A heuristic approach to optimal arrangement of multiple heat sources under conjugate natural convection

Steady state numerical computations and experiments were performed to study three-dimensional, conjugate laminar natural convection heat transfer from multiple identical heat generating modules (heat sources) in a vertical duct. The heat sources were mounted on a wall at different positions in a defined grid of 5 × 5 positions. Air is used as the cooling medium. The governing flow and energy equations were solved using FLUENT 6.3. The optimum geometric configuration of the five heat sources that maximizes the heat transfer was determined by the introduction of a dimensionless distance parameter and an exhaustive search. The heuristic procedure based on the geometric parameter was tested for varying number of heat sources and for different heat source strengths. Experiments were performed to study the effect of modified Grashof number and the duct spacing on maximum temperatures of different configurations in order to support the numerical findings. Additionally, the temperatures of the heat sources arranged in the optimum configuration obtained by the heuristic approach have been experimentally validated.