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 for five discrete heat sources (aluminum) of nonidentical sizes arranged at different positions on a substrate board (bakelite) to determine the optimal configuration. The optimal configuration is one for which the maximum temperature excess (difference between the maximum temperature among the heat sources of that configuration, and the ambient temperature) is the lowest among all the other possible configurations and is determined by a heuristic nondimensional geometric parameter λ. The maximum temperature excess is found to decrease with λ, signifying an increase in heat transfer coefficient. In view of this, the configuration with highest λ is deemed to be the optimal one. The effect of surface radiation on the heat transfer characteristic of heat sources is also studied by painting their surface with black, which reduces their temperature by as much as 12%. An empirical correlation is developed for the nondimensional maximum temperature excess (θ) in terms of λ, by taking into account the effect of surface radiation. The correlation when applied for highest λ of the configuration returns the minimum value of θ at the optimal condition, which is a key engineering quantity that is sought in problems of this class.