## The Mpemba effect

Can hot water freeze more quickly than cold water? Of course, when you pose a question as absurd on its face as that, the answer is going to turn out to be yes.

This phenomenon is called the Mpemba Effect, after the Tanzanian high school student who observed it.

In the demonstration video above, I thought that the near-boiling water froze more rapidly because when it was thrown up in the air, it dispersed into smaller particles of steam or vapour (I’m not sure why this happens, but there are videos showing people emptying containers of boiling water in Antarctica, only to have the water go up in vapour before any of it hits the ground). Despite having a higher initial temperature, these smaller particles are much easier to freeze due to the greater overall surface area to volume ratio. On the other hand, the cold water comes out as one body of water.

While that was probably one contributing factor, the same effect is achieved if you place two containers of hot and cold water into a freezer without disturbing them. So, it turns out that the answer is not quite so simple. Wikipedia says:

According to an article by Monwhea Jeng: “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 (CFD) is notoriously difficult.”This effect is a heat transfer problem, and 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.