Heat Transfer Handbook part 83 docx

Hereψ is introduced as the ratio ofthe true temperature dif-ference to the temperature head the inlet temperature difdif-ference of the two ﬂuids, The logarithmic mean temperature differ

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0

20

40

60

80

100

Counterflow exchanger performance hot fluid (.mc p h) =C h

Crossflow exchanger with fluids unmixed.

Parallel-flow exchanger performance hot fluid (.mc p h)

Cross exchanger with one fluid mixed Cold fluid (.mc p c) =C c

(.mc p h) (.mc p c)

Cold fluid (.mc p c) Heat transfer surface Heat transfer surface ( )a

( )c

( )b

( )d

0.25

0.25 0.50

0.50

4 0.50 2 0.75 1.33

0.75

0.75 1.00

1.00

Cmin max/C = 0

0

1

2

3

4

5

Number of Transfer Units,N tu=US C/ min

Mixed fluid Unmixed fluid Hot fluid

Cold fluid

C

Cunmixedmixed = 0, ⬁

C

Cunmixedmixed = 1

arrange-ments (From Kakac¸, 1991, with permission.)

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40

20

60

40

70

60

80

90

100

Multipass cross-counter-flow exchanger / = 1 unmixed flow within passesCmin maxC

(.mcp h)

Multipass counterflow exchanger performance (parallel-counterflow passes)

Cold fluid(.mc p c)

Hot fluid ( )e

( )g

( )f

( )h

Effect of number of shell passes forCmin max/C = 1

Exchanger performance effect of flow arrangement forCmin max/C = 1

Exchanger performance effect ofCmin max/C

Counterflow / = 1.0

Cmin maxC

Cmin max/C = 0.9

Crossflow both fluids unmixed / = 0.9

Cmin maxC

Cmin max/C = 1.0 0

0

1

2

3

4

5

Number of Transfer Units,N tu=US C/ min

One pass Two passes Three passes

Four passes Counterflow ( = )n ⬁

Counterflow

Two-pass arrangement

one fluid mixed

Crossflow fluids unmixed

Parallel-counterflow one shell pass Parallel flow

Counterflow ( = )n ⬁

Four passes

Three passes

Two passes (1–2 exchanger) One pass (1–2 exchanger)

exchanger arrangements (From Kakac¸, 1991, with permission.)

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exchanger arrangements (From Kakac¸, 1991, with permission.)

ForCmin = CshellandCmax = Ctube: For the effectiveness, use eq (11.46a) with

C∗replaced by 1/C∗, Ntureplaced byC∗Ntu, and replaced by C∗ When C∗ = 1,

use eq (11.46b), and whenNtu−→ ∞ when Cmin = Cshell,

C∗+ 2 + (C∗2+ 4)1/2

Graphs ofthe 10 arrangements just considered are shown in Fig 11.5

11.3.3 P–Ntu,cMethod

In shell-and-tube heat exchangers, any possible confusion deriving from selection of theCmin ﬂuid is avoided through use oftheP –Ntu,c method The method uses the cold-side capacity rate, so that

forC c = Cmin

C∗ forCc = Cmax

(11.47)

(11.48)

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0.0 0.2 0.3 0.4 0.6 0.8 1 2 3 4 5 6 8 10

N tu,c

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

3.0 4.0 5.0 6.0 8.0 10.0

2.5 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4

0.2

R =0

F =0.7 0.75 0.8 0.95 0.9 0.85

tt Tt21 1

⫺ ⫺

Shell fluid

Tube fluid

shell-and-tube heat exchanger with the shell ﬂuid mixed (From Kakac¸, 1991, with permission.)

and it may be recalled that

(11.29b) The parameterP is the temperature effectiveness and is similar to the exchanger

effectiveness It is a function of Ntu,c , R, and the ﬂow arrangement

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In theP –Ntu,cmethod, the total heat flow from the hot fluid to the cold fluid will be

and theP –Ntu,crelationships can be derived from the–Nturelationships by replacing

has an–Nturepresentation of

= 1− e −Ntu(1−C

∗)

theP –Ntu,crepresentation is

1− Re −Ntu(1−R)

Figure 11.6 is a chart ofP plotted against Ntu,c for the 1–2 shell-and-tube heat

exchanger with the shell ﬂuid mixed

Theψ–P method proposed by Mueller (1967) combines the variables ofthe LMTD

and–Ntu methods Hereψ is introduced as the ratio ofthe true temperature

dif-ference to the temperature head (the inlet temperature difdif-ference of the two ﬂuids,

The logarithmic mean temperature difference correction factor

LMTDc which can be written as

whereNcf is the number of transfer units for the counterﬂow exchanger obtained by solving eq (11.37),

= 1− e −Ntu(1−C

∗)

forNtu:

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



1

1− Rln

1− RP

P

(11.52)

Equations (11.30), (11.31), and (11.52) can be combined to yield

ψ = ln [(1 − RP )/(1 − P )]FP (1 − R) (11.53)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

P = T t2 t t1

⫺

⫺ 0.0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

␺

0.95 0.9

0.8 0.75

F = 0.5

3.0 2.5

2.0 1.8 1.6 1.4 1.2 1.0

1

NTU c

0.9

0.8 0.7 0.6 0.5

0.4

exchanger with the shell ﬂuid mixed (From Kakac¸, 1991, with permission.)

