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

 

[IRstuff]

the basal metabolic rate for a human is something like 70 watts. If they're exercising vigorously, the metabolic rate might pop up to 3x

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

https://www.youtube.com/watch?v=BKorP55Aqvg

faq731-376 forum1529 Entire Forum list

http://www.eng-tips.com/forumlist.cfm

 

[Paul Arthur]

Thanks IRstuff for responding.

Heat loss from humans to air is a simple thing, at rest is typically about 115W total made up of convection and radiation losses. This goes up to 440W with heavy activity.

This however doesn't apply if you are in a cold body of water at 10degC where the heat loss would have to be significantly more.

How much more I don't know and is part of my question.

 

[MintJulep]

Seems like this might be useful.

https://www.ashrae.org/news/esociet...-behind-the-new-indoor-swimming-pools-chapter

 

[Paul Arthur]

Thanks for that MintJulep,
ASHRAE's Natatorium section is useful for warm water pools but says nothing about cold water pools and chiller capacity required which we use for sports recovery.
I'm in the pool industry and know no industry guidelines on cold water pools and energy loads of same, hence my questions in this forum.

 

[IRstuff]

Q = -h * ΔT, where h is the effective heat transfer coefficient, ala Fourier's Law

To some degree, the body will compensate as much as humanly, or physiologically, possible to maintain core body temperature, by altering h, such as with vasoconstriction to minimize blood flow to the extremities, etc., of by increasing physical activity to generate more heat, i.e., changing Q or h to maintain T_core = T_ambient - (Q/h)

However, if the temperature difference is too large or exposure is too long, the body's ability to crank up heat generation or prevent heat loss is overcome, and hypothermia ensues.

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

https://www.youtube.com/watch?v=BKorP55Aqvg

faq731-376 forum1529 Entire Forum list

http://www.eng-tips.com/forumlist.cfm

 

[Paul Arthur]

Hi IRstuff,
Let me explain more.
I'm trying to establish the cooling load to maintain a large tub of cold water at 10deg and this will be in a warm humid room.
It's for a sporting club and part of their exercise routine.
A group of rather large men can jump into this water, stay there for a little while and then jump out.
The next group will do the same and this could go on for some time.
I have been allowing a heat gain from this bathing load of 250w/person but that's really an educated guess.
I understand already what you have stated but I'm trying to get a more accurate calculation of the load if that's at all possible.
This is of course only a minor part of the problem.
There are sensible heat gains through the walls and floor of the tub as well as to the water treatment plant. These are easy.
What's not easy is the people gain and the gains from the air above.
Paul

 

[LittleInch]

Well if this was a pipe with metal walls so essentially the same temp as the water you would be looking at about 20W/m2/K for convection.

Nothing will be precise as this sounds like a plunge pool / Ice bath type thing so you have an element of chilling the body of large men. Plus the splashing, dripping a they get in and out.

So as quite a bit of margin, say 25%

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

 

[Paul Arthur]

Yes, these are large cold tubs, not ice though and yes, it's a difficult problem.
I just want to get some sort of sensible steady state calculation together which uses the following parameters for body heat load:
- Average body size (weight)
- Water Temp
- Air Temp
- Air humidity
- Air velocity
- Output w/person
Paul

 

[LittleInch]

So if the square area is lets say 4m2 and you have 20 C difference, I would estimate from the hotter air you are getting about 1.6kW entering the water.

Adding a decent air velocity to this (indoors?) would increase it a bit, but then your poor large men would probably ger even colder when they get out dripping wet.

Don't know what you're thinking about for the other loads from the "rather large men" - Is this an American football team? - and the side walls and floor, but 5kW of colling doesn't sound unreasonable.

You will probably find though that your key parameter is how long does it take to cool this amount of water down within a reasonable time frame. Between 2 and 4 times the steady system heat loss / gain is not unknown to do it in say one hour. Getting this time frame right for your design is crucial so challenge this time frame when some one chucks out some random figure. But an hour in any sort of setting sounds about the right balance between cost of the cooling equipment and customer expectation / requirement.



