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Heat transfer warm air to cold water 1

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Paul Arthur

Mechanical
Jun 28, 2023
29
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
 
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Wouldn't the heat transfer from a person to the water be just based on the basic heat transfer equation:

Q = hAΔT

Where h is the convectuve heat transfer coefficient between human body and water which a value can be approximated
A is surface area of human body which can be estimated approximately
ΔT is 99.5 F - 50 F considering a constant delta T

Likewise tne same equation will give the flow of heat across the surface of the tank if you use the h-value for the water surface to air, A as surface area of top of tank, and delta T of water to air above.

If any water evaporates it would serve to cool the water so neglect this and your calculation will be conservative.

The hard part is selecting the right h-values but there are tabulated values or methods to calulate I believe for all convective heat transfer configurations in the literature.
 
OK Snickster,
lets explore that idea first in air where we know the heat lost from a lightly clothed human at rest is about 100W.
Say h for a human is about 5w/sqmK
Say 1.7sqm of surface area
Say 37.5degC skin
Say 22degC air
Q=5*1.7*(37.5-22)=129W
This would be for naked.
Considering light clothing, reduce h to say 4W/sqmK = 103W
OK not bad but here's the hard thing, what's the conductive h for a body in water?
If we knew that we would have the answer, but I can't find that.
Same problem for the surface of the water.
 
This is interesting:
Screenshot_2023-06-30_144412_slkgz5.jpg
 
Here's another approach:

A typical person's recommended daily caloric intake is about 2,000 kilocalories. But your guys are athletes, who eat a lot. So let's say 4,000 kilocalories per day.

4,000 kilocalorie --> 4.7 KW-H / 24 H --> 196 Watts
 
At 10degC, I'd guess metabolic rate is going to drop below basal as the body shuts down blood flow to the feet and hands and off skin surfaces in an attempt to conserve heat for core organ functions. They wont be sitting quiet in cold water at 10degC. Outdoor swimming pools are maintained at 22degC in comparison.
 
Hi Mint.....yes and that makes sense for someone in the air but not in the water.
Hi george.....not sure how that helps though
 
It make sense that the OP knows all about this and needs no further help.
 
3DDave
That's hardly helpful.
Yes, I do know a lot about this, more than most for sure.
There are still questions to be asked and issues to be considered though.
The discussion so far has been helpful even if it results in no answer being achieved.
That would just confirm to me that I'm not going bonkers.
Do you know the old saying, "if you don't have anything nice thing to say, don't say it"
 
So, if basal metabolic rate ranges 70-100W per person, my guess is design value for heat gain by cold tub at a chilly 10degC from body heat would be no higher than 50-70watts/person, not 250watts.
 
@Paul: You're answer seems to be here.
Overall-rate-of-heat-loss-during-whole-body-water-immersion-Water-Temperature-Conditions_zadzhn.png


@georgeverhese: BMR by definition applies while sedentary in air at 20ish degrees C. When immersed in cold water heat loss increases. A lot. In response the body tries to generate more heat to maintain temperature, and also tries to reduce heat loss by reducing blood flow to extremities, etc. If the body can't increase heat production and decrease heat loss by enough, then core temp starts to drop, until you die.
 
@mint,
So from this table, at 8degC (close enough to 10degC), for a 100kg person, we've got 116kJ/min heat loss into the cold water = 1930w, or roughly 2000w/person.
And at 20degC, closer to body temp at approx 30degC, it is still very high at 1640w/person, compared to the values from @paul and @IR. What gives here?
 
I can't quite work out the tables in that link but I think they weren't in the bath for very long.... Looks like less than a minute to me. Especially at 2C.

but then the recommendation is apparently 10-15 minutes max?

so maybe this is max cool down rate? So we are dealing with a transient thing here.

Paul,

I admire your desire to find these things out, but there are so many unknowns and variables here with respect to the human bod cooling, I'm not sure you're going to find it.

But you appear to have a working system - Can't you monitor and take measurements of cold water temperature, chiller water temp in / out and flow and work out the heat input when on one is in and then what happens when one or more get in?

Also measure how long each player spends in there.

I wish you luck though when you ask to take a rectal temperature measurement before and after.... [bugeyed]

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
 
"that makes sense for someone in the air but not in the water." isn't helpful.

Yes - heat loss is higher in water. What you don't seem to understand is that the maximum ability to generate heat is FIXED for any individual.

PEOPLE DON"T INCREASE THEIR LIMIT BECAUSE THEY ARE IN WATER. THEY REACH A MAXIMUM AND THEN THEY DIE.

So, look at the rate they can produce, which is, for continuous duty, less than 500 Watts IF THEY ARE WORKING VERY HARD.

Track bicycle riders for a several seconds or so, manage 750 Watts. Long distance riders manage ~500W.

But YOU ALREADY KNOW ALL OF THAT.
 
Google info indicates base metabolic rate at rest is about 70w/person, and this article says immersion in cold water at 14degC increases this by a factor of 3.5 to 250w.


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.
 
True - but that doesn't change the maximum heat produced from all-out athletic effort. Unless they are floating motionless the base rate isn't meaningful. What it mainly means is shivering to keep warm which cuts back on the athletic effort available.
 
Thanks for all of this guys and great to see your enthusiasm!
Let me think and digest all of this over the weekend and pick it back up Monday.
 
Hi Guys,
This is not going to be perfect, as expected, but I think is as good as I'm going to get re bather cooling loads.
It's based on mass as my previous post.
It assumes the bather is in for a short 3 mins and then gets out, heats back up and then gets back in after 3 mins. Typical of use.
Load_chuw7g.jpg
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This seems to correlate with my experience of using my own spa daily.
At 40degC water, the body would gain heat and not lose it. I would overheat at this temp and why spas should not be run at this temp.
At 35degC water, the heat lost is 58W which is close enough to how much a body needs to lose to keep it's temperature steady. I could stay in this water temp forever.
I feel cold in pools at 25degC unless I'm working out. This is why FINA controlled swimming events use this water temp. Heat loss shows at 292W.
Then at 10degC it shows as 642W which kind of seems high to me but, that's not a constant load on the water as they are only in the water for 50% of the time.
So, the load at 10degC on the water comes out at 321W which I think I'm comfortable with.
Unless anyone can see any glaring errors in this logic, then I'm done with this part of the post and the discussion has helped me heaps to clarify my thoughts.
Moving onto the "Heat transfer warm air to cold water" now.......
 
Hey 3DDave,
No, I don't work for them but why do you ask?
Paul
 
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