Consider the conditions of Example 9.3, including the effect of adding insulation of thickness t and thermal conductivity k = 0.035 W/m. K to the duct. We wish to now include the effect of radiation on the outer surface temperatures and the total heat loss per unit length of duct.

(a) If Ts,i = 45°C, t = 25 mm, ε = 1, and Tsur = 288 K, what are the temperatures of the side, top, and bottom surfaces? What are the corresponding heat losses per unit length of duct?

(b) For the top surface, compute and plot Ts,2 and q' as a function of insulation thickness for 0 < t < 50mm. The exposed duct surface (t = 0) may also be assumed to have an emissivity of B = 1. 9.36 An electrical heater in the form of a horizontal disk of 400-mm diameter is used to heat the bottom of a tank filled with engine oil at a temperature of 5°C. Calculate the power required to maintain the heater surface temperature at 70°C.