11.7.6 Overall Heat Transfer Coefficient Because the air- and tube-side heat transfer coefficients, the bond and tube metal resistances, and the tube-side fouling factor all apply at very
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[875],(79)
Lines: 3275 to 3330
———
-0.55058pt PgVar
———
Normal Page PgEnds: TEX [875],(79)
d e=Sb da + S f (S f Pf /2NL)
S
1/2
with the diagonal pitch given by eq (11.165) In eq (11.173), the range ofpara-meters is
1000< Re < 10,000 24.78 mm < Pt < 49.55 mm
10.67 mm < d b < 26.01 mm 16.20 mm < d e < 34.00 mm
5.20 mm < b = d a − d b
2 < 9.70 mm 0.48 mm < P t d − d b
b < 1.64
0.25 mm < δ f < 0.70 mm 4.34 < Pt − d b
Pf− δf + 1 < 25.2
2.28 mm < P f < 5.92 mm 0.45 < Pt − d b
Pd − d r < 2.50
20.32 mm < P l < 52.40 mm
Ganguli et al (1985) proposed the following correlation for three or more rows of finned tubes:
Nu= hdb
k = 0.38Re0.6· Pr1/3
Sb S
0.15
(11.174) where
Re=dbG µ
The correlation ofeq (11.174) is valid for
1800< Re < 100,000 2.30 mm < P f < 3.629 mm
11.176 mm < db < 19.05 mm 27.432 mm < Pt < 98.552 mm
5.842 mm < b = d a − d b
2 < 19.05 mm 1< S S
b < 50
0.254 mm < δf < 0.559 mm
Other correlations include those ofBrauer (1964), Schulenberg (1965), Kuntysh and Iokhvedor (1971), and Mirkovic (1974) More recent correlations include those of Zhukauskas (1974), Weierman (1976), Hofmann (1976), Ehlmady and Biggs (1979), Biery (1981), Gianolio and Cuti (1981), Brandt and Wehle (1983), and Nir (1991)
Many ofthem are cited by Kr¨oger (1998)
11.7.5 Pressure Loss Correlations for Staggered Tubes
Some ofthe earlier correlations for the static pressure drop through bundles ofcircular finned tubes are those ofJameson (1945), Gunter and Shaw (1945), and Ward and
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[876], (80)
Lines: 3330 to 3392
———
0.57925pt PgVar
———
Short Page
* PgEnds: Eject
[876], (80)
Young (1959) A frequently used correlation is that of Robinson and Briggs (1966) for staggered tubes:
∆P = 18.03 Gρ2nr· Re−0.316P
t
d b
−0.927P
t
P d
0.515
(11.175) fornr rows and where
Re= d b G µ
and wherePd is given by eq (11.165) Equation (11.175) is valid for
2000< Re < 50,000 2.31 mm < P f < 2.82 mm
18.64 mm < d b < 40.89 mm 42.85 mm < P t < 114.3 mm
39.68 mm < da < 69.85 mm 37.11 mm < Pl < 98.89 mm
10.52 mm < b = d a − d b
2 < 14.48 mm 1.8 < P t
db < 4.6
Vampola (1966) proposed the correlation
∆P = 0.7315 G2
ρ n r· Re−0.245
Pt − d b db
−0.90
×
P
t − d b
Pf− δ + 1
0.70d
e db
0.90
(11.176)
where the Reynolds number, equivalent diameter, and limits ofapplicability are identical to those following eq (11.173)
11.7.6 Overall Heat Transfer Coefficient
Because the air- and tube-side heat transfer coefficients, the bond and tube metal resistances, and the tube-side fouling factor all apply at very dissimilar surfaces, it is important that all ofthese resistances be corrected and summed properly No provi-sion need be made for air-side fouling because the air-side heat transfer coefficient
is low and becomes the controlling resistance Usually, with the muff-type tube, the resistances are first referred to a hypothetical bare tube having outside diameter,d b With diameter designations in Fig 11.30, there are five inside resistances:
1 The inside film resistance:
rio= h1
i
d b
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[877],(81)
Lines: 3392 to 3414
———
3.51714pt PgVar
———
Short Page
* PgEnds: Eject
[877],(81)
Figure 11.30 Single fin in muff-type tubing Notice that the diameter at the tips and base of the fin are designated asd aandd b, respectively (From Kraus et al., 2001, with permission.)
