Options for thermally shielding the top ceiling of a large furnace include the use of an insulating material of thickness L and thermal conductivity k, case (a), or an air space of equivalent thickness formed by installing a steel sheet above the ceiling, case (b).

(a) Develop mathematical models that could be used to assess which of the two approaches is better. In both cases the interior surface is maintained at the same temperature, T_{s, i}, and the ambient air and surroundings are at equivalent temperatures (T _∞ = T_sur).

(b) If k = 0.090 W/m. K, L = 25 mm, ho = 25 W/m₂ · K, the surfaces are diffuse and gray with ε_i = ε_o = 0.50, T _sd = 900 K, and T_∞ = T_sur = 300 K, what is the outer surface temperature T_{s, o} and the heat loss per unit surface area associated with each option?

(c) For each case, assess the effect of surface radiative properties on the outer surface temperature and the heat loss per unit area for values of ε; = ε_o ranging from 0.1 to 0.9. Plot your results.

Transcribed Image Text:

Air Air T_, h, Insulation, A Air space Furnace cavity -T, E, Furnace cavity la) (b)