Process Heat Transfer
Dedication
This book is dedicated to C.C.S.
Process Heat Transfer
Principles and Applications
R.W. Serth
Department of Chemical and Natural Gas Engineering,
Texas A&M University-Kingsville,
Kingsville, Texas, USA
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1.6 Unsteady-State Conduction 24
1.7 Mechanisms of Heat Conduction 31
2 Convective Heat Transfer 43
2.1 Introduction 44
2.2 Combined Conduction and Convection 44
2.3 Extended Surfaces 47
2.4 Forced Convection in Pipes and Ducts 53
2.5 Forced Convection in External Flow 62
2.6 Free Convection 65
3 Heat Exchangers 85
3.1 Introduction 86
3.2 Double-Pipe Equipment 86
3.3 Shell-and-Tube Equipment 87
3.4 The Overall Heat-Transfer Coefficient 93
3.5 The LMTD Correction Factor 98
3.6 Analysis of Double-Pipe Exchangers 102
3.7 Preliminary Design of Shell-and-Tube Exchangers 106
3.8 Rating a Shell-and-Tube Exchanger 109
3.9 Heat-Exchanger Effectiveness 114
4 Design of Double-Pipe Heat Exchangers 127
4.1 Introduction 128
4.2 Heat-Transfer Coefficients for Exchangers without Fins 128
4.3 Hydraulic Calculations for Exchangers without Fins 128
4.4 Series/Parallel Configurations of Hairpins 131
4.5 Multi-tube Exchangers 132
4.6 Over-Surface and Over-Design 133
4.7 Finned-Pipe Exchangers 141
4.8 Heat-Transfer Coefficients and Friction Factors for Finned Annuli 143
4.9 Wall Temperature for Finned Pipes 145
4.10 Computer Software 152

8.2 An Example: TC3 328
8.3 Design Targets 329
8.4 The Problem Table 329
8.5 Composite Curves 331
8.6 The Grand Composite Curve 334
8.7 Significance of the Pinch 335
8.8 Threshold Problems and Utility Pinches 337
8.9 Feasibility Criteria at the Pinch 337
8.10 Design Strategy 339
8.11 Minimum-Utility Design for TC3 340
8.12 Network Simplification 344
8.13 Number of Shells 347
8.14 Targeting for Number of Shells 348
8.15 Area Targets 353
8.16 The Driving Force Plot 356
8.17 Super Targeting 358
8.18 Targeting by Linear Programming 359
8.19 Computer Software 361
CONTENTS vii
9 Boiling Heat Transfer 385
9.1 Introduction 386
9.2 Pool Boiling 386
9.3 Correlations for Nucleate Boiling on Horizontal Tubes 387
9.4 Two-Phase Flow 402
9.5 Convective Boiling in Tubes 416
9.6 Film Boiling 428
10 Reboilers 443
10.1 Introduction 444
10.2 Types of Reboilers 444
10.3 Design of Kettle Reboilers 449

Appendix D Equivalent Lengths of Pipe Fittings 737
Appendix E Properties of Petroleum Streams 740
Index 743
Preface
This book is based on a course in process heat transfer that I have taught for many years. The course
has been taken by seniors and first-year graduate students who have completed an introductory
course in engineering heat transfer. Although this background is assumed, nearly all students need
some review before proceeding to more advanced material. For this r eason, and also to make the
book self-contained, the first three chapters provide a r eview of essential material normally covered
in an introductory heat transfer course. Furthermore, the book is intended for use by practicing
engineers as well as university students, and it has been written with the aim of facilitating self-study.
Unlike some books in this field, no attempt is made herein to cover the entire panoply of heat trans-
fer equipment. Instead, the book focuses on the types of equipment most widely used in the chemical
process industries, namely, shell-and-tube heat exchangers (including condensers and reboilers),
air-cooled heat exchangers and double-pipe (hairpin) heat exchangers. Within the confines of a sin-
gle volume, this approach allows an in-depth treatment of the material that is most relevant from an
industrial perspective, and provides students with the detailed knowledge needed for engineering
practice. This approach is also consistent with the time available in a one-semester course.
Design of double-pipe exchangers is presented in Chapter 4. Chapters 5–7 comprise a unit dealing
with shell-and-tube exchangers in operations involving single-phase fluids. Design of shell-and-tube
exchangers is covered in Chapter 5 using the Simplified Delaware method for shell-side calcula-
tions. For pedagogical reasons, more sophisticated methods for performing shell-side heat-transfer
and pressure-drop calculations are presented separately in Chapter 6 (full Delaware method) and
Chapter 7 (Stream Analysis method). Heat exchanger networks are covered in Chapter 8. I nor-
mally pr esent this topic at this point in the course to provide a change of pace. However, Chapter
8 is essentially self-contained and can, therefore, be covered at any time. Phase-change operations
are covered in Chapters 9–11. Chapter 9 presents the basics of boiling heat transfer and two-phase
flow. The latter is encountered in both Chapter 10, which deals with the design of reboilers, and
Chapter 11, which covers condensation and condenser design. Design of air-cooled heat exchang-
ers is presented in Chapter 12. The material in this chapter is essentially self-contained and, hence,

