$2\mathrm{.}16$A standard $4-$in$,$ steel pipe $($ID $=4\mathrm{.}026$ in$.,OD=4\mathrm{.}500$ in$.)$ carries superheated steam at $1200F$ in an enclosed space where a fire hazard exists, limiting the outer surface temperature to $100F.$ In order to minimize the insulation cost, two materials are to be used: first a high$-$temperature $($relatively expensive$)$ insulation is to be applied to the pipe, and then magnesia $($a less expensive material$)$ will be applied on the outside. The maximum temperature of the magnesia is to be $600E.$ The following constants are known:

high$-$temperature

insulation

conductivity

magnesia conductivity

outside heat transfer

coefficient

steel conductivity

ambient temperature

$k=0\mathrm{.}06Bt\frac{u}{h}rftF$

$k=0\mathrm{.}045Bt\frac{u}{h}rftF$

$h=2\mathrm{.}0Bt\frac{u}{h}rf{t}^{2}oF$

$k=25Bt\frac{u}{h}rftF$

$T_a=70F$

$($a$)$ Specify the thickness for each insulating material. $($b$)$ Calculate the overall heat transfer coefficient based on the pipe OD$.($c$)$ What fraction of the total resistance is due to $(1)$ steam$-$side resistance, $(2)$ steel pipe resistance, $(3)$ insulation $($the combination of the two$),$ and $(4)$ outside resistance? $($d$)$ How much heat is transferred per hour per foot length of pipe?

Previous answer given was obviously AI generated