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# Heat Transfer rate question

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## Heat Transfer rate question

(OP)
It's been a while since I did heat transfer calculations and am posting hoping you guys can help me.

I have a tank that contains 6 gallons of water at 85C. There's a cooling coil in the tank that has a surface area of about 90in^2. The OD of the tube is. 313in and a wall thickness of. 029in. THe cooling coil has water flowing through it at 1 GPM at an initial temp of 30C. I need to calculate how long it will take to cool the water in the tank to 35C.

Thanks!

### RE: Heat Transfer rate question

Is the coil brazed or soldered to the tank?
Is the water in tank stirred?

Start by simply seeing how much heat you have to remove and how much cooling water flow that will take. If it will take a long time then that may be the limiting factor.
Then start estimating the resistance to heat transfer (ID surface film, tank and coil wall, coil surface film) and see how quickly you can remove heat.
Then you should have a feel for the worst case.

If the water isn't stirred and the coil isn't brazed to the tank then I would expect that simple natural convection from the tank would be a close approximation, a very long time.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

### RE: Heat Transfer rate question

Everything you need is in Process Heat Transfer by Donald Q. Kern. The solved differential equations are in the chapter on Batch and Unsteady State Processes.

It's in Perry's Chemical Engineers' Handbook too. Probably in others as well.

Good luck,
Latexman

To a ChE, the glass is always full - 1/2 air and 1/2 water.

### RE: Heat Transfer rate question

At that small a water volume (mass), the tank and water will lose a notable - probably significantly notable! - amount of heat energy through the tank walls to ambient temperature in the room. If outside, the answer will strongly depend on whether the small tank is in summerchange in temperature air, in nominal winter air, or in exposed sunlight in a hot environment (a probable heat gain)

So.

What is the inside and outside surface area of the tank? ( You can probably assume the tank areas are the same if wall thickness is small.)
Ambient air is stagnant or moving?
What is loss through the wall?
Insulated tank wall?
What is loss through insulation, if present?

Make some assumptions about inside water-to-wall coef, through wall coefficient (look up your wall material properties!), and the wall-to-ambient-air coef.

You are making things more difficult because your problem involves heat changes over time for a small volume of water and small mass of water, tubing, tank wall and ambient while analyzing only a small change in temperature. First, get more info!

### RE: Heat Transfer rate question

It also makes a big difference if the flow in the coil in the tank is from top to bottom or the reverse. Flow from bottom to top will cause faster cooling.

Also the temperature in the cooling tank will not be uniform unless you mix it. Cooling flow from from top to bottom will yield a more uniform tank temperature.

### RE: Heat Transfer rate question

You've got a transient event here, so there is no simple accurate answer available by an equation.

Depends how accurate you want the answer and what your access is to transient analysis.

How much movement of water there is in the "tank", what the coil looks like and how the thermal flow within your tank is will make a lot of difference.

Very basic, Just do this one minute segments.

Assume your 30 C water and your tank water all become the same temperature, whatever that is, prob about 75C?. That then becomes the start point to your new minute with another 1 gallon of water for the tank to heat up starting at 30C. This will be say 68C by the time it finishes. repeat until you get to 35C

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

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