Free surface convection in cylindrical geometries
Abstract
Free surface convection caused by density (Rayleigh) and surface tension gradients (Marangoni) in a gas liquid system are considered. The onset of such convection, the velocity and temperature profiles at onset, and the critical parameters that determine the onset of secondary flow are studied. A mathematical analysis is performed for a right circular cylindrical geometry with solid lateral boundaries, which are insulated to heat conduction and with the bottom plate at constant temperature. The classical Boussinesq approximation is invoked. The resulting momentum and energy equations are solved by solving for the velocity field in terms of an unknown temperature field equation and a nonlinear PDE for temperature results. Using the concepts of bifurcation theory, the properties of the nonlinear operator are investigated and the equation is linearized about the quiescent or linear conduction solution.
 Publication:

Ph.D. Thesis
 Pub Date:
 May 1978
 Bibcode:
 1978PhDT........21N
 Keywords:

 Cylindrical Bodies;
 Density (Mass/Volume);
 Free Convection;
 Interfacial Tension;
 LiquidVapor Interfaces;
 Boussinesq Approximation;
 Space Commercialization;
 Temperature Distribution;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer