Chapter 11 - Heat Exchangers - Chapter Notes, Chemical Engineering, Semester Chemical Engineering Notes | EduRev

Created by: Karan

Chemical Engineering : Chapter 11 - Heat Exchangers - Chapter Notes, Chemical Engineering, Semester Chemical Engineering Notes | EduRev

 Page 1


BOOKCOMP, Inc. — John Wiley & Sons / Page 797 / 2nd Proofs / Heat Transfer Handbook / Bejan
1
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
[First Page]
[797], (1)
Lines: 0 to 89
———
* 17.2201pt PgVar
———
Normal Page
* PgEnds: PageBreak
[797], (1)
CHAPTER11
HeatExchangers
ALLAND.KRAUS
UniversityofAkron
Akron,Ohio
11.1 Introduction
11.2 Governing relationships
11.2.1 Introduction
11.2.2 Exchanger surface area
11.2.3 Overall heat transfer coef?cient
11.2.4 Logarithmic mean temperature difference
11.3 Heat exchanger analysis methods
11.3.1 Logarithmic mean temperature difference correction factor method
11.3.2 –N
tu
method
Speci?c–N
tu
relationships
11.3.3 P–N
tu,c
method
11.3.4 ?–P method
11.3.5 Heat transfer and pressure loss
11.3.6 Summaryofworkingrelationships
11.4 Shell-and-tube heat exchanger
11.4.1 Construction
11.4.2 Physical data
Tube side
Shell side
11.4.3 Heat transfer data
Tube side
Shell side
11.4.4 Pressure loss data
Tube side
Shell side
11.5 Compact heat exchangers
11.5.1 Introduction
11.5.2 Classi?cationofcompactheatexchangers
11.5.3 Geometrical factors and physical data
11.5.4 Heat transfer and ?ow friction data
Heat transfer data
Flow friction data
11.6 Longitudinal ?nned double-pipe exchangers
11.6.1 Introduction
797
Page 2


BOOKCOMP, Inc. — John Wiley & Sons / Page 797 / 2nd Proofs / Heat Transfer Handbook / Bejan
1
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
[First Page]
[797], (1)
Lines: 0 to 89
———
* 17.2201pt PgVar
———
Normal Page
* PgEnds: PageBreak
[797], (1)
CHAPTER11
HeatExchangers
ALLAND.KRAUS
UniversityofAkron
Akron,Ohio
11.1 Introduction
11.2 Governing relationships
11.2.1 Introduction
11.2.2 Exchanger surface area
11.2.3 Overall heat transfer coef?cient
11.2.4 Logarithmic mean temperature difference
11.3 Heat exchanger analysis methods
11.3.1 Logarithmic mean temperature difference correction factor method
11.3.2 –N
tu
method
Speci?c–N
tu
relationships
11.3.3 P–N
tu,c
method
11.3.4 ?–P method
11.3.5 Heat transfer and pressure loss
11.3.6 Summaryofworkingrelationships
11.4 Shell-and-tube heat exchanger
11.4.1 Construction
11.4.2 Physical data
Tube side
Shell side
11.4.3 Heat transfer data
Tube side
Shell side
11.4.4 Pressure loss data
Tube side
Shell side
11.5 Compact heat exchangers
11.5.1 Introduction
11.5.2 Classi?cationofcompactheatexchangers
11.5.3 Geometrical factors and physical data
11.5.4 Heat transfer and ?ow friction data
Heat transfer data
Flow friction data
11.6 Longitudinal ?nned double-pipe exchangers
11.6.1 Introduction
797
BOOKCOMP, Inc. — John Wiley & Sons / Page 798 / 2nd Proofs / Heat Transfer Handbook / Bejan
798 HEATEXCHANGERS
1
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
[798], (2)
Lines: 89 to 168
———
0.97pt PgVar
———
Normal Page
PgEnds: T
E
X
[798], (2)
11.6.2 Physical data for annuli
Extruded ?ns
Welded U-?ns
11.6.3 Overall heat transfer coef?cient revisited
11.6.4 Heat transfer coef?cients in pipes and annuli
11.6.5 Pressure loss in pipes and annuli
11.6.6 Wall temperature and further remarks
11.6.7 Series–parallel arrangements
11.6.8 Multiple ?nned double-pipe exchangers
11.7 Transverse high-?n exchangers
11.7.1 Introduction
11.7.2 Bondorcontactresistanceofhigh-?ntubes
11.7.3 Fin ef?ciency approximation
11.7.4 Air-?n coolers
Physical data
Heat transfer correlations
11.7.5 Pressure loss correlations for staggered tubes
11.7.6 Overall heat transfer coef?cient
11.8 Plate and frame heat exchanger
11.8.1 Introduction
11.8.2 Physical data
11.8.3 Heat transfer and pressure loss
11.9 Regenerators
11.9.1 Introduction
11.9.2 Heat capacity and related parameters
Governing differential equations
11.9.3 –N
tu
method
11.9.4 Heat transfer and pressure loss
Heat transfer coef?cients
Pressure loss
11.10 Fouling
11.10.1 Fouling mechanisms
11.10.2 Fouling factors
Nomenclature
References
11.1 INTRODUCTION
A heat exchanger can be de?ned as any device that transfers heat from one ?uid to
another or from or to a ?uid and the environment. Whereas in direct contact heat
exchangers, there is no intervening surface between ?uids, in indirect contact heat
exchangers, the customary de?nition pertains to a device that is employed in the trans-
fer of heat between two ?uids or between a surface and a ?uid. Heat exchangers may
be classi?ed (Shah, 1981, or Mayinger, 1988) according to (1) transfer processes,
Page 3


