Modelling of natural convective heat transfer at an internal surface

The determination of accurate surface convective heat transfer coefficients (CHTC) to model the heat flow within building interiors is of primary importance due to the effect of convection on the thermal comfort and the overall energy consumption of a building. Numerous theoretical and experimental expressions aiming at modelling the convective heat exchange of buoyancy-driven flows along vertical surfaces have been proposed. However, the case of a uniformly heated surface is not as exhaustively treated as that of the isothermal surface despite its relevance in many situations within building interiors. This paper is concerned with laminar and turbulent heat transfer modelling at internal vertical building surfaces (walls, windows, …) uniformly heated. Expressions of both local and average CHTC are derived from a theoretical analysis based on the integral formalism. A simplified expression of the average CHTC is then given as a function of the convective heat flux density (or the average temperature difference) and tested for building simulation purposes. The theoretical results are shown to be in close agreement with Alamdari and Hammond [F. Alamdari, G.P. Hammond, Improved data correlations for buoyancy-driven convection in rooms, Building Services Engineering Research & Technology 4 (1983) 106–112] improved correlation, as well as with experimental data derived from measurements performed on real-size enclosures. Despite the three-dimensionality and limited size of full-scale rooms, less than 10% difference is observed.