# Heat transfer from copper coil

## Main Question or Discussion Point

Hi,

I am currently doing my final year project in college. I am using a copper pipe which is 8m long with 8.5mm ID and 10mm OD. The pipe is bent into a coil which will be placed inside a acrylic box. The aim is to pump water through the coil to get the box to a desired temperature. At the moment I am trying to characterise the coil. For testing, the coil is left out of the box and is subject to ambient air temperature of ~20 degrees. I need to know the relationship between temperature transfer from the coil i.e. power output from the coil when different flow rates and water temperatures are applied. Any help would much be appreciated. I need to develop a transfer function that can be implemented into a Simulink model.

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Hmmmm, well, as for the internal convection, you can kind of cheat and find the pressure difference at the inlet and outlet of the pipes for a given flow rate. This can be translated into a Nusselt number.

friction factor = (P_inlet-P_outlet)*(D/L)/(0.5*density*V_average^2)

V_average can be calculated if the flow rate is known:

volumetric flow rate = density*cross sectional area of pipe*V_average

Chilton-Colburn analogy then gives us:

friction factor/8 = Nu/( Re*Pr^(1/3) )

As for solving for the external convection while suspended in either the air or a water tank or whatever, it kind of depends on how the coil is oriented. There are some good correlations for cylinders you could probably apply to the shape of the coil without too much error, but they would not accurately describe the flow inside the coil.

If the cylinder is oriented vertically, you can estimate with vertical plate correlations, use:

Nu = 0.59*Ra^(1/4) for 10^4 < Ra < 10^9
Nu = 0.10*Ra^(1/3) for 10^9 < Ra < 10^13

If the axis of the coil is oriented horizontally, use:

Nu = {0.60 + (0.387*Ra^(1/6))/[ {1+[0.559/Pr]^(9/16)}^(8/27) ] }^2 for Ra < 10^12

These are just a starting point. You'll probably want to run some tests and develop a correction for the whole system under a given flow rate and input temperature (or temperature difference between inlet and ambient). It's a complex system, I'd have to think about how to best treat it, but that's a start anyway.

Ziga Casar
Hi,

Thanks for the reply. What i essentially need for the model is a transfer function that relates input water temperature and flow rate to the coil to heat transfer from the coil per degree difference in input water temperature and surrounding air temperature?

Kind regards

With variable temperature along the surface, that becomes quite difficult. That's why my final recommendation was to run some tests and come up with your own correlation. Using averaged temperatures you can at least get an idea of the order of magnitude. Especially in the air, isothermal tubing probably becomes reasonable. Submerged in water, that assumption probably won't hold.

If there are major changes to the average tube temperature along the length of the tube, you can assume a variable average temperature along the axis of the wound cylinder.