warm and cool breath

Here, perhaps is another explanation:

http://www.uh.edu/engines/epi1796.htm
...Cooling soup is another matter. We purse our lips to raise the pressure of the air in our mouth. The temperature of exiting air drops and the air accelerates. That fast-moving air draws the surrounding room temperature are into it. The resulting jet is therefore close to room temperature when it passes over the much hotter soup. ...
http://www.uh.edu/engines/epi1796.htm

Oh, no. This is just as bad. Think about it: is raising the pressure of the air in your mouth heating it up? Does closing your mouth and pushing with your lungs burn your mouth? There is no significant temperature effect from the trivial pressure changes the human diaphragm can produce.

OTOH, cooling soup benefits from blowing b/c the rate of heat transfer is proportional to the temperature difference. As the air absorbs heat from the soup's surface, it heats up, and absorbs heat less slowly, until it's finally the same temperature. To speed up the process, keep funnelling body-temperature air across the surface, and it will always be drawing heat as quickly as possible.

This is the same principle as a radiator: keep the air flowing past, and it'll cool. Or convection cooling strategies, which work better on vertical surfaces than horizontal ones, because the air flow is continuous.

Or putting your hand out the car window and feeling the breeze.
According to the air pressure theory, the side with the pressure should be getting hot, right?

You need a lot more pressure for this to work. (It *does* work for falling objects - my understanding is that meteors and space shuttles heat up b/c of the air pressure buildup, rather than friction alone)
 
Here, perhaps is another explanation:

...Cooling soup is another matter. We purse our lips to raise the pressure of the air in our mouth. The temperature of exiting air drops and the air accelerates. That fast-moving air draws the surrounding room temperature are into it. The resulting jet is therefore close to room temperature when it passes over the much hotter soup. ...


Bingo, a fast moving stream quickly turns turbid, and slows while taking a greater volume of air along with it. a slow ,wide stream has much less mixing, and less transfer of momentum.
 

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