
- Three Dimensional Flow;
- Boundary Value Problems;
- Convective Heat Transfer;
- Cylindrical Bodies;
- Nusselt Number;
- Perturbation Theory;
- Prandtl Number;
- Rayleigh Number;
- Fluid Mechanics and Heat Transfer;
- CONVECTION;
- THEORY