Pipes and tubes are common barriers over which heat exchange takes place.

**HEAT TRANSFER IN PIPES AND TUBES**

Pipes
and tubes are common barriers over which heat exchange takes place. Conduction
is complicated in this case by the changing area over which heat is
transferred. If equation (3.2) is to be retained, some value of A must be
derived from the length of the pipe, *l*,
and the internal and external radii, r_{1} and r_{2},
respectively. When the pipe is thin walled and the ratio r_{2}/r_{1}
is less than approximately 1.5, the heat transfer area can be based on an
arithmetic mean of the two radii. Equation (3.2) then becomes

This
equation is inaccurate for thick-walled pipes. Heat transfer area must then be
calculated from the logarithmic mean radius, r_{m}. The equation for
heat transfer is then

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