Kuppan T. Heat Exchanger Design Handbook

84

Chapter

2

Table

10

Continued

Eq.

no./

Value for

R

=

1

Flow arrangement

Ref. General formula and special cases

m

T24

[39]

(1

-

D)'

For

R

=

0.25

(B

-

4RG)

1

B=(l

+H)(l

+E)?

t

G=(l -D)?(D?+E?)

1-2

TEMA

H

shell: overall counterflow

+D'(l+E)'

arrangement; shell fluid mixed, tube

fluid mixed between passes

1

-e-a

D=------

4R+

1

a=E(4R+

1)

8

NTU

P=-(4R-

1)

8

losses are neglected, the shell-side pressure loss is approximately one-eighth of that same heat

exchanger arranged as the conventional

E,-?

or

El..,

exchanger. The possible flow arrange-

ments are

1.

Divided-flow shell with one tube pass. This arrangement is equivalent to the

El.?

exchanger

with unmixed shell fluid.

2.

Divided-flow shell with two tube passes.

3.

Divided-flow shell with four tube passes.

4.

Divided-flow shell with infinite number

of

tube passes.

Jaw [41] analyzed the cases with two and four tube passes. Extending the number of tube

passes to infinity, the case becomes identical to that of mixed-mixed crossflow, as derived by

Gardner [42a]. Divided flow shell with one tube pass arrangement is equivalent to

El-:

ex-

changer with unmixed shell fluid as presented by Gardner [42b]. The difference in

P

is negligi-

ble for four or more passes compared to the two passes arrangement in the region of interest,

i.e.,

F

>

0.5.

The thermal effectiveness relations for JI.,, J1.:, J1-.,, and

JI.,

arrangements are given

by

Eqs. T25, T26, T27,

and

T28,

respectively, in Table

11.

The thermal effectiveness charts

for

Jl.l,

JI.?,

and

J,..,

are given in Figs.

37, 38,

and

39,

respectively.

85

Heat Exchanger

The

rmo

h

y

draulic Fundamentals

86

Chapter

2

Heat Exchanger Thermohydraulic Fundamentals

87

TEMA

X

Shell

This exchanger is for very-low-pressure applications. For an exchanger, the thermal effec-

tiveness is same as single-pass crossflow with both fluids unmixed, that is, the unmixed-un-

mixed case [l]. An

XI.?

crossflow shell and tube exchanger is equivalent to Fig. 40(a) for both

fluids unmixed throughout with overall parallel flow (shell fluid entering at the tube inlet pass

end) and Fig. 40(b) for overall counterflow (shell fluid entering at the tube exit pass end),

respectively. The thermal relation formulas are discussed

in

Section

6.6.

6.5

Thermal Effectiveness

of

Multiple Heat Exchangers

Since the thermal effectiveness of a basic heat exchanger is sometimes low, to enhance the

exchanger effectiveness multipassing in the same unit or connecting multiple exchangers is

resorted to. Sometimes, to utilize the allowable pressure drop effectively, multipassing is also

employed; this

in

turn

enhance the thermal effectiveness. Multipassing by multiple units is

possible both with compact exchangers and shell and tube exchangers. With multipassing, two

or more exchangers can be coupled either in

an

overall parallel or in

an

overall countercurrent

scheme as shown in Fig. 41. Multipassing is also possible in a single unit of a compact ex-

changer (Fig. 42).

Fundamental formulas for the global effectiveness of multiple units are given next. These

equations are not valid for multiple tubeside passes of various TEMA shells. The following

idealizations are employed, in addition to those already listed at the beginning of this section:

1. Each pass has the same effectiveness, although any basic flow arrangement may be em-

ployed in any pass. If each pass has the same flow arrangement, then NTU

is

equally

distributed between

N

passes, and NTU per pass (NTU,) is given by NTUIN.

2.

The fluid properties are idealized as constant

so

that

C*

or

R

is the same for each pass.

The final results of this analysis are valid regardless of which fluid

is

being

C,,,,

or

C,,,.

Two-Pass Exchangers

The expression for the global effectiveness for the parallel flow case is given by Pignotti [43]:

P2

=

PA

+

PB

-

PAPB(

1

+

R)

(72)

and

for the counterflow case by

where

PA

and

PB

are the thermal effectiveness of individual heat exchangers and

R

is the

capacity rate ratio.

N-Pass Exchangers

Counterf7ow

Arrangement. The effectiveness

PN

of

an N-pass assembly, in terms of the efec-

tiveness

P,

of

each unit, which is equal for all units, has been described by Domingos

[44].

For overall countercurrent connection, the effectiveness is given by

P,

=

for

R+:

1

(744

88

Chapter

2

Table

11

J

Shell (Referred

to

Tube Side)

Eq.

no./

Value for

R=

1

Flow arrangement

Ref. General formula

and special

cases

12

T25

[40]

(2R-

1)

21~+(9-'~~''

For

R

=

0.5,

I

PI

=

1

-

[

]

(2R

+

1)

2~

-

4-(R-05)

1

+$-I

1

P,=l------

Q,

=

pu

2

+

NTU

;

1-1:

'I

I

1-1

TEMA

J

shell: shell fluid

mixed

z3

[411

=

2

Same as

E'Zq.

