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

 

[Paul Arthur]

But where did you come up with S + A?
Sounds like you are stalking me
That's why I just changed my user name

 

[3DDave]

Yeah. That's the problem - a company that specializes in swimming pools in Australia has a user with same name as that company founder and president. LOL

So, either you are Paul S. or you are stealing his identity. Either way, don't care.

As I previously predicted, you already had an answer for the immersion part of the question, one which has been weirdly drawn out and is not what I would expect from an engineer, hence my interest in the actual source. Often this sort of question is from some marketing guy who is trying to cope with convincing a customer he has experience.

You did fail to mention the duration - during which metabolic output of the Bather is insignificant because the goal is a body-sized cold pack to reduce surface muscle temperatures. Basically the same as a sack of raw meat.

Here's a better way of phrasing the second part:

I have a humidifier and a dehumidifier in a small room. How much water can the dehumidifier remove per hour? The humidifier can provide unlimited water vapor to support some temp and some RH. The film thickness is guaranteed to be zero.

 

[Paul Arthur]

Hi Dave,
Not worried, I don't work for that company, I own it . I would appreciate it if you would remove the company name though and I'll do the same.
I'm always questioning what I do and exploring what others might think and some would say, I'm not your ordinary engineer!
I'll turn my mind to the heating of the water from the air tomorrow.

 

[3DDave]

Sure, as a favor to you Paul. Anything to help. LOL.

 

[Paul Arthur]

Thanks, I'm well known here so removing the country also would help keep my anonymity.
Air to water tomorrow!

 

[georgeverghese]

Paul,
I happen to go the 50m pool at Bexley North once a week - this pool appears on your company website. Its a bit chilly these days, but the water is manageably warm. Its closed for 2 weeks for Council managed maintenance work.
Best of luck with your work.

 

[IRstuff]

Sorry, but what you show is not valid for the problem you present:

> the specific heat of the body isn't relevant, since this isn't a bulk material heat transfer problem
> you essentially have perfect heat transfer, since you don't use a heat transfer coefficient anywhere, for either the body or the water
> the deltaT is overly large, since there are actually multiple temperature differences -- core body temperature to extremities, and skin and skin to water
> the usage of the delta temperature in your equation implies the body is dropping 30%*(37.5-10) or 8.25 C change in body temperature; that large a body temperature change would reduce the delta temperature and the amount of heat loss.

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[Paul Arthur]

All interesting points IRstuff but, we don’t have the answers to what you have quoted.
I’m not convinced a suitable heat transfer coefficient of a cooling body to water exists.
Also I’m not trying to simulate the body cooling as it will but, the body will start to react and produce more energy to compensate.
As I said, it isn’t perfect as there are too many unknown factors but it is what it is and it seems to correlate to my own experience of water temperatures.
If you have a better way of doing it, please put the formulas down and let me analysis it.

 

[Paul Arthur]

Hi George,
Good to hear Bexley is still performing!

 

[LittleInch]

The heating from the air bit is going to be very sensitive to air flows and velocity from other things like fans and A/C units not to mention the effect of large men getting in and out.

In a perfectly still room with sides on the pool, you could easily get an insulating layer of air on top of the pool in the same manner as a floating cover filled with air.

Any sort of disturbance of that layer and you're going to get heat transfer, but still probably a bit less than my 20W/m2/K. so maybe 5 or 10.

But can't you just measure this overnight?
With a cover and without a cover.

too many variables and assumptions will be needed and even then you'll be 50% out.

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

 

[Paul Arthur]

It seems I’m not the only one who is interested in heat loss from a human in cold water!

https://physics.stackexchange.com/questions/371642/heat-loss-through-skin-into-water

In that post they use the simple equation H=K⋅A⋅ΔT/Δx,
where:
H is heat loss,
K is the thermal conductivity of skin (0.3Wm⋅K, according to this page),
A is the surface area of a human (1.7m2, according to this page),
ΔT is the temperature difference (37−20=17), and
Δx is the thickness of the skin (∼1mm, according to this site).
At a water temp of 20degC that came to 8760W. I don’t think so but it’s an alternative way of going about the problem.

 

[Paul Arthur]

On further investigation, I found a thermal model in this paper P3, which tries to work out survivability in cold water.

https://www.worldscientific.com/doi/pdf/10.4015/S1016237205000251?download=true

Anyone have a view on this approach? Worth doing some sums I think?

 

[LittleInch]

Looks pretty good to me.

Note at 10C in uninsulated conditions like a plunge pool the "survival" time is only 4 minutes....

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

 

[MintJulep]

According to

https://link.springer.com/article/10.1007/s11517-017-1657-3

"Modelling accidental hypothermia effects on a human body under different pathophysiological conditions"

The reference convective heat transfer coefficient between water and skin (h c o n,o u t ) is assumed to be equal to 0.100 W/(K c m 2) (corresponding to “treading water” condition)

 

[LittleInch]

Are you sure? That's 1kW per m2 per Kelvin.

Humans are apparently about 1.7m2



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

 

[IRstuff]

Paywalled

https://pubmed.ncbi.nlm.nih.gov/19340696/#:~:text=The measurements of the thermal,1) K(-1)).

The measurements of the thermal properties of biological tissue samples are based on a transient method. Thermal property measurements show that subcutaneous fat has the lowest thermal conductivity (0.23 W m(-1) K(-1)), while muscle gives the highest values (0.46 W m(-1) K(-1)).

However, that's not necessarily the issue. The question is what is the power output from the body given an internal physiological response to prevent hypothermia to the body.
BTW, the stack exchange cite results in a silly answer because equations cannot be arbitrarily used willy-nilly. The poster used a thin layer of skin as the heat transfer medium and got kW of transfer for their trouble, but as the responders point out, you don't have an infinite heat source behind that layer of skin, so the power value is only valid for about 20 seconds of exposure, which can be verified by calculating the total thermal mass of the volume (I used water at 27.5 C) of skin divided by the 8670 W. After that, the heat must come from the internal structures of the body, so if we assume muscle, then about 0.46 W/m-K thermal conductivity

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[IRstuff]

Nevertheless, while all of that is interesting, it's a bit moot. Any power the body generates must express as mechanical work or heat output, and it has to all leave the body. Therefore, if you assume a maximum of 350W per body, that's all that you really to know; how it gets into the water is moot. I would use 350W, since that's supposedly the maximum sustainable power for a 30-minute duration

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[3DDave]

This is a 3 minute transient response. The goal is to produce no more than the minimum heat while the muscles are cooling and the blood vessels are contracting. They are heated above normal from exercise or a hot tub and are jumping into a cold tub to offset the damage.

Another approach to "cold therapy"

https://www.npr.org/2011/10/15/141336088/cryotherapy-why-pro-athletes-like-it-chilly

Seems like a gimmick, but I guess it sells.

 

[Paul Arthur]

A ran the numbers using the total skin resistance and got the following results:

Works out to be less than the Mass method I posted earlier.
I need a calculation for different water temperatures so can't just use a single figure of say 350W.
The mass calc is more conservative @ 321W average whereas the R method comes in at 202W average.
I'm inclined to stay with the mass calc, what do you think? Time to move on to surface loads?

 

[IRstuff]

The body beneath the skin is neither an infinite heat source nor is it infinitely conductive. As I indicated earlier, the muscle tissue that would be under the skin has a thermal conductivity of 0.4 W/m-K

TTFN (ta ta for now)
I can do absolutely anything. I'm an expert!

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