Optimal Distribution of Discrete Heat Sources Under Mixed Convection: A Heuristic Approach

Steady state experiments are conducted in a low speed horizontal wind tunnel under mixed convection regime, for five discrete heat sources (Aluminum) of different sizes arranged at different positions on a substrate board (Bakelite), to determine the optimal configuration. The characteristic length of heat sources varies from 0.005 to 0.011 m. The optimal configuration is one whose maximum temperature excess (temperature difference between the heat source and ambient) is minimum among all the possible configuration of heat sources mounted on the substrate board, and is determined by a heuristic non-dimensional geometric parameter λ. The maximum temperature excess is found to decrease with λ, signifying an increase of heat transfer coefficient. In view of this, configuration with the highest λ value is the optimal one. The effect of surface radiation on the heat transfer characteristic has also been studied by painting the surface of heat sources with black paint, which reduces their temperature by as much as 12%. An empirical correlation is developed for the non-dimensional temperature excess (θ) by taking into account the effect of surface radiation. The correlation when applied for the highest λ to the configuration, returns the maximum value of θ at the optimal value, which is a key engineering quality that is sought in problems of this class.