blowing the hot soup

There exists such immense talent in the LG community. I will be a fool if I do not take advantage of this fact.

Blowing the hot soup usually will cool down the soup faster than not blowing. Furthermore, as we increase the blowing flow rate, we seem to increase the cooling rate. The present question is: will the curve (representing the cooling rate versus the blowing rate) exhibit a peak? Thank you folks in advance.

I'll give it a try:

When the flow rate is very high, you go from a liquid block of soup to a fractal gas of soup droplets and I'm not sure the notion of temperature and hence of cooling rate is well defined there.

Many factors make is a difficult problem:
- the convection of air around the vapor cloud above the soup,
- the convection inside the soup,
- the conduction in the metal of the spoon,
- the change in shape and increase of the surface of the soup,
- the difference between room temperature and lung temperature.

I guess it is not a linear problem, but I don't really see any cause for a peak in the curve, what did you have in mind?

Thanks, Carroll. The problem is indeed not too trivial. But let us try to look at it in a fundamental manner first. Couild we imagine the following analogy: the hot soup is like a relief station giving away bags of potatoes. The cold air flow (full with air molecules) blown by us is like homeless people lining up to receive these potatoes. It seems that the faster these folks take potatoes and leave, the faster the station will deplete the supply.

However, what if these people are being pushed away too quickly such that they do not even have enough time to reach out their hands yet?

There is another different mechanism that seems to suggest that a peak may exist. But let us study one mechanism at a time. :)

Just the description 'cooling down the soup with blowing' contains a few assumptions (for example the soup largely staying in the bowl) that will break down when the blowing velocity gets too large. I'd expect this to take place before for any reason a peak would be reached.

(Ignoring these problems one could argue at some point the heat generated by the friction between air and water will at some point even heat the soup. But I assure you: there won't be any soup left long before that happens. :-) )

I run out off puff long before such an air-flow limit.

However, my pet dragon has much bigger lungs...

Is it soup that is being blown or space itself in which soup is contained? If the second is the case, what if speed/rate of blowing (moving boundaries apart) is greater the the speed of light? What if soup is made of something that has negative pressure so that it actually is getting hotter while being blown? What if soup occupy whole space before it is started to be blown?

Ok. It seems it is high time to stop asking silly questions and go to sleep.

Googling Newton's laws of cooling should give you some information :-)

OK, gentlemen (and ladies?), no more hot soup from the kitchen. Let us consider a horizontal plate maintained at 80C. Let us blow (a) an airflow (at 20C) or (b) a helium flow (also at 20C) over this plate from left to right (in x direction) at a speed of 10 m/s. The plate is 0.1m long and is very wide, so that we can assume this problem to be two-dimensional. Some facts should be noted first:

(1) k_h > k_a (k: thermal conductivity; h: helium; a: air)

(2) j_0 = - kA(dT/dy)_y=0 (j_0: cooling rate at the plate in Watts; A: surface area. This equation is known as Fourier law)

Then, we seem to have a catch-22 problem (or a chicken/egg problem) here. We all know that the helium flow may induce larger cooling rates due to a larger k value. However, at the same time, dT/dy)_y=0 for the helium flow is also smaller than that of the airflow.

Question: These two factors (k and temperature gradient) oppose each other. Will there ever be a possibility that the former will be overwhelmed by the latter?

btw: thanks, David. j is also equal to hA(80 - 20) according to Newton's law of cooling, where h can be determined from j once j is determined.

I have an idea...ice cubes!

Rather than trying to compute the subject matter I did a direct experiment.

I took a high power air compressor and blew it on a small bowl of hot tomato soup. Turns out all the soup disappeared into thin air. Therefore, I shall assume that blowing extra hard will break the strong force of the nucleus and the soup will be sent into another dimension.

Obviously string theory at work here.

Or the air could have blown the soup out of the bowl. This will require further experimentation. I'll keep you all updated but my bet is on the string theory.

Thank you, mtbikesman, for your comment and for carrying out the experiment.

String theory? Perhaps you and I will be nominated for Nobel prize in particle physics soon. :)

Sorry, from your message, I cannot tell if you are joking or being serious. The problem presented in this post is largely macro-scale based.

If you contain the soup in some manner, so that it is guaranteed to stay in the bowl, I'd say at some point blowing harder will no longer cool down the soup. Instead, due to the friction between the air and the soup, blowing on it will actually make it hotter. Just imagine pouring the soup out from a rocket above our athmosphere. When it reaches the athmosphere at a very high speed, that will be the same as blowing on it with very high speed, and I'm pretty sure the soup would become very hot and evaporate rather quickly.

The moving current of air will cause lower air pressure over the surface of the soup, encouraging further evaporation which will cool down the remaining soup even more.

@mbikesman. In pursuing your string theory investigations, if you have to tie a knot, please make sure that it is not a granny knot.

Marius, I think that you are correct. Roughly, when the blowing speed is > 100 m/s, (or Mach number > 0.3), the heat due to the friction will become significant. To actually confirm your prediction computationally and experimentally can be a legitimate research topic sponsored by Norwegian Science Foundation. :)

David, I think that you are also correct based on the Bernoulli principle. However, we have to be careful when applying Bernoulli principle to our problems, which must be non-viscous flows.

Imagine a molecule of soup flying out of it. It brings away some kinetic energy with it, therefore the soup is cooled. However, with some probability (depending on pressure) the molecule will get knocked back into the soup.

Now the answer to the question depends on whether we are able to maintain pressure with increased blowing. If yes, then the soup will get hotter, because the molecules knocked back into the soup will bring a lot of kinetic energy that they got from collision with the air. But if not, then we have effectively blown all the air out of the room, creating a perfect vacuum. Then the soup will obviously get colder.

@David, it was a slip knot. Thus the soup "slipped" into another state of existence. BWA HA HA HA!

However, when I gave it more thought here is what I came up with.

Soup cools when it is in contact with air that is cooler than the soup. What affects the rate of cooling is the surface area of the soup and the temperature difference. The temperature difference does not increase when you blow harder.

The soup cools when you blow on it because you are constantly replacing the air with cooler air touching the surface of the soup. In a stagnant state the soup will heat up the air touching the surface and since the temperature difference between the soup and the stagnant air is less than when you blow on it it will cool at a slower rate.

If you blow hard or if you blow softly, you replace the contact air faster than the soup can heat it up and the soup will cool at the same rate.

Back to my first experiment. I found a mysterious red substance all over the walls and my cat was licking it up. So I got mad at the cat and put it in a box. Now the cat is neither dead or alive according to my physics text. I think it is haunted so I am not returning to this room for at least a few weeks. Hope the cat can survive on soup.

A nice video from Veritasium explaining why the soup gets colder: you remove the part with most entropy at the interface between (ordered) liquid and (disordered) vapor cloud...

A connection to your post on information theory: disorder or randomness is the information.

https://www.youtube.com/watch?v=7jT5rbE69ho around the end of the video.

See also Vsauce, "What is not random?" https://www.youtube.com/watch?v=sMb00lz-IfE.