The direct-contact heat transfer to a dispersed population of immiscible evaporating droplets is analyzed. Also studied is a population balance formulation for the distribution of two-phase bubbles, which is similar to that utilized in particle and droplet dispersion analysis and is capable of including bubble coalescence and break-up. It is shown that the method of classes is useful particularly in solving such problems when the growth functions are size-and time-dependent and nonquadratic. The method is applied to a liquid cool-down, representing the initial chilling stage of a direct-contact batch crystallizer or coldstorage unit wherein a vessel containing a liquid is chilled by injecting a dispersion of refrigerant droplets. Transient bubble population characteristics, volumetric heat transfer coefficient, total heat transfer, and liquid temperature are predicted, along with the liquid refrigerant holdup.
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