Generalization of heat-transfer results for turbulent free convection adjacent to horizontal surfaces

Abstract

The common character of upward heat transfer in bottom-heated and internally heated fluid layers is demonstrated. This is accomplished by comparing their heat-transfer characteristics on the basis of a modified Nusselt number, defined in terms of an implicit length scale, in contrast to the conventional Nusselt number which contains the total layer depth. The implicit length scale is derived from dimensional considerations and depends only upon parameters relevant to the thermal boundary layer adjacent to the solid surface. The modified Nusselt number was found to have an extremely weak dependence upon the Rayleigh number, the variation being only two-fold over a 10 7-fold variation of Rayleigh number. More importantly, the heat transfer data for bottom-heated layers (i.e. Rayleigh-Bénard convection) were shown to be almost identical to those for internally heated layers. These results suggest that factors outside of the boundary layer, such as the method of heating, have little influence upon the heat-transfer coefficients of the two systems. The relationship between the implicit boundary-layer length scale used herein and the critical boundary-layer thickness used in the boundary-layer instability models of Howard and others is discussed. Least square correlation of the combined data for both bottom and internal heating is also presented.