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I wanted to do some rough "back of the envelope"-calculations of heat losses from pipes, with water circulating in them, to compare to the results of various programs' simulations.

I was not very successful as I was perhaps hoping to get rough estimates in the range 20-200% off, but right now I'm in the magnitude of 1000s times off from the simulations.

I'm not entirely sure of if I simply don't know what I'm doing and I have the completely wrong approach, or if there is something I fail to see along the way.

As a rough example a 15 mm pipe with an inner diameter of 13 mms:

from:

https://www.engineeringtoolbox.com/conductive-heat-loss-cylinder-pipe-d_1487.html

Conductive heat loss through the wall of a cylinder or pipe can be expressed as

*Q =*

*(ti - to) / [ln(ro / ri) / k]**2 π L*I'm calculating the heat loss as W/m so I have:

*Q =*

The thermal conductivity of copper ~ 400 W/mK ( https://www.engineeringtoolbox.com/thermal-conductivity-d_429.html)

dT = 22 degrees Celsius

ro = 7.5 mm

ri = 6.5 mm

*(T_inside - T_outside) / ln(ro / ri)**2 π * k **The thermal conductivity of copper ~ 400 W/mK ( https://www.engineeringtoolbox.com/thermal-conductivity-d_429.html)

dT = 22 degrees Celsius

ro = 7.5 mm

ri = 6.5 mm

*Q = (*

= 386 385 W/m

To get an idea of the magnitude I look at the following data to get an approximation. These are close to the various simulations I've seen, even if there are some larger differences at times.

As an example the value estimated for 1/2" pipe with the same temperature difference is 26 W/m

https://www.engineeringtoolbox.com/copper-pipe-heat-loss-d_19.html

*22 C) / ln(7.5 mm / 6.5 mm)**2 π * 400 W/(m K) **= 386 385 W/m

To get an idea of the magnitude I look at the following data to get an approximation. These are close to the various simulations I've seen, even if there are some larger differences at times.

As an example the value estimated for 1/2" pipe with the same temperature difference is 26 W/m

https://www.engineeringtoolbox.com/copper-pipe-heat-loss-d_19.html

So I'm not even close and I'm stuck and don't know what the approach I should take.

My questions therefore are:

-What am I doing wrong and how should I do this the right way?

-If I'm not directly doing anything wrong then how should I interpret these results?