Axisymmetric natural convection-driven evaporation of hot water 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. This paper considers experimentally and theoretically the cooling of a circular pool of water. A model is derived that takes into account conduction, natural convection, evaporation and thermal radiation. The governing equations are nondimensionalized and asymptotically reduced to yield a one-dimensional moving boundary problem that is solved numerically. Whilst the model may need some refinement in the future, the preliminary results are encouraging, indicating that it can predict the occurrence of the Mpemba effect.