Superheated steam at an average temperature $T_1=320C$ is transported through a cast iron pipe $(k=80\frac{W}{m}*K)$ whose inner and outer diameters are $D_1=5cm$ and $D_2=5\mathrm{.}5cm,$ respectively. The pipe is covered with $4-$cm$-$thick gypsum plaster insulation with $k=0\mathrm{.}5\frac{W}{m}*K.$ Heat is lost to the surroundings at $T_2=10C$ by natural convection and radiation, with a combined heat transfer coefficient of $h_2=18\frac{W}{m^2}*K.$

$1\mathrm{.}1$ Sketch the thermal resistance

$1\mathrm{.}2$ Taking the heat transfer coefficient inside the pipe to be $h_1=60\frac{W}{m^2}*K,$ calculate:

$($a$)$ the rate of heat loss from the steam per unit length of the pipe.

$($b$)$ the temperature drops across the pipe shell and the insulation.

$[16]$

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