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# Heat transfer

## Heat transfer

(OP)
Looking for a formula to calculate heat transfer to water.

Specifically: water temperature 45 degrees F, plastic tank with 600 gallons of water, constant room temperature.

Would like to adjust the variables to determine time and temperature of the water.

Considering pretreating the water prior to heating; temperature change a factor.

### RE: Heat transfer

(OP)
The water would be pretreated and temporarily stored in a tank. The water would eventually reach room temperature. I would like to be able to look at various scenarios; adjust the variables.

I would assume a constant room temperature and would want to determine how long it would take the water to increase x degrees.

The tank would be an 850 gallon plastic (polyethylene resin, 48" diameter); the surface area could also be a variable, as this specific tank would not be filled all the way.

### RE: Heat transfer

Take a course in heat transfer or read a Heat Transfer book

### RE: Heat transfer

Sound pretty similar to a test question I had back in the 60's about figuring out the time it would take to warm up a can of beer that was initially stored in a refrigerator. Yeah, there is no short cut here as I recommend that you follow willard3's advice.

### RE: Heat transfer

The basic natural convection heat transfer "formula" remains unchanged since Newton's time:

Q = htc * area * delta_temperature as a starting point.

However, transient analysis is substantially more complicated. Nevertheless, the problem as described yields a lower bound of 76 hrs to reach 65F in 70F ambient, but this is the ABSOLUTE best case, which is impossible to achieve, and assumes infinite thermal conductivity, fixed deltaT, and infinite mixing in the water, etc.

https://en.wikipedia.org/wiki/Convective_heat_tran...
https://en.wikipedia.org/wiki/Biot_number
https://en.wikipedia.org/wiki/Fourier_number
https://en.wikipedia.org/wiki/Thermal_diffusivity
https://hal.archives-ouvertes.fr/hal-00743917/docu...

TTFN (ta ta for now)
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### RE: Heat transfer

(OP)
IRstuff,

Thank you for the help.

### RE: Heat transfer

But it won't be a constant "room temperature" either unless you are in an internal air conditioned room/heated room.

Initial temperature is 45 deg F. What is your critical final water temperature - sounds like you are worried about the room heating up 600 gallons of chilled water, assuming the room is hotter than 45 degrees on most days In which case condensation of the room humidity will be a problem too - for draining off that condensed water on the plastic.

What is your proposed insulation thickness and plastic wall thickness of the 600 gallon container?

Is the water stagnant or moving? (Probably stagnant.)
Is the room air stagnant or fan-driven?

### RE: Heat transfer

(OP)
Internal conditioned space.
Initial temperature may vary 40-50 F
Tank is uninsulated
We anticipate that the water temperature will increase.
The question is how long would it take.
Eventually the water will be heated to 180 degrees for brewing beer.
The change in temperature would reduce the required BTUs.

### RE: Heat transfer

The time will easily vary by a factor of 2 based on the shape (diameter and length) of the 500 gal tank holding the (4150 pounds) water, and the orientation of the tank (vertical up in the air, on the floor, horizontal).

### RE: Heat transfer

(OP)
IRstuff,

That is true (BTU consumption); this will happen anyway when the water is processed/stored. It would reduce the number of tankless water heaters required.

racookpe1978,

The temperature of the slab would also be a factor; slab on grade, uninsulated.

Thank you both for the feedback.

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