Is it possible to stir the tea so that it cools more slowly? I recently learned that stirring the tea with vertical movements speeds up the cooling process. As a result, I had a question, and whether it is possible to stir it so that it cools down, as slowly as possible. Conditions: the spoon is an aluminum tea spoon, take its shape as a rectangle, the temperature of the tea is 363K, normal environmental conditions.
 A: Stirring helps heat transfer (i.o.w. cooling) because it decreases the film thickness of the tea boundary layer with the cup and thereby increases the convection heat transfer coefficient $h$.
Stirring also ensures the tea is at homogeneous temperature, which maximises the temperature difference between the tea and the environment and this, in accordance with Newton's law of cooling, also promotes heat transfer.
So stirring always increases cooling rate. The only way to minimise cooling rate is to stir as slowly as possible.
Newton's law of cooling is formulated mathematically as:
$$\dot{Q}=hA\Delta T$$
where $\dot{Q}$ is the rate of heat transfer, $h$ is convection heat transfer coefficient and $\Delta T$ is the temperature difference between the tea and the environment.
A: There are more factors involved here.
Stirring in a way than causes turbulence does not have the same effect as stirring in circles, creating a vortex. Moreover, heat loss due to evaporation and surface radiation may or may not exceed heat loss due to wall contact, depending on environmental conditions and the choice of material the cup is made of.
In general, convection itself does not cool the tea down at all, unless it can make it flow out of the cup. Convection merely facilitates radiation, evaporation and conduction. In this sense, making the tea less temperature homogeneous by stirring the hotter tea away from the surfaces, may have an insulating effect. Vortex flow being known to concentrate heat in its center, like in a vortex tube, supports the possibility of this. I have however no knowledge of experiments in this respect.
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