a) A 35-m long cast iron thermal pipe (k=80 W/m.K) carries 350C steam in a power plant which passes through a surrounding at 20C. The cross-section of the pipe is shown The inner and outer diameter of the pipe is r=10cm and r=15cm. respectively. If the heat transfer coefficient inside the pipe and the combined heat transfer coefficient on the outer surface of the pipe (without insulation) is h = 60 W/m K and h2-25 W/m.K, respectively. i. ii. Calculate the rate of heat loss from the steam pipe to the surrounding, when there is no insulation. Show the thermal resistance network diagram. Design a suitable insulation layer by choosing a material from Table 16-1 and determining its radius, r3 such that 90% of the heat loss can be saved. Show the new thermal resistance network diagram. b) The steam in the thermal pipe then enters a well-insulated throttling valve to reduce the pressure in the steam line from 8 MPa and 350C to 2 MPa. Determine the final temperature of the steam at the outlet of the throttling valve. TABLE 16-1 The thermal conductivities of some materials at room temperature Material & Wim-K 2300 429 401 317 237 Diamond Silver Copper Gold Aluminum Iron Mercury (0) Glass Brick Water (1) Human skin Wood look Helium (g) Soft rubber Glass fiber Air (g) Urethane, rigid foam 80.2 8.54 0.78 0.72 0.607 0.37 0.17 0.152 0.13 0.043 0.026 0.026 Tsurt = 20C Cast iron thermal pipe (without insulation layer) Insulation layer Tur -20C steam