BOOKCOMP, Inc. — John Wiley & Sons / Page 797 / 2nd Proofs / Heat Transfer Handbook / Bejan
1
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
[First Page]
[797], (1)
Lines: 0 to 89
———
* 17.2201pt PgVar
———
Normal Page
* PgEnds: PageBreak
[797], (1)
CHAPTER11
HeatExchangers
ALLAND.KRAUS
UniversityofAkron
Akron,Ohio
11.1 Introduction
11.2 Governing relationships
11.2.1 Introduction
11.2.2 Exchanger surface area
11.2.3 Overall heat transfer coef?cient
11.2.4 Logarithmic mean temperature difference
11.3 Heat exchanger analysis methods
11.3.1 Logarithmic mean temperature difference correction factor method
11.3.2 –N
tu
method
Speci?c–N
tu
relationships
11.3.3 P–N
tu,c
method
11.3.4 ?–P method
11.3.5 Heat transfer and pressure loss
11.3.6 Summaryofworkingrelationships
11.4 Shell-and-tube heat exchanger
11.4.1 Construction
11.4.2 Physical data
Tube side
Shell side
11.4.3 Heat transfer data
Tube side
Shell side
11.4.4 Pressure loss data
Tube side
Shell side
11.5 Compact heat exchangers
11.5.1 Introduction
11.5.2 Classi?cationofcompactheatexchangers
11.5.3 Geometrical factors and physical data
11.5.4 Heat transfer and ?ow friction data
Heat transfer data
Flow friction data
11.6 Longitudinal ?nned double-pipe exchangers
11.6.1 Introduction
797
BOOKCOMP, Inc. — John Wiley & Sons / Page 798 / 2nd Proofs / Heat Transfer Handbook / Bejan
798 HEATEXCHANGERS
1
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
[798], (2)
Lines: 89 to 168
———
0.97pt PgVar
———
Normal Page
PgEnds: T
E
X
[798], (2)
11.6.2 Physical data for annuli
Extruded ?ns
Welded U-?ns
11.6.3 Overall heat transfer coef?cient revisited
11.6.4 Heat transfer coef?cients in pipes and annuli
11.6.5 Pressure loss in pipes and annuli
11.6.6 Wall temperature and further remarks
11.6.7 Series–parallel arrangements
11.6.8 Multiple ?nned double-pipe exchangers
11.7 Transverse high-?n exchangers
11.7.1 Introduction
11.7.2 Bondorcontactresistanceofhigh-?ntubes
11.7.3 Fin ef?ciency approximation
11.7.4 Air-?n coolers
Physical data
Heat transfer correlations
11.7.5 Pressure loss correlations for staggered tubes
11.7.6 Overall heat transfer coef?cient
11.8 Plate and frame heat exchanger
11.8.1 Introduction
11.8.2 Physical data
11.8.3 Heat transfer and pressure loss
11.9 Regenerators
11.9.1 Introduction
11.9.2 Heat capacity and related parameters
Governing differential equations
11.9.3 –N
tu
method
11.9.4 Heat transfer and pressure loss
Heat transfer coef?cients
Pressure loss
11.10 Fouling
11.10.1 Fouling mechanisms
11.10.2 Fouling factors
Nomenclature
References
11.1 INTRODUCTION
A heat exchanger can be de?ned as any device that transfers heat from one ?uid to
another or from or to a ?uid and the environment. Whereas in direct contact heat
exchangers, there is no intervening surface between ?uids, in indirect contact heat
exchangers, the customary de?nition pertains to a device that is employed in the trans-
fer of heat between two ?uids or between a surface and a ?uid. Heat exchangers may
be classi?ed (Shah, 1981, or Mayinger, 1988) according to (1) transfer processes,
