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Fully Non-Dimensional Nusselt Number Correlation for Transient Natural Convection in Tanks

A fully non-dimensional correlation for the Nusselt number associated to cooling processes in vertical storage tanks under laminar natural convection is presented. The derived correlation depends on the average temperature and can be used for the improvement of temperature profiles found from global methods. A Finite Volume method is employed using a transient bi-dimensional model in cylindrical coordinates and is experimentally validated. Forty cases of cooling with four aspect ratios, five overall heat transfer coefficients and two different volumes are considered. Thermal losses for the environment in all tank walls (top, bottom and sidewalls) are allowable. The Buckingham theorem is applied to determine the non-dimensional groups in the cooling of thermal reservoirs and the corresponding correlations, in agreement with the numerical results.