Evaporative cooling and the Mpemba effect

The Mpemba effect is popularly summarized by the statement that “hot water can freeze faster than cold”, and has been observed experimentally since the time of Aristotle; however, there exist almost no theoretical models that predict the effect. With a view to initiating rigorous modelling activity on this topic, this paper analyzes in some depth the only available model in literature, which considers the potential role of evaporative cooling and treats the cooling water as a lumped mass. Certain omissions in the original work are highlighted and corrected, and results are obtained for a wide range of operating conditions—in particular, initial liquid temperature and cooling temperature. The implications and importance of the results of the model for experimental design are discussed, as are extensions of the model to handle more realistic 1-, 2- and 3-dimensional configurations.