Boundary layer solution for the RayleighBenard convection problem
Abstract
A solution of a RayleighBenard convection problem as a boundary layer problem using the method of matched asymptotic expansions (MAE) is described. Temperature and flow boundary layers are considered. It is shown that in the case with free boundary conditions no flow boundary layers occur. With rigid boundaries buoyancy effects are felt in the horizontal boundary layers even in the lowest order creating a flow boundary layer there. Temperature profiles for the boundary layers are obtained as series expansions in terms of temperature modes. Mode amplitudes may be determined, given the temperature profile at a nonsingular cross section of the boundary layer. The MAE, however, prescribes the initial temperature profiles for the layers in the corner, where the boundary layers become singular (infinite layer thickness). This difficulty can not be resolved within the framework of MAE, but a rational approximation to the solution can be devised.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 December 1983
 Bibcode:
 1983STIN...8429189Z
 Keywords:

 Asymptotic Methods;
 Boundary Layer Flow;
 Convection;
 Flow Equations;
 Boundary Conditions;
 Buoyancy;
 Corner Flow;
 Series Expansion;
 Temperature Profiles;
 Fluid Mechanics and Heat Transfer