The wall of a drying oven is constructed by sandwiching an insulation material of thermal conductivity k = 0.05 W/m ∙ K between thin metal sheets. The oven air is at T_∞,i = 300°C, and the corresponding convection coefficient is hi = 30 W/m² ∙ K. The inner wall surface absorbs a radiant flux of q _rad = 100 W/m² from hotter objects within the oven. The room air is at T_{∞, 0} = 25°C, and the overall coefficient for convection and radiation from the outer surface is ho = 10 W/m² ∙ K.

(a) Draw the thermal circuit for the wall and label all temperatures, heat rates, and thermal resistances.

(b) What insulation thickness L is required to maintain the outer wall surface at a safe-to-touch temperature of T_o = 40°C?

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Insulation, k Absorbed radiation, Grad -T. Oven air Room air 11 11