Derive the general heat conduction equation in cylindrical coordinates by applying the first law to the volume element.

Answer 1

For transient situations with no heat generation and azimuthal symmetry, see the derivation of Eq. 2-28 at
http://wwwme.nchu.edu.tw/Enter/html/lab/lab516/Heat%20Transfer/chapter_2.pdf

In this case, T depends upon time (t) and r only.

There is a more complicated equation where there are variations with length z and aximutual angle phi.