Convection, Conduction, and Overall U$.$ A gas at $450K$ is flowing inside a $2-$in$.$ steel pipe, Schedule $40.$ The pipe is insulated with $71mm$ of lagging having a mean $k=0\mathrm{.}0623\frac{W}{m*K}.$ The convective heat$-$transfer coefficient of the gas inside the pipe is $40\mathrm{.}7\frac{W}{m^2.K}$ and the convective coefficient on the outside of the lagging is $20\mathrm{.}8\frac{W}{m^2*K}.$ The air is at a temperature of $300K.$

$($a$)$ Calculate the heat loss per unit length of $1m$ of pipe using resistances.

$($b$)$ Repeat, using the overall $U_0$ based on the outside area $A_0.$