High Rayleigh Number Convection in Shallow Enclosures with Different End Temperatures

Buoyancy-driven laminar convection in shallow horizontal enclosures (width/height ⪢1) with adiabatic horizontal walls and isothermal vertical walls of different temperatures has been investigated for very high Rayleigh numbers (Ra ⪢ 10⁶). It is found that this flow regime, which is characterized by boundary layers lining both the vertical and horizontal walls, differs qualitatively from the low-Ra flow regime, in which the horizontal boundary layers are absent. The decreasing influence of Ra on the Nusselt number and the effect of the aspect ratio are analytically shown and then numerically verified. Comparison is made with existing experimental and numerical data, and a new correlation is proposed for the Nusselt number in this flow regime. An explanation is also advanced regarding the current controversy about the power dependence of the Nusselt number on Ra in narrow vertical channels.