PROBLEM 1.28
KNOWN: Length, diameter, surface temperature and emissivity of steam line. Temperature
and convection coefficient associated with ambient air. Efficiency and fuel cost for gas fired
furnace.
FIND: (a) Rate of heat loss, (b) Annual cost of heat loss.
SCHEMATIC:
ASSUMPTIONS: (1) Steam line operates continuously throughout year, (2) Net radiation
transfer is between small surface (steam line) and large enclosure (plant walls).
ANALYSIS: (a) From Eqs. (1.3a) and (1.7), the heat loss is
()
(
)
44
conv rad s s sur
qq q AhT T T T
∞
⎡⎤
=+= −+ −
⎣⎦
εσ
where
()
2
A DL 0.1m 25m 7.85m .== ×=
ππ
Hence,
()
(
)
22 824444
q 7.85m 10 W/m K 150 25 K 0.8 5.67 10 W/m K 423 298 K
−
⎡⎤
=⋅−+××⋅−
⎣⎦
()()
22
q 7.85m 1,250 1,095 W/m 9813 8592 W 18,405 W=+=+= <
(b) The annual energy loss is
11
E qt 18,405 W 3600 s/h 24h/d 365 d/y 5.80 10 J== × × × = ×
With a furnace energy consumption of 11
ff
EE/ 6.4510 J,==×
η
the annual cost of the loss is
5
gf
C C E 0.02 $/MJ 6.45 10 MJ $12,900== ×× = <
COMMENTS: The heat loss and related costs are unacceptable and should be reduced by
insulating the steam line.
= 0.8= 0.8