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66131_Ludwig_CH10G 5/30/2001 4:39 PM Page 241

Heat Transfer 241

a. From reference Foo, 223 heat loss through the insulation Pipe temperature, 223
to the ambient air is
D o a c
Q ia U o 1T m T a 2 (10-255) T a c d T s c dd
12 1a b c2 1a b c2
T m (10-261)
The overall heat transfer coefficient for the insulation and b
1 d
the ambient air is 223 1a b c2
1 1D o >22ln1D o >D i 2 1D o 1
(10-256) where a U o A o
U o k o h c D i f o b h c (A p nA cc )
For f o , see Table 10-44. c h c A cp
The overall transfer coefficient for the tracer annulus d nq t A cc
2
A p D p /12, superficial area of pipe, ft /ft
space is
2
A cp 0.23357 D t , cement channel superficial area, ft /ft
2
A cc 2 D t /12, cement contact area, ft /ft
1 1 1 2
(10-257) A o D o /12, external superficial area of insulation, ft /ft
U t h c h s
Q ia Q pa Q ta
For condensing steam, the heat transfer coefficient, h s , is Q tp Q pa
2
approximately 2,000 Btu/(hr) (ft )(°F), and the preceding D o O.D. of insulation, in.
equation approximates to D t O.D. of tracer, in.
T s steam temperature, °F
1T s T ap 2 2 T a ambient temperature, °F
U t h c 0.45 (10-258) h c average of the horizontal and vertical transfer film
D t
coefficients by convection in still air.
b. Heat loss when tracer is surrounded by thermally 2
1T s T ap 2
conducting cement and insulated (otherwise same as (a), U t h c 0.45 (10-262)
see Figure 10-167): D t
Assume T ap T m , annulus space temperature
Q ia U o 1D o >122 1T ap T a 2 (10-259)
pipe temperature, °F.
Annulus space temperature, T ap ;
Annulus space temperature,
nq t A cc 1T s T m 2
nq t A cc 1T s T m 2
T ap T m , °F (10-260) T ap T m h c 1A p nA cc 2 (10-263)
h c 1A p nA cc 2
Then the pipe temperature, T m is 223

a c
T a c d T s c dd
1a b c2 1a b c2
Table 10-44 T m b (10-264)
Wind Velocity Factor, f o @dT 150°F Mean 1 d
a b c
Wind velocity, mph f o
The heat transfer from annulus space through insulation
0 2.5 to air:
5 3.8
10 4.8
Q ia heat transfer from annulus space through insulation
15 5.5
to air, Btu/hr/ft pipe
20 6
Q pa heat transfer from process pipe to annulus space,
25 6.5
Btu/hr/ft pipe
30 7
Q ta heat transfer from tracer to annulus space, Btu/hr/ft
35 7.3
pipe
40 7.7
Q tp heat transfer from tracer to process pipe, Btu/hr/ft
45 8
pipe
Note: dT T wall T a Q ap heat transfer from annulus space to pipe, Btu/hr/ft
Used by permission: Foo, K. W. Hydrocarbon Processing, V. 73, No. 1, ©1994. pipe
Gulf Publishing Company, Inc., Houston, Texas. All rights reserved.) n number of tracers