Q $(3).$ A gas at $450K$ is flowing inside a $2-$in$.$ steel pipe, Schedule $40.$ The pipe is insulated with $51mm$ 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 $30\mathrm{.}7\frac{W}{m^2}*K$ and the convective coefficient on the outside of the lagging is $10\mathrm{.}8.$ 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 $A_0.$