## Heat flow through walls of copper tube

Today I calculate how much heat will flow through the walls of a standard 2 inch copper tube, when the temperature difference is 1 kelvin. It turns out to be quite a large number.

Thermal conductivities at 300K:

Properties of 2 inch nominal copper tubing from copper.org:

• Outside diameter 2.125 inch
• Inside diameter 1.959 inch
• Wall thickness 0.083 inch
• The average diameter is (2.125inch+1.95inch)/2 = 2.0375 inch.
• The circumferance is (pi 2.0375 inch) = 6.400995 inch.
• The surface area of a 10 foot tube is (pi 2.0375 inch)(10 foot) = 0.49555991 meter^2
• The heat flow in kilowatts per kelvin is (401 W/m K)(pi 2.0375 inch)(10 foot)/(0.083 inch) = 94.260282 kW/K

Thus, a 2 inch by 10 foot copper tube with 0.083 inch wall thickness will pass 94 kilojoules of heat per second with a temperature drop of only one kelvin.

The volume of this tube is (pi (1.95 inch)^2) (10 foot) = 23.490999 liters.

Calculations as usual are done using the Gnu units program.

```\$ units -V
units version 1.80 with readline, units database in /usr/share/units.dat
\$ grep Version /usr/share/units.dat
# 16 June 2002 Version 1.34```