Natural Convection in Shallow, Horizontal Air Layers Encountered in Electronic Cooling

Abstract

A numerical study of natural convection induced in a horizontal, enclosed air layer due to a discrete, constant heat flux source at the bottom surface is carried out in this paper. The nature of the transition from conduction to a cellular convection regime for this discrete-heating case is characterized. Multiple sources are also considered and the results are compared to those for a single source. The governing equations of continuity, momentum, and energy conservation are formulated for a two-dimensional layer. The important parameters are the overall aspect ratio (length/height of the layer), the ratio of source length to total length, and the Rayleigh number. The effect of varying these parameters is investigated, and heat transfer correlations are derived, for both single and multiple sources, in the form Nu s ∝ C (Ra)c> , where Nu s is the Nusselt number averaged over each source. The value of C is found to depend strongly on the aspect ratio and the source size. Based on the heat transfer results, the tendency of each geometric configuration to fully attain transition to the convection regime is evaluated. This can provide guidelines for maintaining certain critical dimensions that best exploit natural convection effects, in systems where fan-driven cooling is not available.