BOOKCOMP, Inc. — John Wiley & Sons / Page 799 / 2nd Proofs / Heat Transfer Handbook / Bejan
GOVERNINGRELATIONSHIPS 799
1
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
[799], (3)
Lines: 168 to 199
———
1.7pt PgVar
———
Normal Page
PgEnds: T
E
X
[799], (3)
(2)numberof?uids,(3)construction,(4)heattransfermechanisms,(5)surfacecom-
pactness,(6)?owarrangement,(7)numberof?uidpasses,and(8)typeofsurface.
Recuperators are direct-transfer heat exchangers in which heat transfer occurs
between two ?uid streams at different temperature levels in a space that is separated
by a thin solid wall (a parting sheet or tube wall). Heat is transferred by convection
from the hot (hotter) ?uid to the wall surface and by convection from the wall surface
to the cold (cooler) ?uid. The recuperator is a surface heat exchanger.
Regenerators are heat exchangers in which a hot ?uid and a cold ?uid ?ow al-
ternately through the same surface at prescribed time intervals. The surface of the
regenerator receives heat by convection from the hot ?uid and then releases it by
convectiontothecold?uid.Theprocessistransient;thatis,thetemperatureofthe
surface (and of the ?uids themselves) varies with time during the heating and cooling
of the common surface. The regenerator is a also surface heat exchanger.
In direct-contact heat exchangers, heat is transferred by partial or complete mix-
ingofthehotandcold?uidstreams.Hotandcold?uidsthatenterthistypeofex-
changer separately leave together as a single mixed stream. The temptation to refer
to the direct-contact heat exchanger as a mixer should be resisted. Direct contact
is discussed in Chapter 19. In the present chapter we discuss the shell-and-tube heat
exchanger, the compact heat exchanger, the longitudinal high-?n exchanger, the trans-
verse high-?n exchanger including the air-?n cooler, the plate-and-frame heat ex-
changer, the regenerator, and fouling.
11.2 GOVERNINGRELATIONSHIPS
11.2.1 Introduction
Assume that there are two process streams in a heat exchanger, a hot stream ?owing
with a capacity rate C
h
=? m
h
C
ph
and a cooler (or cold stream) ?owing with a
capacity rate C
c
=? m
c
c
ph
. Then, conservation ofenergy demands that the heat
transferred between the streams be described by the enthalpy balance
q = C
h
(T
1
- T
2
)= C
c
(t
2
- t
1
) (11.1)
where the subscripts 1 and 2 refer to the inlet and outlet of the exchanger and where
the T’s and t’s are employed to indicate hot- and cold-?uid temperatures, respectively.
Equation(11.1)representsanidealthatmustholdintheabsenceoflosses,and
while it describes the heat that will be transferred (the duty oftheheatexchanger)
for the case of prescribed ?ow and temperature conditions, it does not provide an
indicationofthesizeoftheheatexchangernecessarytoperformthisduty.Thesize
oftheexchangerderivesfromastatementofthe rate equation:
q = U?S?
m
= U
h
?
ov,h
S
h
?
m
= U
c
?
ov,c
S
c
?
m
(11.2)
where S
h
and S
c
are the surface areas on the hot and cold sides of the exchanger, U
h
and U
c
are the overall heat transfer coef?cients referred to the hot and cold sides of
Page 4