should not be unduly concerned if their results differ somewhat from those presented in the text.
Indeed, even the same version of a code, when run on different machines, can produce slightly
different results due to differences in round-off errors. With these caveats, it is hoped that the
detailed computer examples will prove helpful in learning to use the software packages, as well as
in understanding their idiosyncrasies and limitations.
I have made a concerted effort to introduce the complexities of the subject matter gradually
throughout the book in order to avoid overwhelming the reader with a massive amount of detail
at any one time. As a result, information on shell-and-tube exchangers is spread over a number of
chapters, and some of the finer details are introduced in the context of example problems, including
computer examples. Although there is an obvious downside to this strategy, I nevertheless believe
that it represents good pedagogy.
Both English units, which are still widely used by American industry, and SI units are used in this
book. Students in the United States need to be pr oficient in both sets of units, and the same is true
of students in countries that do a large amount of business with U.S. firms. In order to minimize
the need for unit conversion, however, working equations are either given in dimensionless form
or, when this is not practical, they are given in both sets of units.
I would like to take this opportunity to thank the many students who have contributed to this
effort over the years, both directly and indirectly through their participation in my course. I would
also like to express my deep appreciation to my colleagues in the Department of Chemical and
Natural Gas Engineering at TAMUK, Dr. Ali Pilehvari and Mrs. Wanda Pounds. Without their help,
encouragement and friendship, this book would not have been written.
Conversion Factors
Acceleration 1 m/s
2
=4.2520 ×10
7
ft/h
2
Area 1m
2

3
Heat transfer coefficient 1 W/m
2
·K =0.17612 Btu/h ·ft
2
·
◦
F
Heat transfer rate 1W =3.4123 Btu/h
Kinematic viscosity and thermal 1m
2
/s =3.875 ×10
4
ft
2
/h
diffusivity
Latent heat and specific enthalpy 1 kJ/kg =0.42995 Btu/lbm
Length 1m =3.2808 ft
Mass 1kg =2.2046 lbm
Mass flow rate 1 kg/s =7936.6 lbm/h
Mass flux 1 kg/s ·m
2
=737.35 lbm/h ·ft
2
Power 1kW =3412 Btu/h
=1.341 hp
Pressure (stress) 1Pa(1N/m
2
) =0.020886 lbf/ft

Temperature difference 1K =1
◦
C =1.8
◦
F =1.8
◦
R
Thermal conductivity
1 W/m ·K =0.57782 Btu/h ·ft ·
◦
F
Thermal resistance 1 K/W =0.52750
◦
F ·h/Btu
Viscosity 1 kg/m ·s =1000 cp =2419 lbm/ft ·h
Volume
1m
3
=35.314 ft
3
=264.17 gal
Volumetric flow rate 1m
3
/s =2118.9 ft
3
/min(cfm)
=1.5850 ×10
4
gal/min (gpm)
lbf: pound force and lbm: pound mass.

