(Solved): Problem 1 (30 pts) Steam flowing through a long, thin-walled pipe maintains the pipe wall at a uni ...

Problem 1 (30 pts) Steam flowing through a long, thin-walled pipe maintains the pipe wall at a uniform temperature of $600\mathrm{K}$. The pipe is covered with an insulation blanket comprised of two different materials, $\mathrm{A}\left({\mathrm{k}}_{\mathrm{A}}=2\mathrm{W}/\mathrm{m}?\mathrm{K}\right)$ and $\mathrm{B}\left({\mathrm{k}}_{\mathrm{B}}=0.5\mathrm{W}/\mathrm{m}?\mathrm{K}\right)$. The inner radius of the insulation blanket is $r_1=50\mathrm{mm}$ and the outer radius is $r_2=100\mathrm{mm}$. The nsulation blancket is covered by a layer of material 3 with ${\mathrm{k}}_3=0.2\mathrm{W}/\mathrm{m}?\mathrm{K}$ and an outer radius ${\mathrm{r}}_3=120\mathrm{mm}$, which is expsosed to an convective environment $(T_{?}=300\mathrm{K}$ and $h=25\mathrm{W}/{\mathrm{m}}^2?\mathrm{K})$. (a, 10pts) Sketch the thermal circuit of the system. Label all pertinent nodes and resistances. (b, 10pts) For the prescribed conditions, what is the total heat loss from the pipe to the environment? (c, $5\mathrm{pts})$ Calculate the temperature at $r_2$. Note that as an approximation, you may consider the temperature at $r_2$ is the same. (d, 5 pts) What is the outer surface temperature at $r_3$ ?