Heat transfer warm air to cold water 1

[Paul Arthur]

Hi Guys,
I'm struggling with the calculation of the amount of heat a cold body of water, say at 10degC, will receive from warm air above, say at 30degC 50%rh.
I'm not worried about radiation at this time as this is indoors.
I want to consider evaporation and sensible heat transfer.
I'm also interested in the amount of heat a bather if submerged would give out to the water.
Any help would be gratefully received.
Cheers
Paul

 

[LittleInch]

Time to move on to surface loads?

Yes please - I can't wait after 60 posts already....

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Paul Arthur]

LittleInch I agree!

IRStuff
To quote you "I would use 350W, since that's supposedly the maximum sustainable power for a 30-minute duration"
How does that relate to the two options I have presented?

 

[Paul Arthur]

Guys,
Surface loads! Should be way easier.
Here are my thoughts on the exchange of heat between the water and air.
Evaporation Water at 10degC has a saturated water vapour pressure of 1227 N/sqm
Air at 30degC 50% rh has a vapour water pressure of 2167 N/sqm
Evaporation is therefore zero.
Radiation Indoor so not an issue.
Convection Assume low air surface velocities
Typical Free Convection Gas - Forced liquid (flowing) water is 5 - 15 W/m2K
Air Temp 30degC
Water Temp 10degC
Area 1sqm
Heat Transfer Coeff 10-15W/sqmK say
Q = Area*HT*(Ta-Tw) 200-300W/sqm
Thoughts please.
Thanks

 

[3DDave]

You will be condensing heated water vapor into the bath.

 

[Paul Arthur]

Agreed, but how do you calculate that I wonder?

 

[georgeverghese]

To get a ballpark estimate of water vapor condensation heat input, see my response on the 1st of July.

 

[3DDave]

It will also be condensing and running down off the chilled occupants. The amount will vary depending on the amount of air circulation and where it is moving.

I thought I wrote that this is putting a humidifier next to a dehumdifier and looking at the power required to run the dehumidifier. Obviously a very difficult situation to describe, much less analyze,

 

[LittleInch]

It's all about the surface air velocity.

But I think this will get you in the right ball park.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[Paul Arthur]

Hi George,
Did you mean this:
“I'd suggest heat pickup from condensation of water vapor in 30degC air at 50%RH at the air - cold water interface be estimated by assuming a cross current of say 5mm depth of 0.5m/sec of warm air, which goes from 30degC, 50% RH to 20degC, 50% RH at the other end of the cold tub.”
Not sure this is going to help. The air velocity over the water will be quite low <0.2m/s, the surface current will also be low as well.
I know this is a suggested approximation but I’m far from convinced.
Any comment on what I thought might be a solution?

 

[1503-44]

see

https://www.engineeringtoolbox.com/evaporation-water-surface-d_690.html

https://www.sciencedirect.com/science/article/abs/pii/S0378778810002665

https://www.sciencedirect.com/science/article/abs/pii/S0378778817325938

--Einstein gave the same test to students every year. When asked why he would do something like that, "Because the answers had changed."

 

[georgeverghese]

@Paul,
Okay, so use 0.2m/sec air velocity over the water surface.

Also note the external heat pickup over the side walls of this tub will also be by condensation of water vapor in the 30degC air, and the external condensing heat transfer coeff will be much more than that for plain natural convection - sensible heat transfer.

 

[Paul Arthur]

Thanks, and I'm going to go think about this and explore some other options.
Thanks for everyone's input.