An overhead 25-m-long, uninsulated industrial steam pipe of 100-mm diameter is routed through a building whose walls and air are at 25°C. Pressurized steam maintains a pipe surface temperature of 150 C, and the coefficient associated with natural convection is h 10 W/m2 · K. The surface emissivity is ε = 0.8.
(a) What is the rate of heat loss from the steam line?
(b) If the steam is generated in a gas-fired boiler operating at an efficiency of ηf = 0.90 and natural gas is priced at Cg = $0.02 per MJ, what is the annual cost of heat loss from the line?