T26

:2

~26

1

+

2R

[1+

AA

-

2Bh (1

+

C)]

oRh+

1

A=---

I

1

1-2

TEMA

J

shell: shell fluid

1

B=

mixed and tube fluid mixed

be-

tween passes

C=l+-

R(lr-'Y2

qlRh-

1

Here,

R

is the heat capacity rate ratio, which is the same for the individual unit, as for the

overall assembly. Alternately, if

PN

is known, then the individual component effectiveness

can

be determined from the following formulas:

-

PN

for

R

=

1

N-

PN(N

-

1)

Parallel Flow Arrangement.

Refer to Table

12

for thermal relation formulas.

6.6

Multipass Crossflow Exchangers

Two or more crossflow units can be coupled in two or more passes either in

an

overall parallel

flow

or

in

an

overall counterflow arrangement. When both fluids are mixed in the interpass,

Heat Exchanger Thermohydraulic Fundamentals

89

Table

11

Continued

Eq.

no./

Value

for

R

=

1

Ref.

General formula

and special cases

1-4

J

Shell: shell fluid mixed

and tube fluid mixed between

9

R('+A)'2

passes

C=

$RA-

1

qRA+

1

l+h

___

(m.'-lI

M

ROr-'

y2

D=l+-

ORA-

1

$=ern

h=

d

4R

m

1!2

T28

[42]

P=

1

Same as

Eq.

T28

-+---

ROR

9

1

(9R-

1)

$-

1

NTU

@=ern

Lime

of

1-N

J

Shell for

N

+

00:

shell fluid mixed and tube

fluid mixed between passes;

stream

symmetric

the resulting flow arrangement can be differentiated only by the flow arrangements in each

pass (unmixed-mixed or mixed-mixed). However, if one fluid is unmixed throughout, the

order in which the streams enter the next pass must be differentiated. The coupling of the

unmixed fluid from one pass to the other pass can be two types as shown in Fig. 43:

(1)

identical order coupling, and

(2)

inverted order coupling. The coupling is referred to an identi-

cal order if the stream leaving one pass enters the next pass from the

same

side as in the

previous pass, as in Fig. 43(a), whereas a coupling is considered to be in an inverted order if

the stream leaving one pass enters the next pass from the opposite side of the previous pass,

as in Fig. 43(b). Inverted-order coupling is very convenient for manufacturing and installation

of heat exchangers. Thermal effectiveness must decrease for constant

NTU

whenever irrevers-

ibilities take place, which may be due to mixing between passes, or due to higher local temper-

90

Chapter

2

8.3

0.4

O.s

0.6

0.7

0.8

8.9

F),

.

Thermal effectiveness

Figure

37

TEMA

J,

,

shell.

Shell

fluid mixed.

F

as

a

function

of

P

for constant

R

(solid lines) and constant

NTU

(dashed lines).

1.0

91

Heat Exchanger Therinohydraulic Fundamentals

-

0.9

5

0.8

e

c

.-

0

c)

3

0

;i

0.7

r

-

0.6

0.5

c.

Thermal

effectiveness

Figure

38

TEMA

J,

shell.

Shell

fluid mixed and tube fluid mixed between passes. F as a function

of

P

for constant

R

(solid lines)

and constant

NTU

(dashed lines), with

F

min

to

avoid temperature cross (horizontal bowl-shaped curve).

92

Chapter

2

1

.0

0.8

L

0

c.

U

0.8

r:

0

.-

Y

0

U

0.7

0.6

0.5

8.1

0.2

0.3

e,

Thermal

effectiveness

Figure

39

TEMA

J,,

shell.

Shell

fluid mixed and tube fluid mixed between passes.

F

as a function of

P

for

constant

R

(solid

lines) and constant

NTU

(dashed lines).

93

Heat Exchanger Thermohydraulic Fundamentals

2-

2

I

t

Figure

40

XI.?

shell arrangement equivalent with two pass crossflow heat exchanger. (a) Parallel

flow;

(b)

counterflow.

ature difference between the fluids, which occurs when the order of the flow arrangement is

inverted

[28].

Some of the possible cases of two-pass heat exchangers are shown in Fig. 44.

All

these cases were analyzed by Stevens et

al.

1291,

some analytically and others by numerical

integration, whereas Back

[3]

solved all possible flow arrangements of two passes units ana-

lytically. Multipass crossflow arrangements with complete mixing between passes were ana-

lyzed by Domingos

[44],

and the formulas are also presented in Ref.

2.

Multipassing with Complete Mixing Between Passes.

Equations

T29

to

T33

in Table

12

de-

fine thermal relation formulas for various multipass crossflow arrangements with complete

mixing between passes. Thermal effectiveness charts are given for the following cases

of

two-

and three-pass cross-counterflow arrangements with complete mixing between passes:

Weaker fluid is mixed in all the passes: For the two-pass arrangement (IV-a or I-d of Fig.

44) the thermal effectiveness chart is given in Fig. 45, and in Fig. 46 for the three-pass

arrangements.

Stronger fluid is mixed in all the passes: For the two-pass arrangement (IV-a or I-d of Fig.

44), the thermal effectiveness chart is given in Fig. 47, and in Fig. 48 for the three-pass

arrangements,

Both the fluids unmixed-unmixed in all the passes: For the two-pass arrangements (IV-d

Kuppan T. Heat Exchanger Design Handbook

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