Kuppan T. Heat Exchanger Design Handbook

94

Chapter

2

1

ti

--c

CROS$-tOOWTER

FLON

-

*

CROSB

-

PARALLEL

FLOW

it

FLUID

1

r

3 r

FLUID

2

FLUID

1

.L

A ,

c

FLUID

1

i

J

FLUID

2

(e)

FLUID

2

__e

FLUID

1

+

(f)

L

-

FLUID

1

'c-

L

Figure

41

Multipass assemblies.

95

Heat Exchanger Thermohydraulic Fundamentals

f

Figure

42

Multipassing in the same unit.

Table

12

Multiple Assemblies

of

Heat Exchangers

Eq.

no./

Flow arrangement Ref. General formula Value for

C*

=

1

and C

=

0

Fluid

2

Fluid

1

h'

T29

[441

1

-

E[

1

-

E,(

1

+

C*)]

~j,

=

0.5

[

1

-

(I

-

2E,)']

\=I

for

C*

=

1

Eh'

=

1

+

c*

=

1

-(I

-E,)'

for

C*

=

0

l-[l-Ep(l+C*)IK

N-pass exchanger (N

=

3

as

Ex

=

1

+

c*

~,,=0.5

[l

-(1

-2~\)"]

shown): parallel-cross-

for

C*

=

I

flow arrangement; fluids

Note

C*

=

C:,

and NTU

=

N NTU,

mixed between passes;

=

1

-(I

-E*)"\

each pass having the

E,

=

___

[l-{l-EN(l+C*)}i'n]

for

C*

=

0

same effectiveness

E,

1

+

c*

Fluid

2

Fluid

1

T30

[44]

Eh'

=

1

-

E,C*

c*

-

I=

I

[l-tl

N-pass exchanger,

(N

=

3

as

shown): counter-cross-

flow arrangement; fluids

mixed between passes,

\

1-Ep

I

Ey

=

NE,

for

C*

=

1

and each pass having the

1

+(N-

l)~,,

same effectiveness

E,

=

1

-(I

-E,,)~

for

c*=O

Note

C*

=

C:,

and

NTU

=

N NTU,

1

-

E&*

I/N

1-

____

I

1-EN

E,

=

EY

for

C*

=

1

E,

=

N-(N-

1)

EN

=

1

-

(1

-

Ey)

liN

for C*

=

0

96

Chapter

2

Table

12

Continued

Eq.

no./

Flow arrangement Ref. General formula

Value for

C*

=

1 and

C

=

0

Cmax

fluid

T31

[44]

C*

N-pass exchanger (N

=

3

as

shown):

C,,,,

stream

is

in

parallel,

C,,,

stream is in

series; series fluid mixed

between passes, and each

pass having the same ef-

fectiveness

E,

Cmin

fluid

T32

[U]

Parallel stream as

C,,,

stream and

E,,

=

1

-

(1

-

&,bN

1

for

C:=

1

--

NC*

1-20

-

NC*)

for N

-+

00,

C*

=

0

cmax

fluid

C*

=

I/NC;, NTU

=

NTUJC*

E,=

1

-(I

-E~)l"

N-pass exchanger

(N=

3

as

shown):

C,,,

stream in

1

for

C:

=

1

-

1

N

C*

parallel,

C,,,

stream is in

E,=-[l

-(1

-&h.)I"]

G

=

1 for N

+

00,

C:

=

0

series; series fluid is

mixed between passes,

and each pass having the

same effectiveness

E,

T33

[44]

Parallel stream as

C,,,

stream and

C*

=

1

only when N

=

1

C,,,,/N

>

C,,,,

and C*

S

1/N

c

&h=

1

-(I

Eh

=

1

-

(1

-

E,)~

for

C;

=

1

-

I

C*

=

C$/N,

NTU

=

NTU, N

=

1

-

e-NTL

for

C*

=

0

&p

=

1

-

(1

-

&N)

'IN

E,

=

1

-

(1

-

EN)

for

C:

=

1

=

1

-

e-mLP

for

C:

=

0

97

Heat Exchanger Thennohydraulic Fundamentals

TLh

Tuk

I

kid

fluid

Pass

Return

or

Header

Tub

fluid

Tuba

-

7

f

luld

Figure

43

Two pass parallel-cross flow

with

both

fluids unmixed throughout; coupling

of

tubefluid

between passes.

(a)

Identical order coupling;

(b)

inverted order coupling. The cases (c) and (d) are

symbolic representations

of

cases (a) and

(b),

respectively

[l].

of Fig.

44),

the thermal effectiveness chart is given in Fig. 49, and in Fig.

50

for the three-

pas

s

arrangement

s.

Two Passes with One Fluid Unmixed Throughout, Cross-Counterjlow Arrangement.

