Optimal Ground Tube Length for Cooling of Electronics Shelters

This paper presents a theoretical, numerical, and experimental study to investigate the possibility of optimizing the configuration (geometry) of underground heat exchangers for maximum heat transfer. The first part of the study identifies a novel fundamental optimization principle for maximizing heat transfer between a tube and its surroundings, which is expected to be present in any buried tube heat exchanger design. The second part presents a practical application of the fundamental principle: a simplified physical model to determine the temperature field inside an electronics shelter that uses an earth-air heat exchanger and the soil as a heat sink. A volume elements methodology is employed to obtain a system of ordinary differential equations with time as the independent variable that combines principles of classical thermodynamics and heat transfer. This allows the computation of the temperature and relative humidity fields at every instant inside the shelter. The numerical results obtained with the proposed model are validated by means of direct comparison with experimental temperature and relative humidity measurements. It is shown that the tube length can be optimized such that the maximum temperature reached inside the shelter is minimal. The results also demonstrate the potential of the utilization of buried tubes for cooling electronic packages. Since accuracy and low computational time are combined, the model is shown to be efficient and could be used as a tool for simulation, design, and optimization of electronic packages cooled by underground heat exchangers.