# Why water cools from outside to inside?

It is a well-known fact that

Water kept in a container, on cooling, results in freezing with initially at the circumference of surface (1D), then on the surface (2D) and then throughout the volume (3D).

Why does it happen that way?

My attempt:

I thought that this may be due to their exposure levels.The outer surface is more exposed to cooling than the inner ones and hence cools first.However, I am not satisfied with this explanation.

I think there is some relation between this and degrees of freedom.I feel as there are more degrees of freedom in 3-D, there's more movement you should suppress to lower its energy, so maybe they freeze slower.

Is the above reasoning correct? I would also like to know different ways to reason out this.

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– user7951
Jul 4 '20 at 14:06
• I was thinking that more degrees of freedom in 3D would mean that the energy that needs to be suppressed in order to cool down the body is more.Idk if this is a valid argument.Can anyone confirm? Jul 5 '20 at 14:47

This has everything to do with heat conduction, Setting aside freezing or melting for the time being, the two things that are happening in combination are (1) heat conduction and (2) the capacity of a parcel of solid to store thermal energy by its temperature changing. Heat conduction is driven by a spatial gradient in temperature, with heat flowing from a hotter region to a colder region.

So if the outside surface temperature of an object is suddenly increased, the interior temperatures will not change at all initially, and the temperature gradient will be zero everywhere, except at the surface, at which it will be very high. This will cause heat to begin flowing into the very outer layer of the object. The heat that flows into this outer layer will cause its temperature to begin rising (to store at least part of the heat). This temperature rise will then create a temperature gradient for heat to begin flowing into the next layer inward, where its temperature will begin rising. This kind of sequence continues until, later, the temperature at the very center of the object begins to change. So, as a result of conductive heat transfer, the temperature rise propagates like a wave traveling inward into the object.

This can all be described mathematically and modeled by the so-called transient heat conduction equation.

• Thanks for giving this informative answer! What do you think about relating why this happens with degrees of freedom as I had mentioned in the question? Is that wrong? (Because I see none of the answers have any argument along those lines) Jul 5 '20 at 6:00
• I have no idea what you are getting at when you refer to degrees of freedom. If you mean that, usually with a 3D object, only part of the surface is exposed to heat transfer from the outside, that would reduce it to more of a 1d or 2D situation. If you mean that it is easier to heat and cool a 3D object if all ifs surfaces are exposed the heating and cooling. then that, of course, would speed up the heat transfer. Jul 5 '20 at 11:46
• I was thinking that more degrees of freedom in 3D would mean that the energy that needs to be suppressed in order to cool down the body is more.Idk if this is a valid argument. Jul 5 '20 at 12:46
• Sorry. I still don't follow. Maybe someone else can relate to this. Jul 5 '20 at 14:24

The cooling takes place at the surface provided that it is at a lower temperature than the interior, experimentally this is confirmed. The mechanism is by collisions between molecules transferring energy to one another, those with more energy transfer to those with less, this takes place in time and space and is macroscopically measured by the thermal diffusivity coefficient. We can describe this using Ficks' laws and an example is shown in the figure which I had recently calculated for other purposes. It illustrates what happens after a small circular region of a thin sample of absorbing material is excited by a laser. You can observe how the heat spreads both in time and space. The total energy remains the same so as the spatial extent increases the temperature at the centre falls but increases elsewhere. The circle shows the region initially heated.

(Ficks law was solved numerically $$\displaystyle \frac{\partial U}{\partial t}=D\left(\frac{\partial^2 U}{\partial x^2}+\frac{\partial^2 U}{\partial y^2}\right)$$ with $$D = 0.08 \;\mathrm{mm^2/s}$$ which is typical of many liquids.)

Definitely in agreement with Chet, but does this not also have something to do with increased nucleation sites at bounds of the container?

If a container of water was super cooled and a foreign object was introduced at the center of the container, we would observe freezing from the center outward.