ft/h
2
Stefan-Boltzman constant σ
SB
5.670 ×10
−8
W/ m
2
·K
4
1.714 ×10
−9
Btu/h ·ft
2
·
◦
R
4
Acknowledgements
Item Special Credit Line
Figure 3.1 Reprinted, with permission, from Extended Surface Heat Transfer by D. Q. Kern and
A. D. Kraus. Copyright © 1972 by The McGraw-Hill Companies, Inc.
Table 3.1 Reprinted, with permission, from Perry’s Chemical Engineers’ Handbook, 7th edn.,
R. H. Perry and D. W. Green, eds. Copyright © 1997 by The McGraw-Hill Companies, Inc.
Figure 3.6 Reprinted, with permission, from Extended Surface Heat Transfer by D. Q. Kern and
A. D. Kraus. Copyright © 1972 by The McGraw-Hill Companies, Inc.
Figure 3.7 Reprinted, with permission, from Extended Surface Heat Transfer by D. Q. Kern and
A. D. Kraus. Copyright © 1972 by The McGraw-Hill Companies, Inc.
Table 3.2 Reproduced, with permission, from J. W. Palen and J. Taborek, Solution of shell side flow
pressure drop and heat transfer by stream analysis method, Chem. Eng. Prog. Symposium

ACKNOWLEDGEMENTS xiii
Item Special Credit Line
Figure 9.2 Copyright © 1997 from Boiling Heat Transfer and Two-Phase Flow, 2nd edn., by
L. S. Tong and Y. S. Tang. Reproduced by permission of Taylor & Francis, a division
of Informa plc.
Figures 10.1–10.5 Copyright © 1988 from Heat Exchanger Design Handbook by E. U. Schlünder, Editor-
in-Chief. Reproduced by per mission of Taylor & Francis, a division of Informa plc.
Figure 10.6 Reproduced, with permission, from A. W. Sloley, Properly design thermosyphon
reboilers, Chem. Eng. Prog., 93, No. 3, 52–64, 1997. Copyright © 1997 by AIChE.
Table 10.1 Copyright © 1988 from Heat Exchanger Design Handbook by E. U. Schlünder, Editor-
in-Chief. Reproduced by per mission of Taylor & Francis, a division of Informa plc.
Appendix 10.A Reprinted, with permission, from Chemical Engineers’ Handbook, 5th edn.,
R. H. Perry and C. H. Chilton, eds. Copyright © 1973 by The McGraw-Hill
Companies, Inc.
Figure 11.1 Copyright © 1988 from Heat Exchanger Design Handbook by E. U. Schlünder, Editor-
in-Chief. Reproduced by per mission of Taylor & Francis, a division of Informa plc.
Figure 11.3 Copyright © 1998 from Heat Exchangers: Selection, Rating and Thermal Design by
S. Kakac and H. Liu. Reproduced by permission of Taylor & Francis, a division of
Informa plc.
Figure 11.6 Copyright © 1988 from Heat Exchanger Design Handbook by E. U. Schlünder, Editor-
in-Chief. Reproduced by per mission of Taylor & Francis, a division of Informa plc.
Figure 11.7 Copyright © 1988 from Heat Exchanger Design Handbook by E. U. Schlünder, Editor-
in-Chief. Reproduced by per mission of Taylor & Francis, a division of Informa plc.
Figure 11.8 Reprinted, with permission, from Distillation Operation by H. Z. Kister. Copyright ©
1990 by The McGraw-Hill Companies, Inc.
Figure 11.11 Reprinted, with permission, from G. Breber, J. W. Palen and J. Taborek, Prediction
of tubeside condensation of pure components using flow regime criteria, J. Heat
Transfer, 102, 471–476, 1980. Originally published by ASME.
Figure 11.12 Copyright © 1998 from Heat Exchangers: Selection, Rating and Thermal Design by
S. Kakac and H. Liu. Reproduced by permission of Taylor & Francis, a division of

Table A.17 Reprinted, with permission, from Chemical Engineers’ Handbook, 5th edn., R. H. Perry and
C. H. Chilton, eds. Copyright © 1973 by The McGraw-Hill Companies, Inc.
Figure A.1 Reprinted, with permission, from Chemical Engineers’ Handbook, 5th edn., R. H. Perry and
C. H. Chilton, eds. Copyright © 1973 by The McGraw-Hill Companies, Inc.
Table A.18 Reprinted, with permission, from Chemical Engineers’ Handbook, 5th edn., R. H. Perry and
C. H. Chilton, eds. Copyright © 1973 by The McGraw-Hill Companies, Inc.
Figure A.2 Reprinted, with permission, from Chemical Engineers’ Handbook, 5th edn., R. H. Perry and
C. H. Chilton, eds. Copyright © 1973 by The McGraw-Hill Companies, Inc.
1
HEAT
CONDUCTION
Contents
1.1 Introduction 2
1.2 Fourier’s Law of Heat Conduction 2
1.3 The Heat Conduction Equation 6
1.4 Thermal Resistance 15
1.5 The Conduction Shape Factor 19
1.6 Unsteady-State Conduction 24
1.7 Mechanisms of Heat Conduction 31
1/2 HEAT CONDUCTION
1.1 Introduction
Heat conduction is one of the three basic modes of thermal energy transport (convection and
radiation being the other two) and is involved in virtually all process heat-transfer operations. In
commercial heat exchange equipment, for example, heat is conducted through a solid wall (often
a tube wall) that separates two fluids having different temperatures. Furthermore, the concept of
thermal resistance, which follows from the fundamental equations of heat conduction, is widely used
in the analysis of problems arising in the design and operation of industrial equipment. In addition,
many routine pr ocess engineering problems can be solved with acceptable accuracy using simple
solutions of the heat conduction equation for rectangular, cylindrical, and spherical geometries.
This chapter provides an introduction to the macroscopic theory of heat conduction and its engi-

