Discuss the below in detail
Q: A salesman for insulation material claims that insulating exposed steam pipes in the basement of a large hotel will be cost effective. Suppose saturated steam at 5.7 bars flows through a 30 cm OD steel pipe with a 3 cm wall thickness. The pipe is surrounded by air at 20°C. The convective heat transfer coefficient on the outer surface of the pipe is estimated to be 25 W/(m2 K). The cost of generating steam is estimated to be $5 per 109 J and the salesman offers to install a 5 cm thick layer of 85% magnesia insulation on the pipes for $200/m or a 10 cm thick layer for $300/m. Estimate the payback time for these two alternatives assuming that the steam line operates all year long and make a recommendation to the hotel owner. Assume that the surface of the pipe as well as the insulation have a low emissivity and radiative heat transfer is negligible.
GIVEN
Steam pipe in a hotel basement
Pipe outside diameter (Do) = 30 cm = 0.3 m
Pipe wall thickness (Ls) = 3 cm = 0.03 m
Surrounding air temperature (T?^?) = 20°C
Convective heat transfer coefficient (hc) = 25 W/(m2 K)
Cost of steam = $5/109 J
Insulation is 85% magnesia
ASSUMPTIONS
The pipe and insulation are black (e = 1.0)
The convective resistance on the inside of the pipe is negligible, therefore the inside pipe surface temperature is equal to the steam temperature
The pipe is made of 1% carbon steel
Constant thermalconductivities
