How Much Air Is Needed to Cool Water in a Copper Tube?

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To cool water in a copper tube from 70°C to 35°C in under two minutes, approximately 250 W of cooling power is required. The water is flowing through a 3/8" diameter pipe, and the user can adjust the flow rate to dispense 8oz of water in the specified time. Ambient air temperatures range from 22-27°C, which will influence the cooling efficiency. To determine the necessary airflow, the specific heat of air and the desired temperature change should be calculated, factoring in a safety margin. The discussion highlights the need for a fan system to maintain consistent cooling as water flows through the tube.
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I was asked to determine how much Air is needed to cool a copper tube. The air will be blowing on the outside surface of the tube as there will be water running through the tube.

The starting temperature of the water will be 70°C and the goal end temperature is 35°C...all done in less than 2 minutes. I already know that it will take ~250 W to do this; however, how would I determine the amount of air needed? Am I looking for the velocity of the air to cool it? If so, what equation should I use to solve for this?

I won't be able to have room temperature water available to cool the solution, neither will I be able to use ice. This needs to be repeated on command, so I'll need a fan that will kick on to cool the piping as the 70°C starts flowing through.

As you can see I'm quite rusty on my heat transfer and thermodynamics. It doesn't help that I can't find my textbook from when I was in school either!
 
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A few questions:
  • Is the water flowing through the pipe or is it being stagnantly held in place? If it's flowing, at what velocity?
  • What's the length and diameter of the pipe?
  • What temperature is the ambient air at?
 
If you know the required power you can simply multiply the desired airflow by the specific heat of air and desired delta-T... then add a safety factor.
 
Sorry about that. I'll answer your questions in order...

1. The water is flowing through the pipe, but the velocity is not determined yet. I can make it as fast or slow as I want so long as I can dispense 8oz of water in 2 minutes which is what I need to cool (sorry for leaving that important fact out).

2. The pipe is 3/8" diameter and right now it's in an aluminum box that's 5"x6"x1.5". I can have copper tubing leading into it as well though.

3. The ambient air is at 22-27 deg C

ddelaiarro said:
A few questions:
  • Is the water flowing through the pipe or is it being stagnantly held in place? If it's flowing, at what velocity?
  • What's the length and diameter of the pipe?
  • What temperature is the ambient air at?
 

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