A salesperson 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

Question

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 = $5/109J

Insulation is 85% magnesia

FIND

Payback time for

(a) Insulation thickness (LIa) = 5 cm = 0.05 m; Cost = $200/m

(b) Insulation thickness (LIb) = 10 cm = 0.10 m; Cost = $300/m

Make a recommendation to the hotel owner.

ASSUMPTIONS

The pipe and insulation are black (? = 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 thermal conductivities

SKETCH

Answer 1

The rate of heat loss and cost of the uninsulated pipe will be calculated first.

The thermal circuit for the uninsulated pipe is shown below



Evaluating the individual resistances



The rate of heat transfer for the uninsulated pipe is



The cost to supply this heat loss is

cost = (3148 w/m) (J/W s) (3600 s/h) (24 h/day) (365 days/yr) ($5/109J) = $496/(yr m)

For the insulated pipe the thermal circuit is



The resistance of the insulation is given by:



(a) The rate of heat transfer for the pipe with 5 cm of insulation is



The cost of this heat loss is

cost = (166 w/m) (J/W s) (3600 s/h) (24 h/day) (365 days/yr) ($5/109J) = $26/yr m

Comparing this cost to that of the uninsulated pipe we can calculate the payback period



Payback period = 0.43 yr = 5 months

(b) The rate of heat loss for the pipe with 10 cm of insulation is



The cost of this heat loss

cost = (95.7 w/m) (J/W s) (3600 s/h) (24 h/day) (365 days/yr) ($5/109J) = $15/yr m

Comparing this cost to that of the uninsulated pipe we can calculate the payback period