BOOKCOMP, Inc. — John Wiley & Sons / Page 797 / 2nd Proofs / Heat Transfer Handbook / Bejan
1
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
[First Page]
[797], (1)
Lines: 0 to 89
———
* 17.2201pt PgVar
———
Normal Page
* PgEnds: PageBreak
[797], (1)
CHAPTER11
HeatExchangers
ALLAND.KRAUS
UniversityofAkron
Akron,Ohio
11.1 Introduction
11.2 Governing relationships
11.2.1 Introduction
11.2.2 Exchanger surface area
11.2.3 Overall heat transfer coef?cient
11.2.4 Logarithmic mean temperature difference
11.3 Heat exchanger analysis methods
11.3.1 Logarithmic mean temperature difference correction factor method
11.3.2 –N
tu
method
Speci?c–N
tu
relationships
11.3.3 P–N
tu,c
method
11.3.4 ?–P method
11.3.5 Heat transfer and pressure loss
11.3.6 Summaryofworkingrelationships
11.4 Shell-and-tube heat exchanger
11.4.1 Construction
11.4.2 Physical data
Tube side
Shell side
11.4.3 Heat transfer data
Tube side
Shell side
11.4.4 Pressure loss data
Tube side
Shell side
11.5 Compact heat exchangers
11.5.1 Introduction
11.5.2 Classi?cationofcompactheatexchangers
11.5.3 Geometrical factors and physical data
11.5.4 Heat transfer and ?ow friction data
Heat transfer data
Flow friction data
11.6 Longitudinal ?nned double-pipe exchangers
11.6.1 Introduction
797
BOOKCOMP, Inc. — John Wiley & Sons / Page 798 / 2nd Proofs / Heat Transfer Handbook / Bejan
798 HEATEXCHANGERS
1
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
[798], (2)
Lines: 89 to 168
———
0.97pt PgVar
———
Normal Page
PgEnds: T
E
X
[798], (2)
11.6.2 Physical data for annuli
Extruded ?ns
Welded U-?ns
11.6.3 Overall heat transfer coef?cient revisited
11.6.4 Heat transfer coef?cients in pipes and annuli
11.6.5 Pressure loss in pipes and annuli
11.6.6 Wall temperature and further remarks
11.6.7 Series–parallel arrangements
11.6.8 Multiple ?nned double-pipe exchangers
11.7 Transverse high-?n exchangers
11.7.1 Introduction
11.7.2 Bondorcontactresistanceofhigh-?ntubes
11.7.3 Fin ef?ciency approximation
11.7.4 Air-?n coolers
Physical data
Heat transfer correlations
11.7.5 Pressure loss correlations for staggered tubes
11.7.6 Overall heat transfer coef?cient
11.8 Plate and frame heat exchanger
11.8.1 Introduction
11.8.2 Physical data
11.8.3 Heat transfer and pressure loss
11.9 Regenerators
11.9.1 Introduction
11.9.2 Heat capacity and related parameters
Governing differential equations
11.9.3 –N
tu
method
11.9.4 Heat transfer and pressure loss
Heat transfer coef?cients
Pressure loss
11.10 Fouling
11.10.1 Fouling mechanisms
11.10.2 Fouling factors
Nomenclature
References
11.1 INTRODUCTION
A heat exchanger can be de?ned as any device that transfers heat from one ?uid to
another or from or to a ?uid and the environment. Whereas in direct contact heat
exchangers, there is no intervening surface between ?uids, in indirect contact heat
exchangers, the customary de?nition pertains to a device that is employed in the trans-
fer of heat between two ?uids or between a surface and a ?uid. Heat exchangers may
be classi?ed (Shah, 1981, or Mayinger, 1988) according to (1) transfer processes,
BOOKCOMP, Inc. — John Wiley & Sons / Page 799 / 2nd Proofs / Heat Transfer Handbook / Bejan
GOVERNINGRELATIONSHIPS 799
1
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
[799], (3)
Lines: 168 to 199
———
1.7pt PgVar
———
Normal Page
PgEnds: T
E
X
[799], (3)
(2)numberof?uids,(3)construction,(4)heattransfermechanisms,(5)surfacecom-
pactness,(6)?owarrangement,(7)numberof?uidpasses,and(8)typeofsurface.
Recuperators are direct-transfer heat exchangers in which heat transfer occurs
between two ?uid streams at different temperature levels in a space that is separated
by a thin solid wall (a parting sheet or tube wall). Heat is transferred by convection
from the hot (hotter) ?uid to the wall surface and by convection from the wall surface
