A pipe with outer diameter D = 6 cm carries steam at 3'}, = 100 °C

A pipe with outer diameter D = 6 cm carries steam at 3'}, = 100 °C. The heat transfer coef?cient between the steam and the inner surface of the pipe is large and the pipe wall is thin and thermally conductive. The pipe is surrounded by air at Ta; =20 c'C. You are interested in designing an insulation blanket that is economically optimal. The insulation blanket is wrapped on the external surface of the pipe. The insulation has conductivity km = 0.15 me'K and thickness has = 1 cm. The outer surface of the insulation has emissivity g = 0.5 and radiates to surroundings that are at Tsur = Tr. Assume that this is a natural convection problem He, the only ?uid motions is driven by buoyancy forces). Plot the rate of heat transfer per unit length as a ?unction of insulation thickness for various values of the emissivity. For an emissivity of g = 0.5, plot the energy cost, insulation cost, and total cost as a function of the insulation thickness. You should see that there is an optimal insulation thickness that causes the lowest possible total ?ve year cost.