Problem $3(25$ points$)$:

Steam at $Z=-280C$ nows in a cast iron pipe $(k=80\frac{W}{m}K)$ whose inner and outer diameters are $D_1=4cm$ and $D_2=4\mathrm{.}5cm,$ respectively. The pipe is covered with $2-cm-$thick glass wool insulation with $A=0\mathrm{.}07\frac{W}{m}*K.$ Heat is lost to the surroundings at $T_{ea}=10C$ by natural convection with a heat transfer coefficient of $h_{z-2}20\frac{W}{m^2}*K.$ Taking the heat transfer coefficient inside the pipe to be $h_1=70\frac{W}{m^2}*K$ and length of the pipe as $L=1m,$ determine:

a$)$ the rate of heat loss from the steam pipe.

b$)$ the temperature drops across the pipe shell $(T_1-T_2)$ and the insulation $(T_2-T_3).$