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so that

which shows that

ψ = f (P,R, ﬂow arrangement)

The plot ofψ as a function of P is known as a Mueller chart (Mueller, 1967), and

Fig 11.7 shows such a chart for a 1–2 shell-and-tube heat exchanger with the shell ﬂuid mixed

The relationships presented thus far refer to the principles of heat transfer and the conservation ofenergy among the streams that make up the heat exchangers The energy analysis is completed by taking into account the pumping power needed to force the streams through the heat exchanger structure Relations for pumping power

or pressure loss calculations are presented in Section 11.4.4

Qualitatively speaking, in a heat exchanger with changing flow architecture, the heat exchanger performance and the pumping power performance compete with one another For example, structural modifications such as the employment ofextended surface (fins) that lead to heat transfer enhancement also cause an increase in pumping power Trade-offs between these competing effects have been addressed extensively

in thermal design (Bejan et al., 1996) For example, the conﬁned thermodynamic irreversibility due to heat transfer and pumping power can be minimized by proper selection ofthe dimensions and aspect ratios ofthe ﬂow passages (Bejan, 1997, 2000)

A summary ofthe pertinent relationships employed in the analysis ofheat exchangers follows

• For the logarithmic mean temperature difference correction factor method (the

LMTD method),

θm= LMTD = ∆T1− ∆T2

ln(∆T1/∆T2) =

∆T2− ∆T1 ln(∆T2/∆T1) (11.24)

where

∆T1= T1− t2 ∆T2= T2− t1

(11.29a)

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(11.29b)

F = f (P,R, ﬂow arrangement)

• For the –Ntumethod,

= Ch(T2− T1)

Cmin(T1− t1) (11.35)

= f (Ntu,C∗, ﬂow arrangement)

• For the P –Ntu,cmethod,

c = Cmin

• For the ψ–P method,

ψ = f (P, R, ﬂow arrangement)

Shell-and-tube heat exchangers are fabricated with round tubes mounted in cylin-drical shells with their axes coaxial with the shell axis The differences between the many variations ofthis basic type ofheat exchanger lie mainly in their construction features and the provisions made for handling differential thermal expansion between tubes and shell

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A widely accepted standard is published by the Tubular Exchanger Manufacturers’

Association (TEMA) This standard is intended to supplement the ASME as well as other boiler and pressure vessel codes The TEMA (1998) standard was prepared

by a committee comprising representatives of27 U.S manufacturing companies, and their combined expertise and experience provide exchangers ofhigh integrity at reasonable cost TEMA provides a standard designation system that is summarized in Fig 11.8 Six examples ofthe shell-and-tube heat exchanger arrangements are shown

in Fig 11.9

One pass shell

Two pass shell with longitudinal baffle

Split flow

Shell Types Front End

Stationary Head Types

Channel and removable cover

Bonnet (integral cover)

Channel integral with tube-sheet and removable cover

Special high pressure closure

Rear End Head Types

Fixed tubesheet like “A” stationary head

Fixed tubesheet like “B” stationary head

Fixed tubesheet like “N” stationary head

Outside packed floating head

Floating head with backing device

Pull through floating head

U-Tube bundle

Externally sealed floating tubesheet

Double split flow

Divided flow

Kettle type reboiler

Cross flow

A

F

M

C

N

J

S

D

K

T

X

W U

Removable tube bundle only

Saunders, 1988, with permission.)

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( )a

( )b

( )c

( )d

( )e

( )f

de-signed to give essentially counterﬂow conditions The toroidal expansion joint in the center ofthe shell accommodates differential thermal expansion between the tubes and the shell

(b) U-tube shell shell-and-tube heat exchanger (c) Two-pass bafﬂed single-pass-shell single-pass-shell-and-tube heat exchanger (d) Heat exchanger similar to that of(c) except for the

ﬂoating head used to accommodate differential thermal expansion between the tubes and the

shell (e) Heat exchanger that is similar to the heat exchanger in (d) but with a different type ofﬂoating head (f ) Single-tube-pass bafﬂed single-pass-shell shell-and-tube heat exchanger

with a packed joint floating head and double header sheets to assure that no fluid leaks from one fluid circuit into the other (Courtesy ofthe Patterson-Kelley Co and reproduced from Fraas,

1989, with permission.)

Tiêu đề	Heat Exchanger Analysis Methods
Trường học	John Wiley & Sons
Chuyên ngành	Heat Transfer
Thể loại	Thesis

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