A steam pipe of 0.12-m outside diameter is insulated with a layer of calcium silicate.

(a) If the insulation is 20 mm thick and its inner and outer surfaces are maintained at T_s,1 = 800 K and T_s.2 = 490 K, respectively, what is the heat loss per unit length (q') of the pipe?

(b) We wish to explore the effect of insulation thickness on the heat loss q' and outer surface temperature T_s.2. with the inner surface temperature fixed at T_S.1 = 800 K. The outer surface is exposed to an airflow (T_∞ = 25°C) that maintains a convection coefficient of h = 25 W/m² ∙ K and to large surroundings for which Tsur = T_∞ = 25°C. The surface emissivity of calcium silicate is approximately 0.8. Compute and plot the temperature distribution in the insulation as a function of the dimensionless radial coordinate, (r – r₁) / (r₂ – r₁), where r₁ = 0.06 m and r₂ is a variable (0.06 < r₂ < 0.20 m). Compute and plot the heat loss as a function of the insulation thickness for 0 < (r₂ – r₁) < 0.14 m.