A radiant heater, which is used for surface treatment processes, consists of a long cylindrical heating element of diameter D₁ = 0.005 m and emissivity ?₁ = 0.80. The heater is partially enveloped by a long, thin parabolic reflector whose inner and outer surface emissivities are ?_2i = 0.10 and ?₂₀ = 0.80, respectively. Inner and outer surface areas per unit length of the reflector are each A_2i = A_2o = 0.20 m, and the average convection coefficient for the combined inner and outer surfaces is h _{2(i, o)} = 2 W/m² ? K. The system may be assumed to be in an infinite, quiescent medium of atmospheric air at T_? = 300 K and to be exposed to large surroundings at T_sur = 300 K.

(a) Sketch the appropriate radiation circuit, and write expressions for each of the network resistances.

(b) If, under steady-state conditions, electrical power is dissipated in the heater at P₁ = 1500 W/m and the heater surface temperature is T₁ = 1200 K, what is the net rate at which radiant energy is transferred from the heater?

(c) What is the net rate at which radiant energy is transferred from the heater to the surroundings?

(d) What is the temperature, T₂, of the reflector?

Surroundings Heater e, D,. T. q Air, T. 135 Air, T Ez A Reflector