AbstractThe 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 cold‐storage 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.