The "Overall heat transfer coefficient" $(U)$ is an expression of heat transfer resistances written with respect

to a reference area. The expression is introduced in equations $3\mathrm{.}17-3\mathrm{.}19($pgs$.104-105)$ for plane systems

and $3\mathrm{.}35-3\mathrm{.}37($pgs$.126-127)$ for radial systems. Using U$,$ you can write expressions for heat transfer rate

like you have done for walls and cylinders made of multiple materials $($for example: $q_x=UAT$ or $q_r=$

$UAT).U$ can be calculated using ${\displaystyle \underset{?}{\overset{?}{}}}{R}_t=\frac{1}{UA}$ and thermal resistances due to fouling can be represented $($as

an example: