Options for thermally shielding the top ceiling of alarge

Chapter 13, Problem 13.109

(choose chapter or problem)

Options for thermally shielding the top ceiling of alarge furnace include the use of an insulating mate- rial of thickness Land thermal conductivity k, case(a), or an air space of equivalent thickness formed byinstalling a steel sheet above the ceiling, case (b).(a) Develop mathematical models that could beused to assess which of the two approaches isbetter. In both cases the interior surface is main- tained at the same temperature, Ts,i, and theambient air and surroundings are at equivalenttemperatures (T??Tsur) b) I fk?0.090 W/m?K,L?25 mm,ho?25W/m2?K, the surfaces are diffuse and gray with?i??o?0.50, Ts,i?900 K, and T??Tsur?300 K, what is the outer surface temperature Ts,oand the heat loss per unit surface area associatedwith each option?(c) For each case, assess the effect of surface radia-tive properties on the outer surface temperatureand the heat loss per unit area for values of?i??oranging from 0.1 to 0.9. Plot your results.