| |
The temperature inside the surface of the cylinder is  and outside the surface of the cylinder is  such that temperature difference  drives the heat. If the length of the cylinder is very long compared to its diameter, it can be considered for an axis-symmetric cylinder that heat flows in the radial direction. For one dimensional flow of heat at steady state, equation 5 reduces to
 |
(6) |
Boundary conditions are
 |
(7) |
Integration of equation 6 and with boundary condition expressed in equation 7, the temperature profile is given by
 |
(8) |
Heat flow  is
For some purposes, heat flow through the thickness of the pipe wall or the insulation is required with the inside and outside areas,  and  . In terms of area equation 9 becomes
|