2 The inside fouling resistance:
r dio = r di db
3 The liner metal resistance is based on the mean liner diameter, and with the metal thickness
δl= do − d i
2 the liner metal resistance is
rmol =δk l
l
2d b
d o + d i (11.179)
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[878], (82)
Lines: 3414 to 3496
———
-1.77864pt PgVar
———
Normal Page PgEnds: TEX [878], (82)
4 The bond resistance given by the tube manufacturer or calculated from the procedure ofSection 11.2.3 is transferred appropriately via
rBo = r B d b
5 The tube metal resistance is based on the mean tube diameter, and with the metal thickness
δt = d b − d g
2 the tube metal resistance is
r mot = δt
kt
2db
db + d g (11.181)
The sum ofthese resistances is
R io:
Rio = r io + r dio + r mol + r Bo + r mot
and it is noted that
R io is based on the equivalent bare outside tube surface
The gross outside surface to bare tube surface isS /πd b, so that the total resistance referred to the gross outside surface will be
R is = R io S
The air-side coefficient ishoand the fin efficiency is computed from eq (11.9b)
Then, with no provision for fouling,
r oη= 1
hoηov,o (11.183)
whereηov,ois obtained from eq (11.9b):
ηov,o= 1 −Sf
S (1 − η f )
The overall heat transfer coefficient is then given by
Uo= 1
R is + r oηf (11.184)
11.8.1 Introduction
An exploded view ofthe plate and frame heat exchanger, also referred to as a
gas-keted plate heat exchanger, is shown in Fig 11.31a The terminology plate fin heat
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[879],(83)
Lines: 3496 to 3496
———
* 63.927pt PgVar
———
Normal Page PgEnds: TEX [879],(83)
Figure 11.31 (a) Exploded view ofa typical plate and frame (gasketed-plate) heat exchanger and (b) flow pattern in a plate and frame (gasketed-plate) heat exchanger (From Saunders,
1988, with permission.)
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2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
[880], (84)
Lines: 3496 to 3507
———
2.927pt PgVar
———
Normal Page PgEnds: TEX [880], (84)
exchanger is also in current use but is avoided here because ofthe possibility of
confusion with the plate fin surfaces in compact heat exchangers The exchanger
is composed ofa series ofcorrugated plates that are formed by precision pressing with subsequent assembly into a mounting frame using full peripheral gaskets
Fig-ure 11.31b illustrates the general flow pattern and indicates that the spaces between
the plates form alternate flow channels through which the hot and cold fluids may flow, in this case, in counterflow
Plate and frame heat exchangers have several advantages They are relatively inexpensive and they are easy to dismantle and clean The surface area enhancement due to the many corrugations means that a great deal ofsurface can be packed into a rather small volume Moreover, plate and frame heat exchangers can accommodate a wide range offluids
There are three main disadvantages to their employment Because ofthe gasket, they are vulnerable to leakage and hence must be used at low pressures The rather small equivalent diameter ofthe passages makes the pressure loss relatively high, and the plate and frame heat exchanger may require a substantial investment in the pumping system, which may make the exchanger costwise noncompetitive
Figure 11.32 Typical plates in plate and frame (gasketed-plate) heat exchanger (a) Inter-mating or washboard type and (b) Chevron or herringbone type (From Saunders, 1988, with
permission.)
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[881],(85)
Lines: 3507 to 3526
———
0.927pt PgVar
———
Normal Page PgEnds: TEX [881],(85)
The two most widely employed corrugation types are the intermating or
wash-board type and the chevron or herringbone type Both ofthese are shown in Fig.
