Laminar natural convection in a discretely heated cavity .1. Assessment of three-dimensional effects

Two and three-dimensinoal calculations have been performed for laminar natural convection induced by a 3 X 3 array of discrete heat sources flush-mounted to one vertical wall of a rectangular cavity whose opposite wall was isothermally cooled. Edge effects predicted by the three-dimensional model yielded local and average Nusselt numbers that exceeded those obtained from the two-dimensional model, as well as average surface temperatures that were smaller than the two-dimensional predictions. For heater aspect ratios A(htr) less than or similar to 3, average Nusselt numbers increased with decreasing A(htr). However, For A(htr) greater than or similar to 3, the two and three-dimensional predictions were within 5 percent of each other and results were approximately independent of A(htr). In a companion paper (Heindel et al., 1995a), predictions are compared with experimental results and heat transfer correlations are developed.