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.GIVENSteam pipe in a hotel basementPipe outside diameter (Do) = 30 cm = 0.3 mPipe wall thickness (Ls) = 3 cm = 0.03 mSurrounding air temperature (T??) = 20?CConvective heat transfer coefficient (hc) = 25 W/(m2 K)Cost of steam = $5/109 JInsulation is 85% magnesiaASSUMPTIONSThe pipe and insulation are black (ε = 1.0)The convective resistance on the inside of the pipe is negligible, therefore the inside pipe surfacetemperature is equal to the steam temperatureThe pipe is made of 1% carbon steelConstant thermalconductivities

5 cm 10 cm (a) 10 cm (a) 5 cm Uninsulated Thlck Insulation Thick Plpe Insulation