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

 

[Paul Arthur]

LittleInch that's even more guessing than I'm already doing!
The Cold Tub is in fact 21 sqm and it's a football team full of 6' to 7' players 100kG+.
30kW cooling is a guaranteed solution and 15kW is definitely dodgy! Been there done that!
Cool down is not a problem as we keep the tub at the cold temperature 24/7.
I have calculations which does all of this lot but I'm just looking to fine tune the bathing heat load and water to air heat transfer.
It has to be calculable using various conditions as every project is different.

 

[LittleInch]

Keeping it cold is going to cost you plenty $$$ surely?

And you always need to cool it down once when you fill it.

Plus I imagine you need to empty it to clean it on a regular basis....

But that's my input. Most systems are about hot water versus cooler air as this is is a bit unusual.
"Fine tune" is going to be difficult. How many of the team enter at time is one variable. Plus how hot they are after running around or sitting on the side lines. How long do they stay in the pool for?

Is it important to get it it to +/- 1kW??

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

 

[IRstuff]

30kW cooling is a guaranteed solution and 15kW is definitely dodgy! Been there done that!

Seems to me that you are over thinking this. You have the above, so it would seem plausible to split the difference and come up with a better control scheme to minimize the power consumption. You say that 15 kW is dodgy, so ostensibly, the "un-dodgy" capacity is close to 15 kW, so 22.5kW would not be unreasonable, since it's more than 50% larger than the 15 kW. A better control loop would allow you to tailor the operation to account for increases, or decreases, in heat input. ACs work that way, and they're mostly sized based on rules of thumb

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

https://www.youtube.com/watch?v=BKorP55Aqvg

faq731-376 forum1529 Entire Forum list

http://www.eng-tips.com/forumlist.cfm

 

[Compositepro]

Heat transfer between warm air over cold water, will be close to zero because natural convection cannot occur. Any stirring of the water or air will increase heat transfer considerably.

 

[LittleInch]

In a completely still air velocity maybe, but that's not realistic.

But agree, might be less than "normal" convective heat transfer. Depends how significant this is compared to the other heat inputs.

Or add a thermal air cushion blanket on top when its not in use? same as any other hot tub or swimming pool.

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

 

[Paul Arthur]

Thanks for all of this but running costs is not an issue and the tubs are run at temperature 24/7.
These cold tubs are for large high level professional football teams and the tubs are kept at 10degC right next to a hot tub at 36degC, year round.
Covers are provided for when not in use but often not used.
They are rarely emptied as we treat the water with Ultra Fine Filtration, UV and chlorine.
We are however getting off topic here.
I'm just trying to get some sort of adjustable and semi accurate steady state calculation for a couple of the loads which are difficult.
Loads will include:
- People - up to 250w is my guess
- Evaporation - ???
- Convective - ???
- Sensible loads through the walls and floor - easy
- Water Treatment plant Sensible loads - easy
So, the responses here are a "good chat" but doesn't solve my problem.
I have been trying to find a solution to this problem for quite a long time but without luck.

 

[MintJulep]

Perhaps this study, or one of the similar studies listed at the bottom will have some useful information for you.

https://pubmed.ncbi.nlm.nih.gov/8900834/

An experiment to find the combined evaporation and convective loads seems relatively simple.

 

[Paul Arthur]

Lets talk about bather load more. Here is one solution that I cross check with:

INPUT
Specific heat of the bather (SH) 3.5 kJ/kgK
Body temp (BT) 37.5degC
Pool Temp (PT) 10degC
% of bather effected by temp change 30%
Mass of bather 80kg

CALC
kW=Mass*%*SH*(BT-PT)/60/60
kW=0.6kW

Then it's just a question of making a judgement over now many bathers and for how long over say a hour to provide an average load.
This might be 75% of the pools maximum capacity.
If the max were say 10 bathers that would come to an average load of:
kW= 0.6*10*0.75=4.5kW

Thoughts?

 

[MintJulep]

INPUT
Specific heat of the bather (SH) 3.5 kJ/kgK
Body temp (BT) 37.5degC
Pool Temp (PT) 10degC
% of bather effected by temp change 30%
Mass of bather 80kg

This just treats the people like a chunk of stuff. That's not the case. People generate heat internally.

 

[Paul Arthur]

I agree MintJulep and that's why I use it as a cross check only.
If you change the water temp to say 23degC @ 25% you get 300W which kind of makes sense to me given that in air at that temp the loss is say 120W.