Some of

the possible cases of two passes with one fluid unmixed throughout with cross-counterflow

arrangements are given here, and these cases were solved by Stevens et al. [29]:

Two-pass cross-counterflow arrangement. Fluid

1

unmixed throughout, inverted-order cou-

pling; fluid 2 mixed throughout (11-a

of

Fig.

44).

Two-pass cross-counterflow arangement. Fluid

1

mixed throughout; fluid

2

unmixed

throughout, inverted-order coupling (I-b of Fig.

44).

Two-pass cross-counterflow arrangement. Fluid

1

unmixed throughout, identical-order

coupling; fluid 2 mixed throughout (111-a

of

Fig.

44).

Two-pass cross-counterflow arrangement. Fluid

1

mixed throughout; fluid

2

unmixed

throughout, identical-order coupling (I-c of Fig.

44).

Thermal relation formulas (T34T37) for these cases are given in Table 13, and thermal effec-

tiveness charts are given in Figs. 51, 52, 53, and

54,

respectively.

Two Passes with Both Fluids Unmixed-Unmixed in Each Pass and One Fluid Unmixed

Throughout, Cross-Counterfow Arrangement.

Possible cases of two passes with both fluids

unmixed-unmixed in each pass and one fluid unmixed throughout with cross-counterflow ar-

rangements are:

1.

Two-pass cross-counterflow arrangement. Fluid

1

unmixed throughout, inverted-order cou-

pling; fluid 2 unmixed in each pass and mixed between passes (11-d of Fig.

44).

2. Two-pass cross-counterflow arrangement. Fluid

1

unmixed in each pass and mixed

be-

tween passes; fluid

2

unmixed throughout, inverted-order coupling (IV-b

of

Fig.

44).

98

Clza

p

te

r

2

I

FLUID

4

UNMIXED

IN

ANY

PASS

FWIDI

MIXED

UNMIXED

6ETWEEN

PASSES

MIXED

6ETWEEN

2-

fa

IN-TED

2-

ORDER

IEEclTlCAL

ORDER

ttt

2

m

a

I,

PASSES

2-c

m

2-

=

f'

2-

m

f'

2-

Figure

44

Some

of

the possible cases

of

two pass

heat exchangers

1291.

99

Heat Exchanger Thermohydraulic Fundamentals

6.9

a

-8

c

0

.d

U

Q)

::

3

3.7

0.0

n.5

8.1

8.2

0.3

8.4

0.5

0.8

0,3

0.8

0.9

1

.a

e,

Thermal effectiveness

Figure

45

Two pass cross-countefflow arrangement with complete mixing between passes. Each pass

is

unmixed-mixed arrange-

ment with weaker fluid mixed (iv-a

or

I-d

of

Fig.

44);

F-R-P-NTU

chart;

F

as

a function

of

P

for constant

R

(solid lines) and

constant

NTU

(dashed lines).

100

Chapter

2

1

.e

a.0

c.

..-I

U

2.7

U

ci

2.6

8.1

0.2

8.3

8.4

0.6

8.7

8.8

0.8

1

.a

y,

Thermal

effectiveness

Figure

46

Three

pass cross-counterflow arrangement with complete mixing between passes. Each pass is unmixed-mixed arrange-

ment

with weaker fluid

mixed;

F-R-P-NTU

chart;

F

as

a

function of

P

for

constant

R

(solid lines) and constant

NTU

(dashed lines).

101

Heat Exchanger Thermohydraulic Fundamentals

2.7

y,

Thermal effectiveness

Figure

47

Two pass cross-counterflow arrangement with complete mixing between passes. Each pass is unmixed-mixed arrange-

ment with stronger fluid mixed (iv-a or I-d

of

Fig.

44);

F-R-P-NTU chart;

F

as

a

function of

P

for constant R (solid lines) and

constant NTU (dashed lines).

102

Chapter

2

0.1

8.2

0.3

0.4

8.6

0.6

0.7

0.8

O.a

1

.e

q,

Thermal

effectiveness

Figure

48

Three pass cross-counterflow arrangcment with complete mixing between passes. Each

pass

is unmixed-mixed arrange-

ment with stronger fluid mixed; F-R-P-NTU chart; F

as

a

function of P for constant R (solid lines) and constant NTU (dashed lines).

Heat Exchanger The

mo

h ydrau

I

ic Fundamenta

Is

I03

139

08

07

06

05

04

03

02

01

00

Figure

49

(a) Two pass cross-counterflow arrangement with complete mixing between passes. In

each

pass

both the fluids unmixed (iv-d

of

Fig.

44);

R-P-NTU

chart.

(b)

F-R-P-NTU

chart;

F

as

a

function

of

P

for

constant

R

(solid lines) and constant

NTU

(dashed lines).

Kuppan T. Heat Exchanger Design Handbook

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