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Old Jun 11th 2014, 09:59 AM   #1
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fluid flow / heat question

I have a copper pipe dipped inside water while the air is flowing through the pipe. The water outside the pipe is at 30 degree celsius and air inside the pipe is at 45 (purpose being cooling air)

What I want to know using thermal conductivity (and anything else ) is the expected length of pipe I need to ensure that the air inside ultimately achieves complete thermal equilibrium with water as it travels further away in the pipe.

Pleasee suggest any directions or give suggestions. Any input is welcome.

For the sake of simplification, lets discuss 2 scenarios one in which air is not being forced and the other where air has a forced velocity.

the stuff I have calculated so far doesnt making much sense :s

q = 2 *pi* k* (dT) / ln(do / di) (1)
q = heat transfer (W) >> / unit length
A = heat transfer area (m2) >> 1 inch pipe = pi*0.0254
k = thermal conductivity (W/m oC) >> copper = 401
dT = temperature difference (oC) >> 15 degrees
do/di=ratio between outer/inner diameter >> 1.5


the above shows that only a metre of pipe is sufficient to extract 93KW of energy from the air :s, what am I calculating wrong or ignoring ? I think I need to take into account conductivity of air itself :s

please help..
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Old Jun 11th 2014, 01:10 PM   #2
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The problem is that you assume that the air is a constant 15 degrees warmer than the water. But as heat is extracted from the air it cools, so dT becomes less. If you assume that the air thoroughly mixes as it flows then the temp of the air cools as heat is extracted:

Delta T = Q/C_air

where C_air is the heat capacity of air. For for nitrigen C is 19.9 J/mol-K.
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Old Jun 11th 2014, 02:02 PM   #3
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@ChipB thanks & You are absolutely right, just realized temperature difference isn't constant but lets say if the temperature dropped 1 degree at a time in 15 steps then for that one degree : 1) most importantly how long would it take 2) how long does the pipe need to be .

p.s. btw i am aware that the rate of heat transfer varies with temperature difference but lets assume its constant for the sake of this question :s

Last edited by denisrud; Jun 11th 2014 at 02:08 PM.
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Old Jun 12th 2014, 02:12 AM   #4
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something else..

I was thinking that I should take into account thermal conductivity of air itself after all it is the substance being cooled.

The equation for convection can be expressed as:

q = hc A dT
q = heat transferred per unit time (W)
A = heat transfer area of the surface per unit length m2 /// pi*d/// pi*0.0254
hc= convective heat transfer coefficient of the process at 20 m/s /// hc = 10.45 - v + 10 v^1/2 /// hc=10.45-20+10(20)^.5= 41
dT = temperature difference /// 15 degrees

q=35*pi*0.0254*15=41 Watts !

I am confused! The one through metal shows 93000 and this shows 41 Watts, I might as well use iron instead of copper because the rate at which heat will flow from air to copper pipe will be miniscule compared to its thermal conductivity capacity! So according to the figures if I were going to extract 5kw of energy , I would need 121 meters of copper pipe, not to mention the huge probability of heat penetration from external environment ! Something is not right :s

I really hope I am wrong in this calculation otherwise this project will become unfeasible & I really wanted to do this in real...

Last edited by denisrud; Jun 12th 2014 at 02:41 AM.
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Old Jun 12th 2014, 08:03 AM   #5
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There are engineers whoo spend an entire career designing heat exchangers like this. I am not one of those engineers, but can offer the following:

First, heat transfer by convection is indeed a slow process. One way to speed it up is to increase the surface area of the pipe - in a heat ecxhanger that typically means multiple parallel pipes instead onf aone large pipe, and fins that provide more surface area.

Heat transfer by convection is not an exact science, as it depends on factors such as charecteristics of the air flow (laminar or turbulent). Consequently it's not clear to me that the formula for h_c you used is appropriate for this problem.

The fact that the copper pipe can transfer heat to the water quicker than the air delivers it is a good thing - otherwise the pipe would heat up and the air won't get as cool.

You have not said anything about the outside water - it conducts heat from the surface of the pipe through convection, and you need to consider whether it removes heat from the pipe wall at least as quickly as the hot air delivers heat into the pipe wall.

You originally said you want the air to reach thermal equilibrium with the pipe - do you mean you want it to exit at 30 degrees? You are probably aware that this would require an infintely long pipe. So I suggest you set a threshold exit temp that you are willing to live with, such as 35 degrees C.

Finally, at the nend of the day you're going to have to build a prototype and see how it behaves. This shouldn't be too difficult to do - since the cooling rate deoends on delta T between air and water you can run a controlled experiment using a small tub of ice water and room air pumped through a pipe coil, and see how the temp drop of the air behaves.
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