A long and thin$-$walled pipe with a radius of $r_1=50mm$ is used to transfer steam and the inner surface temperature of the pipe is kept constant at $T_{s1}=400K.$ The pipe is covered with a $50$ mm $-$thick insulation comprised of two different materials. The upper half of the pipe is covered with material A with a thermal conductivity of $k_A=1\mathrm{.}5\frac{W}{m}.K$ and the lower half of the pipe is covered with material B with a thermal conductivity of $k_B=0\mathrm{.}5\frac{W}{m}.K.$ The outer surface of the insulated pipe is exposed to air at $T_{}=300K$ and $h=30$ W$/$m$^2.$

a$.$ Sketch the thermal resistance network of the system and label

b$.$ Calculate the total heat loss from the pipe

c$.$ Calculate the outer surface temperatures of material A and and $($:$T_{s,2(B)}$