The Boundary Layer Natural Convection Regime in a Rectangular Cavity With Uniform Heat Flux From the Side

Abstract

This paper summarizes an analytical and numerical study of buoyancy-driven convection in a rectangular cavity filled with fluid. The new feature of this study, suggested by architectural applications of the convection phenomenon, is the presence of constant heat flux heating and cooling along the vertical side walls. It is shown analytically that in the boundary layer regime the boundary layer thickness must be constant (independent of altitude), that the core must be motionless and linearly stratified, and that the vertical walls temperature must vary linearly with the same gradient as the core temperature. The Nusselt number (q″/ΔT)H/k was found to be equal to 0.34 (H/L)1/9 Ra2/9, where H/L is the height/length ratio and Ra = gβq″ H4/ (kαν). The second part of the paper presents a numerical study of the same phenomenon: the numerical results agree very well with the analytical predictions made in the first part of the paper.