Page 121 - Applied Process Design For Chemical And Petrochemical Plants Volume III

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88 Applied Process Design for Chemical and Petrochemical Plants

1 of the fluids. Often, bulk average temperatures are used, but
U o (10-37)
1 A o A o 1 these may not be sufficiently accurate. Film coefficients
r o r w a b r i a b should be more accurately evaluated at or close to the tube wall
h o A avg A i A i
h i a b temperatures.
A o
The ratio multiplier, A o /A i , is usually omitted for general
where process design from the r i factor for inside fouling. For thin-
U o overall heat transfer coefficient corrected for fouling walled (18—12 ga) and highly conductive metal tubes, such as
conditions, Btu/hr (ft ) (°F), and referenced to out- high copper alloys, the resistance of the tube wall can usually
2
side tube surface area be omitted with little, if any, significant effect on U. Each of
h o film coefficient of fluid on outside of tube,
these omissions should be looked at in the light of the prob-
2
Btu/hr (ft ) (°F)
lem and not as a blind rule. It is important to appreciate that
h i film coefficient of fluid on inside of tube,
the tube wall resistance of such useful tube wall materials as
Btu/hr (ft ) (°F)
2
®
®
Teflon and other plastics, Karbate and other impervious
r o fouling resistance (factor) associated with fluid on
graphites, glass, plastic-lined steel, and even some exotic met-
2
outside of tube, hr (ft ) (°F)/Btu
r i fouling resistance (factor) associated with fluid on als, etc., cannot be omitted as they are usually sufficiently
2
inside of tube, hr (ft ) (°F)/Btu thick as to have a significant impact. Refer to Table 10-13A
2
*r w resistance of tube wall L w /k w , hr (ft )(°F.)/Btu for thermal conductivity, k, values for many common metal
t L w thickness of tube wall, in. or ft, as consistent tubes and allow a calculation of r w , tube wall resistance. Note
**k w thermal conductivity of material of tube wall, (Btu- that the conversion for thermal conductivity is
2
ft)/[(hr) (ft ) (°F)]
Btu Btu
A o outside area of unit length of tube, ft /ft, Table 10-3 2 0.08333 2 (10-39)
2
2
A i inside area of unit length of tube, ft /ft, Table 10-3 1hr21ft 21°F>in.2 1hr21ft 21°F>ft2
A avg average of inside and outside tube area for unit 2
and Btu> 1hr2 1ft2 1°F2 Btu-ft> 1hr2 1ft 2 1°F2
length, ft /ft
2
2
2
Note: Btu/(hr) (ft ) (°F/ft) 12 Btu/(hr) (ft ) (°F/in.)
Table 10-14 tabulates a few unusual and useful thermal
t corrected mean temperature difference, °F
A o A total required net effective outside heat transfer conductivity data.
surface referenced to tube length measured between Note that individual heat transfer coefficients are not
inside dimensions between tubesheets additive, but their reciprocals, or resistances, are
r w resistance of tube wall referred to outside surface of
1 1 A o 1
tube wall, including extended surface, if present 107 r o r w a b r i (10-40)
U h o A avg a i
d 1d2 h i a b
* r w also for bare tubes: cln d reference, 107 A o
24k 1d 2t2
2
(hr) (°F) (ft outside surface)/Btu 1/h o resistance of outside fluid film
d O.D. bare tube (or, root diameter of fin tube), in. 1/h i resistance of inside fluid film
t tube wall thickness, in.
N number of fins/in. Sometimes one of the fluid-side scale resistances can be
2
** K k thermal conductivity, Btu ft/(hr) (ft ) (°F) neglected or assumed to be so small as to be of little value, in
(Note the difference in units.) For conversion,
which case only the significant resistances and/or film coef-
see Table 10-13A.
ficients need to be used in arriving at the overall coefficient,
w fin height, in.
U. Note that A o , A i , and A avg can be substituted by d o , d it , and
ln natural logarithm
d avg respectively. Theoretically, d avg and A avg should be the
** = must be consistent units, also *
logarithmic average, but for most practical cases, the use of
the arithmetic average is completely satisfactory.
For integral circumferentially finned tubes: 107
Recognize that only the heat that flows through the sum
t 3d 2Nw1d w24
r w (10-38) of all the resistances can flow through any one resistance
12k 1d t2
considered individually, even though by itself, a resistance
In actual exchanger operational practice, the U values at may be capable of conducting or transferring more heat.
the hot and cold terminals of the heat exchanger are not the Film coefficients defined on an inside tube surface area
same and can be significantly different if evaluated only at basis when converted to the larger outside surface area
the spot conditions. In order to obtain an overall coefficient become
U that represents the transfer of heat throughout the
exchanger, the U should be evaluated at the caloric temper- A i d it
h io h i a b h i a b (10-41)
ature for physical properties and individual film coefficients A o d o