Three-Dimensional Study of Combined Conduction, Radiation, and Natural Convection From Discrete Heat Sources in a Horizontal Narrow-Aspect-Ratio Enclosure

Three-dimensional natural convection flow and heat transfer were numerically studied for a three-by-three array of discrete protruding heat sources on a horizontal substrate in an air-filled, rectangular, narrow-aspect-ratio enclosure with length, width, and height ratio of 6:6:1. The governing equations for natural convection in air, coupled with conjugate conduction and radiation within the enclosure were solved using a finite volume method. The study examines the complex thermal interactions between the heat sources, substrate, and enclosure walls as affected by the thermal conductance of the walls and substrate with the intent of determining which physical effects and level of detail are necessary to accurately predict thermal behavior of discretely heated enclosures. The influence of radiation on the overall heat transfer is given particular attention. The three-dimensionality of the problem was evident in the overall flow characteristics and in the convective heat transfer edge effects on the heat source surfaces. Excellent agreement between temperature predictions on the heat sources and substrate and experimental measurements was obtained for modified Rayleigh numbers in the range of 9.7 × 105 to 1.6 × 107.