The wall of an oven used to cure plastic parts is of thickness L = 0.05 m and is exposed to large surroundings and air at its outer surface. The air and the surroundings are at 300 K.

(a) If the temperature of the outer surface is 400 K and its convection coefficient and emissivity are h = 20 W/m2 ∙ K and ε = 0.8, respectively, what is the temperature of the inner surface if the wall has a thermal conductivity of k = 0.7 W/m ∙ K?

(b) Consider conditions for which the temperature of the inner surface is maintained at 600 K, while the air and large surroundings to which the outer surface is exposed are maintained at 300 K. Explore the effects of variations in k, h, and B on (i) the temperature of the outer surface, (ii) the heat flux through the wall, and (iii) the heat fluxes associated with convection and radiation heat transfer from the outer surface. Specifically, compute and plot the foregoing dependent variables for parametric variations about baseline conditions of k = 10 W/m. K, h = 20 W/m2 ∙ K, and B = 0.5. Suggested ranges of the independent variables are 0.1 ≤ k ≤ 400 W/m ∙ K, 2 ≤ h ≤ 200 W/m2 ∙ K, and 0.05 ≤ ε ≤ 1. Discuss the physical implications of your results. Under what conditions will the temperature of the outer surface be less than 45°C, which is a reasonable upper limit to avoid burn injuries if contact is made?