A 50 meter long pipe with outer diameter of 10 cm carries steam at 150C. The pipe passes through an open space with a temperature of 15C. The current cost associated with the heat loss from the pipe is $40,436/year. a. There is a proposal to wrap the pipe with 4 cm thick insulation (k=0.1644 W/m*K), and paint it with Red Primer (emissivity = 0.83). Based on assumptions that the outer surface of the insulation will be 30C and the convective coefficient outside the insulated pipe will be 20 W/mK, Calculate the total rate of heat loss for the insulated pipe due to convection and radiation. [3 Marks b. Calculate the annual savings (assuming these conditions remain constant all year) due to the insulation if the steam is generated in a natural gas furnace that has an efficiency of 75% and the price of natural gas is $0.52/therm. (1 therm= 105,500 kJ) [4 Marks]