Convection in a vertical slot

A boundary-layer approximation is used to describe the convective regime in a laterally heated vertical slot at large Prandtl numbers. The determination of the core flow requires the solution of the vertical boundary-layer equations in a rectangle, subject to appropriate boundary conditions on each of the four walls. Solutions based on a spectral decomposition in the vertical direction allow a comparison with experimental and numerical results, and an appraisal of an approximate solution frequently used as a basis for stability studies. Both the numerical results and an approximate stability argument lead to a simple criterion for the appearance of multiple rolls in the slot which appears to be in good agreement with experiments.