Chapter 13, Problem 13.124P

A long rod heater of diameter $D_1=10\text{mm}$ and emissivity ${\epsilon }_1=1.0$ is coaxial with a well-insulated, semi-cylindrical reflector of diameter $D_2=1\text{m}$ . A long panel of width $W=1\text{m}$ is aligned with the reflector and is separated from the healer by a distance of $H=1\text{m}$ . The panel is coaled with a special paint $\left({\epsilon }_3=0.7\right)$ , which is cured by maintaining it at 400 K. The panel is well insulated on its back side, and the entire system is located in a large room where the walls and the atmospheric, quiescent air are at 300 K. Heat transfer by convection may be neglected for the reflector surface.

(a) Sketch the equivalent thermal circuit for the system and label all pertinent resistances and potentials.
(b) Expressing your results in terms of appropriate variables, write the system of equations needed to determine the heater and reflector temperatures, T₁and T₂, respectively. Determine these temperatures for the prescribed conditions.
(c) Determine the rate at which electrical power must be supplied per unit length of the rod heater.