to the cold (cooler) ?uid. The recuperator is a surface heat exchanger.
Regenerators are heat exchangers in which a hot ?uid and a cold ?uid ?ow al-
ternately through the same surface at prescribed time intervals. The surface of the
regenerator receives heat by convection from the hot ?uid and then releases it by
convectiontothecold?uid.Theprocessistransient;thatis,thetemperatureofthe
surface (and of the ?uids themselves) varies with time during the heating and cooling
of the common surface. The regenerator is a also surface heat exchanger.
In direct-contact heat exchangers, heat is transferred by partial or complete mix-
ingofthehotandcold?uidstreams.Hotandcold?uidsthatenterthistypeofex-
changer separately leave together as a single mixed stream. The temptation to refer
to the direct-contact heat exchanger as a mixer should be resisted. Direct contact
is discussed in Chapter 19. In the present chapter we discuss the shell-and-tube heat
exchanger, the compact heat exchanger, the longitudinal high-?n exchanger, the trans-
verse high-?n exchanger including the air-?n cooler, the plate-and-frame heat ex-
changer, the regenerator, and fouling.
11.2 GOVERNINGRELATIONSHIPS
11.2.1 Introduction
Assume that there are two process streams in a heat exchanger, a hot stream ?owing
with a capacity rate C
h
=? m
h
C
ph
and a cooler (or cold stream) ?owing with a
capacity rate C
c
=? m
c
c
ph
. Then, conservation ofenergy demands that the heat
transferred between the streams be described by the enthalpy balance
q = C
h
(T
1
- T
2
)= C
c
(t
2
- t
1
) (11.1)
where the subscripts 1 and 2 refer to the inlet and outlet of the exchanger and where
the T’s and t’s are employed to indicate hot- and cold-?uid temperatures, respectively.
Equation(11.1)representsanidealthatmustholdintheabsenceoflosses,and
while it describes the heat that will be transferred (the duty oftheheatexchanger)
for the case of prescribed ?ow and temperature conditions, it does not provide an
indicationofthesizeoftheheatexchangernecessarytoperformthisduty.Thesize
oftheexchangerderivesfromastatementofthe rate equation:
q = U?S?
m
= U
h
?
ov,h
S
h
?
m
= U
c
?
ov,c
S
c
?
m
(11.2)
where S
h
and S
c
are the surface areas on the hot and cold sides of the exchanger, U
h
and U
c
are the overall heat transfer coef?cients referred to the hot and cold sides of
BOOKCOMP, Inc. — John Wiley & Sons / Page 800 / 2nd Proofs / Heat Transfer Handbook / Bejan
800 HEATEXCHANGERS
1
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
[800], (4)
Lines: 199 to 273
———
0.60005pt PgVar
———
Short Page
PgEnds: T
E
X
[800], (4)
the exchanger and ?
m
is some driving temperature difference. The quantities?
ov,h
and ?
ov,c
are the respective overall ?n ef?ciencies and in the case of an un?nned
exchanger,?
ov,h
=?
ov,c
= 1.
The entire heat exchange process can be represented by
q = U
h
?
ov,h
S
h
?
m
= U
c
?
ov,c
S
c
?
m
= C
h
(T
1
- T
2
)= C
c
(t
2
- t
1
) (11.3)
whichismerelyacombinationofeqs.(11.1)and(11.2).
11.2.2 ExchangerSurfaceArea
Considertheun?nnedtubeoflength L shown in Fig. 11.1a and observe that because
ofthe tube wall thickness d
w
, the inner diameter will be smaller than the outer
diameter and the surface areas will be different:
S
i
=pd
i
L (11.4a)
S
o
=pd
o
L (11.4b)
Inthecaseofthe?nnedtube,shownwithone?nontheinsideandoutsideofthetube
wall in Fig. 11.1b, the ?n surface areas will be
S
fi
= 2n
i
b
i
L (11.5a)
S
fo
= 2n
o
b
o
L (11.5b)
where n
i
and n
o
arethenumberof?nsontheinsideandoutsideofthetubewall,
respectively, and it is presumed that no heat is transferred through the tip of either of
the inner or outer ?ns. In this case, the prime or base surface areas
S
bi
= (pd
i
- n
i
d
fi
)L (11.6a)
S
bo
= (pd
o
- n
o
d
fo
)L (11.6b)
The total surface will then be
S
i
= S
bi
+ S
fi
= (pd
i
- n
i
d
fi
+ 2n
i
b
i
)L
or
S
i
=

