A long rod heater of diameter D110 mm and emis-sivity 11.0

Chapter 13, Problem 13.124

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A long rod heater of diameter D1?10 mm and emis-sivity ?1?1.0 is coaxial with a well-insulated, semi- cylindrical reflector of diameter D2?1 m. A long panelof width W?1 m is aligned with the reflector and isseparated from the heater by a distance of H?1m.The panel is coated with a special paint (?3?0.7),which is cured by maintaining it at 400 K. The panel iswell insulated on its back side, and the entire system is located in a large room where the walls and theatmospheric, quiescent air are at 300 K. Heat transfer byconvection may be neglected for the reflector surface. a) Sketch the equivalent thermal circuit for the system and label all pertinent resistances andpotentials.(b) Expressing your results in terms of appropriatevariables, write the system of equations neededto determine the heater and reflector tempera-tures, T1and T2, respectively. Determine thesetemperatures for the prescribed conditions.(c) Determine the rate at which electrical power mustbe supplied per unit length of the rod heater