Does blowing hot air through cooler water, heat or cool the water?

Question

Inspiration for this question was a discussion about hot tubs in desert locations.

Supposed we have a mass of water with a temperature of 90°F. What is the effect on the temperature of the water of blowing dry air with a temperature of 100°F through the water?

As far as I can tell there are two physical processes with opposing effects on the water's temperature:

1. Dry air absorbs heat from the water through evaporation, and blowing air through the water increases the surface area for this evaporative cooling.

2. Hotter air heats the water through conduction.

My guess is that the former effect would tend to dominate the latter because the thermal mass of air is so low. But there must be some temperature differential at which the conduction overtakes the evaporative cooling. Can this differential be estimated without conducting practical experiments?

Answer 1

The answer is most likely a very strong "it depends", but I think evaporation effects dominate in general.

An evaporation rate calculator offers the following equation:

$$g_h=(25+19v)A\Delta H$$ where $g_h$ is the evaporation rate (in volume per time), v is the air velocity, A is the area of the surface, and $\Delta H$ is the humidity difference. I think key to this is the term $25+19v$. That term is going to have lots of nuanced interactions with how you bubble the air through the medium.

That all being said, I think the situation you describe is reasonably close to that of a swamp box, which cools a house to below-ambient temperatures by evaporating water. The fact that swamp boxes work suggest that in at least some of your possible scenarios, evaporation will dominate.