A wall-mounted natural gas heater uses combustion on a porous catalytic pad to maintain a ceramic plate of emissivity T_c = 0.95 at a uniform temperature of T_c = 1000 K. The ceramic plate is separated from a glass plate by an air gap of thickness L = 50 mm. The surface of the glass is diffuse, and its spectral transmissivity and absorptivity may be approximated as ?_? = 0 and ?_? = 1 for 0 ? 0.4?m, ?_? = 1 and ?_? = 0 for 0.4 1.6 ?m, and ?_? = 0 and ?_? = 0.9 for ? > 1.6?m. The exterior surface of the glass is exposed to quiescent ambient air and large surroundings for which T_? = T_sur = 300 K. The height and width of the heater are H = W = 2 m.

(a) What is the total transmissivity of the glass to irradiation from the ceramic plate? Can the glass be approximated as opaque and gray?

(b) For the prescribed conditions, evaluate the glass temperature, Tg, and the rate of heat transfer from the heater, q".

(c) A fan may be used to control the convection coefficient h_o at the exterior surface of the glass. Compute and plot T_g and q_b as a function of ho for 10 h_o 100 W/m² ? K.

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Combustion products Catalytic pad- Ceramic plate T G - Glass plate. T, Air gap H. T. 111 Air Fuel and air mixture