pd
i
+ n
i
(2b
i
-d
fi
)

L (11.7a)
S
o
=

pd
o
+ n
o
(2b
o
-d
fo
)

L (11.7b)
The ratio of the ?nned surface to the total surface will be
S
fi
S
i
=
2n
i
b
i
L

pd
i
+ n
i
(2b
i
-d
fi
)

L
=
2n
i
b
i
pd
i
+ n
i
(2b
i
-d
fi
)
(11.8a)
Page 5


BOOKCOMP, Inc. — John Wiley & Sons / Page 797 / 2nd Proofs / Heat Transfer Handbook / Bejan
1
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
[First Page]
[797], (1)
Lines: 0 to 89
———
* 17.2201pt PgVar
———
Normal Page
* PgEnds: PageBreak
[797], (1)
CHAPTER11
HeatExchangers
ALLAND.KRAUS
UniversityofAkron
Akron,Ohio
11.1 Introduction
11.2 Governing relationships
11.2.1 Introduction
11.2.2 Exchanger surface area
11.2.3 Overall heat transfer coef?cient
11.2.4 Logarithmic mean temperature difference
11.3 Heat exchanger analysis methods
11.3.1 Logarithmic mean temperature difference correction factor method
11.3.2 –N
tu
method
Speci?c–N
tu
relationships
11.3.3 P–N
tu,c
method
11.3.4 ?–P method
11.3.5 Heat transfer and pressure loss
11.3.6 Summaryofworkingrelationships
11.4 Shell-and-tube heat exchanger
11.4.1 Construction
11.4.2 Physical data
Tube side
Shell side
11.4.3 Heat transfer data
Tube side
Shell side
11.4.4 Pressure loss data
Tube side
Shell side
11.5 Compact heat exchangers
11.5.1 Introduction
11.5.2 Classi?cationofcompactheatexchangers
11.5.3 Geometrical factors and physical data
11.5.4 Heat transfer and ?ow friction data
Heat transfer data
Flow friction data
11.6 Longitudinal ?nned double-pipe exchangers
11.6.1 Introduction
797
BOOKCOMP, Inc. — John Wiley & Sons / Page 798 / 2nd Proofs / Heat Transfer Handbook / Bejan
798 HEATEXCHANGERS
1
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
[798], (2)
Lines: 89 to 168
———
0.97pt PgVar
———
Normal Page
PgEnds: T
E
X
[798], (2)
11.6.2 Physical data for annuli
Extruded ?ns
Welded U-?ns
11.6.3 Overall heat transfer coef?cient revisited
11.6.4 Heat transfer coef?cients in pipes and annuli
11.6.5 Pressure loss in pipes and annuli
11.6.6 Wall temperature and further remarks
11.6.7 Series–parallel arrangements
11.6.8 Multiple ?nned double-pipe exchangers
11.7 Transverse high-?n exchangers
11.7.1 Introduction
11.7.2 Bondorcontactresistanceofhigh-?ntubes
11.7.3 Fin ef?ciency approximation
11.7.4 Air-?n coolers
Physical data
Heat transfer correlations
11.7.5 Pressure loss correlations for staggered tubes
11.7.6 Overall heat transfer coef?cient
11.8 Plate and frame heat exchanger
11.8.1 Introduction
11.8.2 Physical data
11.8.3 Heat transfer and pressure loss
11.9 Regenerators
11.9.1 Introduction
11.9.2 Heat capacity and related parameters
Governing differential equations
11.9.3 –N
tu
method
11.9.4 Heat transfer and pressure loss
Heat transfer coef?cients
Pressure loss
11.10 Fouling
11.10.1 Fouling mechanisms
11.10.2 Fouling factors
Nomenclature
References
11.1 INTRODUCTION
A heat exchanger can be de?ned as any device that transfers heat from one ?uid to
another or from or to a ?uid and the environment. Whereas in direct contact heat
exchangers, there is no intervening surface between ?uids, in indirect contact heat
exchangers, the customary de?nition pertains to a device that is employed in the trans-
fer of heat between two ?uids or between a surface and a ?uid. Heat exchangers may
be classi?ed (Shah, 1981, or Mayinger, 1988) according to (1) transfer processes,
BOOKCOMP, Inc. — John Wiley & Sons / Page 799 / 2nd Proofs / Heat Transfer Handbook / Bejan
GOVERNINGRELATIONSHIPS 799
1
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
[799], (3)
Lines: 168 to 199
———
1.7pt PgVar
———
Normal Page
PgEnds: T
E
X
[799], (3)
(2)numberof?uids,(3)construction,(4)heattransfermechanisms,(5)surfacecom-
pactness,(6)?owarrangement,(7)numberof?uidpasses,and(8)typeofsurface.
Recuperators are direct-transfer heat exchangers in which heat transfer occurs
between two ?uid streams at different temperature levels in a space that is separated
by a thin solid wall (a parting sheet or tube wall). Heat is transferred by convection
