A numerical study is carried out to investigate the influence of discrete heat sources on natural convection heat transfer in a square enclosure filled with air. The enclosure has two vertical boundaries of height H; one of them is cooled at Tc and the other has discrete heat sources [isoflux (q = c) or isothermal (Th = c)]. The enclosure has two horizontal adiabatic boundaries of length L. Results are reported for 0 ≤ Ra ≤ 106, Pr = 0.72, A = 1, aspect ratio ε, the relative size of the heat source to the total height, lies in the range 0.25 ≤ ε ≤ 1 and the discrete heat sources are located at the top or the bottom of the enclosure. Verification of numerical results is obtained at Ra = 0 (conduction limit) with analytical conduction solutions. In addition, a comparison with experimental and numerical data is made which also shows good agreement. The relationships between both Nu, ΔNu (change of thermal conductance) and Ra based on scale length (the size of the heat source S divided by the aspect ratio A) are also investigated here. A relationship Nu and Ra, based on scale length obtained from analytical solutions is correlated as Nu = Nu(Ra, ε). In addition, extrapolation correlations of Nu over the very high range of Rayleigh numbers (Ra ≥ 108) are developed.

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