Transition from Single-to Multi-Cell Natural Convection of Air in Cavities with an Aspect Ratio of 20: A Thermodynamic Approach

Abstract

Transition from mono-cellular to multi-cellular flow in differentially heated cavities with an aspect ratio of 20 is revisited. Our numerical model is based on the Boussinesq equations, modified for including the work of pressure forces. In high enough cavities, this work has significant effects and results are changed. The Nusselt number is increased while convection is reduced, moreover all transitions are delayed. A thermodynamic analysis of transition is developed. The analysis shows that, after transition, the multi-cellular flow topology tends to decrease altogether viscous friction and work of buoyancy forces. In other words, transition weakens its own cause. This is why a threshold exists.

Keywords

• natural convection, numerical model, thermodynamics, irreversibilities