from the hot (hotter) ?uid to the wall surface and by convection from the wall surface
to the cold (cooler) ?uid. The recuperator is a surface heat exchanger.
Regenerators are heat exchangers in which a hot ?uid and a cold ?uid ?ow al-
ternately through the same surface at prescribed time intervals. The surface of the
regenerator receives heat by convection from the hot ?uid and then releases it by
convectiontothecold?uid.Theprocessistransient;thatis,thetemperatureofthe
surface (and of the ?uids themselves) varies with time during the heating and cooling
of the common surface. The regenerator is a also surface heat exchanger.
In direct-contact heat exchangers, heat is transferred by partial or complete mix-
ingofthehotandcold?uidstreams.Hotandcold?uidsthatenterthistypeofex-
changer separately leave together as a single mixed stream. The temptation to refer
to the direct-contact heat exchanger as a mixer should be resisted. Direct contact
is discussed in Chapter 19. In the present chapter we discuss the shell-and-tube heat
exchanger, the compact heat exchanger, the longitudinal high-?n exchanger, the trans-
verse high-?n exchanger including the air-?n cooler, the plate-and-frame heat ex-
changer, the regenerator, and fouling.
11.2 GOVERNINGRELATIONSHIPS
11.2.1 Introduction
Assume that there are two process streams in a heat exchanger, a hot stream ?owing
with a capacity rate C
h
=? m
h
C
ph
and a cooler (or cold stream) ?owing with a
capacity rate C
c
=? m
c
c
ph
. Then, conservation ofenergy demands that the heat
transferred between the streams be described by the enthalpy balance
q = C
h
(T
1
- T
2
)= C
c
(t
2
- t
1
) (11.1)
where the subscripts 1 and 2 refer to the inlet and outlet of the exchanger and where
the T’s and t’s are employed to indicate hot- and cold-?uid temperatures, respectively.
Equation(11.1)representsanidealthatmustholdintheabsenceoflosses,and
while it describes the heat that will be transferred (the duty oftheheatexchanger)
for the case of prescribed ?ow and temperature conditions, it does not provide an
indicationofthesizeoftheheatexchangernecessarytoperformthisduty.Thesize
oftheexchangerderivesfromastatementofthe rate equation:
q = U?S?
m
= U
h
?
ov,h
S
h
?
m
= U
c
?
ov,c
S
c
?
m
(11.2)
where S
h
and S
c
are the surface areas on the hot and cold sides of the exchanger, U
h
and U
c
are the overall heat transfer coef?cients referred to the hot and cold sides of
BOOKCOMP, Inc. — John Wiley & Sons / Page 800 / 2nd Proofs / Heat Transfer Handbook / Bejan
800 HEATEXCHANGERS
1
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
[800], (4)
Lines: 199 to 273
———
0.60005pt PgVar
———
Short Page
PgEnds: T
E
X
[800], (4)
the exchanger and ?
m
is some driving temperature difference. The quantities?
ov,h
and ?
ov,c
are the respective overall ?n ef?ciencies and in the case of an un?nned
exchanger,?
ov,h
=?
ov,c
= 1.
The entire heat exchange process can be represented by
q = U
h
?
ov,h
S
h
?
m
= U
c
?
ov,c
S
c
?
m
= C
h
(T
1
- T
2
)= C
c
(t
2
- t
1
) (11.3)
whichismerelyacombinationofeqs.(11.1)and(11.2).
11.2.2 ExchangerSurfaceArea
Considertheun?nnedtubeoflength L shown in Fig. 11.1a and observe that because
ofthe tube wall thickness d
w
, the inner diameter will be smaller than the outer
diameter and the surface areas will be different:
S
i
=pd
i
L (11.4a)
S
o
=pd
o
L (11.4b)
Inthecaseofthe?nnedtube,shownwithone?nontheinsideandoutsideofthetube
wall in Fig. 11.1b, the ?n surface areas will be
S
fi
= 2n
i
b
i
L (11.5a)
S
fo
= 2n
o
b
o
L (11.5b)
where n
i
and n
o
arethenumberof?nsontheinsideandoutsideofthetubewall,
respectively, and it is presumed that no heat is transferred through the tip of either of
the inner or outer ?ns. In this case, the prime or base surface areas
S
bi
= (pd
i
- n
i
d
fi
)L (11.6a)
S
bo
= (pd
o
- n
o
d
fo
)L (11.6b)
The total surface will then be
S
i
= S
bi
+ S
fi
= (pd
i
- n
i
d
fi
+ 2n
i
b
i
)L
or
S
i
=

