Free surface convection in a bounded cylindrical geometry
Abstract
Surface tensiondriven convection and buoyancydriven convection in a bounded cylindrical geometry with a free surface are studied for a range of aspect ratios and Nusselt numbers. The thermal convection is in a liquid layer contained in a vertical circular cylinder with a single free boundary, the top surface, which is in contact with an inviscid gas phase. A different method is also developed for analyzing free convection problems using Green's functions, reducing the problem to the solution of an integral equation. Linear theory and some aspects of a nonlinear analysis are utilized to determine the critical Marangoni and Rayleigh numbers, the structure of the convective motion, the direction of flow, and the nature of the bifurcation branching.
 Publication:

International Journal of Heat and Mass Transfer
 Pub Date:
 September 1981
 Bibcode:
 1981IJHMT..24.1513V
 Keywords:

 Convective Heat Transfer;
 Cylindrical Tanks;
 Flow Geometry;
 Free Convection;
 Interfacial Tension;
 Numerical Flow Visualization;
 Branching (Mathematics);
 Buoyancy;
 Linear Equations;
 Rayleigh Number;
 Stream Functions (Fluids);
 Temperature Distribution;
 Fluid Mechanics and Heat Transfer