11.32 The corrugations strengthen the individual plates, increase the heat transfer surface area, and actually enhance the heat transfer mechanism
The outside plates ofthe assembly do not contribute the fluid-to-fluid heat transfer
Hence, the effective number ofplates is the total number ofplates minus two This fact becomes less and less important as the number of plates becomes large It may
be noted that an odd number ofplates must be used to assure an equal number of
channels for the hot and cold fluids Figure 11.31a indicates that the frame consists
ofa fixed head at one end and a movable head at the other The fluids enter the device
through ports located in one or both ofthe end plates Ifboth inlet and outlet ports for
both fluids are located at the fixed-heat end, the unit may be opened without disturbing the external piping
A single traverse ofeither fluid from top to bottom (or indeed, bottom to top) is
called a pass and single- or multipass flow is possible Counterflow or co-current flow
is achieved in what is called looped flow or 1/1 arrangement, shown in Fig 11.33a and b In Fig 11.33a, termed the Z or zed arrangement, two ports are present on
both the fixed and movable heads In the U arrangement ofFig 11.33b, all four
Figure 11.33 Countercurrent single-pass flow (a) Z-arrangement and (b) U-arrangement.
(From Saunders, 1988, with permission.)
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[882], (86)
Lines: 3526 to 3557
———
0.98404pt PgVar
———
Normal Page
* PgEnds: Eject
[882], (86)
Figure 11.34 Two-pass/two-pass flow (From Saunders, 1988, with permission.)
Figure 11.35 Two-pass/one-pass flow (From Saunders, 1988, with permission.)
ports are at the fixed-head end The two pass/two pass flow or 2/2 arrangement is shown in Fig 11.34, and the two pass/one pass flow or 2/1 arrangement is shown in
Fig 11.35 Observe that in Fig 11.34, the arrangement is in true counterflow except for the center plate, where co-current flow exists In Fig 11.35, one halfofthe unit
is in counterflow and the other halfis in co-current flow
11.8.2 Physical Data
Figure 11.36a shows a sketch ofa single plate for the chevron configuration The
chevron angle is designated byβ, which can range from 25° to 65° As shown in Fig
11.36b, the mean flow channel gap is b, and it is seen that b is related to the plate
pitchpp1and plate thicknessδpl:
Because the corrugations increase the flat plate area, an enlargement factor Λ is
employed:
Λ = developed length
projected length (11.186) where typically, 1.10 < Λ < 1.25.
The cross-sectional area ofone channel,A1, is given by
wherew is the effective plate width shown in Fig 11.36a With the wetted perimeter
ofone channel,
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[883],(87)
Lines: 3557 to 3580
———
6.13701pt PgVar
———
Normal Page PgEnds: TEX [883],(87)
the channel equivalent diameter will be
d e= 4A1
P W1 =
4bw
2(b + Λw)
Figure 11.36 Plate geometry for Chevron plates in plate and frame (gasketed-plate heat exchanger) (From Saunders, 1988, with permission.)
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[884], (88)
Lines: 3580 to 3641
———
0.82622pt PgVar
———
Normal Page
* PgEnds: Eject
[884], (88)
and becausew b,
de= 2Λb (11.189)
IfNp is high, the total surface area for heat flow may be based on the projected area:
whereL is the length ofeach plate in the flow direction and W is its width.
Because the hot- and cold-side surfaces are identical, the overall heat transfer coefficient will be given by
1/h c + 1/h c + R dc + R dh+ δpl /kp1S m
whereR dcandR dhare the hot- and cold-side fouling resistances For a thin plate of high thermal conductivity,
1/hc + 1/h c + R dc + R dh (11.191)
IfRdc = R dh= 0 (an unfouled or clean exchanger),
U = h h c h h
In the case of plate and frame heat exchanger, the true temperature difference in
q = USθ m
depends on the flow arrangement For true counterflow or co-current flow, eqs (11.25) and (11.26) apply For other arrangements, such as those shown in Figs 11.34 through 11.36, the work ofShah and Focke (1988) should be consulted
11.8.3 Heat Transfer and Pressure Loss
The heat transfer and pressure loss in a plate and frame heat exchanger are based on
a channel Reynolds number evaluated at the bulk temperature ofthe fluid given by eqs (11.131):
Rech= d e Gch
Then the channel Nusselt number will be
Nuch= hd k e = j hkPr1/3φ0.17