Convection regime flow in a vertical slot: continuum of solutions from capped to open ends

Abstract

In a recent publication Buhler (Heat Mass Transfer 39:631–638, 2003) reported new results for conduction regime flow between vertical differentially-heated walls that provide a continuum of solutions between capped and open ends. In this paper we extend Buhler’s work to realize a continuum of solutions of convection regime flow using empirical results for the vertical temperature gradient that develops in tall aspect ratio geometries. The mass flux is determined analytically for this three-parameter family of solutions. Identical viscous and thermal boundary layers exist at the opposing walls when the cavity is capped. However, as the flow evolves to one with open ends, there is an intensification (attenuation) of the boundary layers near the hot (cold) walls. In the limit corresponding to an open-ended cavity, the boundary layer at the cold wall vanishes altogether.