Mpemba effect

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The Mpemba effect is the observation that, in some specific circumstances, hotter water freezes faster than colder water.

The effect is named for its rediscoverer, the Tanzanian high-school student Erasto B. Mpemba. Mpemba first encountered the phenomenon in the classroom of Eugene Marschall at Mkwawa Secondary (formerly High) School, Iringa, Tanzania, where Mpemba was a student. Eugene Marschall, a member of the Teachers for East Africa/TEA program, taught chemistry and physics at this school from 1965 to 1967. Mpemba first noticed the effect in 1963 after his account of the freezing of hot ice cream mix in cookery classes, and went on to publish experimental results with Dr. Denis G. Osborne in 1969.

At first sight, the behaviour seems contrary to thermodynamics. However, most thermodynamicists believe that each observation of the Mpemba effect can be explained with standard physical theory. Many effects can contribute to the observation, depending on the experimental set-up:

Different definition of freezing (Is it the physical definition of the point at which water forms a visible surface layer of ice, or the point at which the entire volume of water becomes a solid block of ice?)
Evaporation, reducing the volume to be frozen. Evaporation is endothermic
Convection, accelerating heat transfers
The insulating effects of frost
The effect of boiling on dissolved gases
Supercooling. It is hypothesized that cold water, when placed in a freezing environment, supercools more than hot water in the same environment, thus solidifying the hot water faster
The effect of solutes such as calcium and magnesium carbonate.

According to an article by Monwhea Jeng, there is no unique explanation yet for why, in some specific circumstances, hotter water freezes faster than colder water. While interesting, the article makes no attempt to focus on the relevant transport phenomena concepts such as temperature and fluid flow fields. Indeed when temperature fields are introduced, the author states:

Analysis of the situation is now quite complex, since we are no longer considering a single parameter, but a scalar function, and computational fluid dynamics is notoriously difficult

This effect is a heat transfer problem, therefore well suited to be studied from a transport phenomena viewpoint, based on continuum mechanics. When heat transfer is analyzed in terms of partial differential equations, whose solutions depend on a number of conditions it becomes clear that measuring only a few lumped parameters, such as the water average temperature is generally insufficient to define the system behaviour, since conditions such as geometry, fluid properties and temperature and flow fields play an important role. The counterintuitiveness of the effect, if analyzed only in terms of simplified thermodynamics illustrates the need to include all the relevant variables and use the best available theoretical tools when approaching a physical problem.

Similar behavior may have been observed by ancient scientists such as Aristotle, and Early Modern scientists such as Francis Bacon and René Descartes. Aristotle's explanation involved a physical property he called antiperistasis, defined as "the supposed increase in the intensity of a quality as a result of being surrounded by its contrary quality". He used the concept of antiperistasis to provide evidence for his conjecture that human bodies and bodies of water were hotter in the winter than in the summer, a theory that was later disproved by Medieval and Renaissance observations.