pd
i
+ n
i
(2b
i
-d
fi
)

L (11.7a)
S
o
=

pd
o
+ n
o
(2b
o
-d
fo
)

L (11.7b)
The ratio of the ?nned surface to the total surface will be
S
fi
S
i
=
2n
i
b
i
L

pd
i
+ n
i
(2b
i
-d
fi
)

L
=
2n
i
b
i
pd
i
+ n
i
(2b
i
-d
fi
)
(11.8a)
BOOKCOMP, Inc. — John Wiley & Sons / Page 801 / 2nd Proofs / Heat Transfer Handbook / Bejan
GOVERNINGRELATIONSHIPS 801
1
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
[801], (5)
Lines: 273 to 308
———
8.11423pt PgVar
———
Short Page
PgEnds: T
E
X
[801], (5)
S
fo
S
o
=
2n
o
b
o
L

pd
o
+ n
o
(2b
o
-d
fi
)

L
=
2n
o
b
o
pd
o
+ n
o
(2b
o
-d
fo
)
(11.8b)
The overall surface ef?ciencies ?
ov,h
and ?
ov,c
are based on the base surface
operating at an ef?ciency of unity and the ?nned surface operating at ?n ef?ciencies
of?
fi
and?
fo
. Hence
?
ov,i
S
i
= S
bi
+?
fi
S
fi
= S
i
- S
fi
+?
fi
S
fi
or
?
ov,i
= 1-
S
fi
S
i

1-?
fi

(11.9a)
and in a similar manner,
?
ov,o
= 1-
S
fo
S
o

1-?
fo

(11.9b)
Figure11.1 Endviewof( a) a bare tube and (b)asmallcentralangleofatubewithboth
internalandexternal?nsoflength, L.
Read More

Share with a friend

Content Category

Related Searches

Chapter 11 - Heat Exchangers - Chapter Notes

,

Chapter 5- Dynamic Behavior, PPT, Chemical Engineering, Semester, Engineering

,

Objective type Questions

,

Summary

,

Exam

,

Sample Paper

,

video lectures

,

Semester Chemical Engineering Notes | EduRev

,

Viva Questions

,

practice quizzes

,

Important questions

,

MCQs

,

mock tests for examination

,

Chapter 11 - Heat Exchangers - Chapter Notes

,

pdf

,

Chapter 13 Heat Exchangers

,

Chapter 14 : Turbomachinery - Notes, Chemical, Engineering, Semester

,

study material

,

Semester Chemical Engineering Notes | EduRev

,

Semester Chemical Engineering Notes | EduRev

,

Chapter - Batch Processing, PPT, Chemical Engineering, Semester, Engineering

,

Previous Year Questions with Solutions

,

shortcuts and tricks

,

Free

,

Chapter 11 - Heat Exchangers - Chapter Notes

,

Chemical Engineering

,

past year papers

,

Chemical Engineering

,

ppt

,

Semester Notes

,

Chemical Engineering

,

Extra Questions

,

Chapter 3: CHEMICAL THERMODYNAMICS - Notes, Engineering, Semester

;