Writing this relationship as an equality, we have:
q
x
=
kA(T
1
− T
2
)
B
(1.1)
T
2
q
x
x
Insulated
Insulated
Insulated
B
q
x
T
1
Figure 1.1 One-dimensional heat conduction in a solid.
HEAT CONDUCTION 1/3
The constant of proportionality, k, is called the thermal conductivity. Equation (1.1) is also applicable
to heat conduction in liquids and gases. However, when temperature differences exist in fluids, con-
vection currents tend to be set up, so that heat is generally not transferred solely by the mechanism
of conduction.

x
→
dT
dx
and Equation (1.3) becomes:
q
x
=−kA
dT
dx
(1.4)
Equation (1.4) is not subject to the restriction of constant k. Furthermore, when k is constant, it can
be integrated to yield Equation (1.1). Hence, Equation (1.4) is the general one-dimensional form of
Fourier’s law. The negative sign is necessary because heat flows in the positive x-direction when
the temperatur e decreases in the x-direction. Thus, according to the standard sign convention that
q
x
is positive when the heat flow is in the positive x-direction, q
x
must be positive when dT /dx is
negative.
It is often convenient to divide Equation (1.4) by the area to give:
ˆ
q
x
≡ q
x
/A =−k
dT
dx

y
→
j
+
ˆ
q
z
→
k
(1.6)
where
→
ˆ
q is the heat flux vector and
→
i
,
→
j
,
→
k
are unit vectors in the x-, y-, z-directions, respectively.
Each of the component fluxes is given by a one-dimensional Fourier expression as follows:
ˆ
q
x
=−k
∂T
∂x

∂z
→
k

(1.8)
The vector in parenthesis is the temperature gradient vector, and is denoted by
→
∇
T . Hence,
→
ˆ
q =−k
→
∇
T (1.9)
Equation (1.9) is the three-dimensional form of Fourier’s law. It is valid for homogeneous, isotropic
materials for which the thermal conductivity is the same in all directions.
Equation (1.9) states that the heat flux vector is proportional to the negative of the temperature
gradient vector. Since the gradient direction is the direction of greatest temperature increase, the
negative gradient direction is the direction of greatest temperature decrease. Hence, Fourier’s law
states that heat flows in the direction of greatest temperature decrease.
Example 1.1
The block of 304 stainless steel shown below is well insulated on the front and back surfaces, and
the temperature in the block varies linearly in both the x- and y-directions, find:
(a) The heat fluxes and heat flows in the x- and y-directions.
(b) The magnitude and direction of the heat flux vector.
5°C

10°C
x

=−k
T
x
=−14.4

−5
0.05

= 1440 W/m
2
ˆ
q
y
=−k
∂T
∂y
=−k
T
y
=−14.4

10
0.1

=−1440 W/m
2
The heat flows are obtained by multiplying the fluxes by the corresponding cross-sectional
areas:
q
x

j
→
ˆ
q =1440
→
i
− 1440
→
j




→
ˆ
q




=[(1440)
2
+ (−1440)
2
]
0.5
= 2036.5 W/m
2
The angle, θ, between the heat flux vector and the x-axis is calculated as follows:
tan θ =

ˆ
q
x


x
A. Similarly, the rate at which thermal
energy leaves the element across the face at x +x is
ˆ
q
x


x+x
A. For a homogeneous heat source
x
x
x
ϩ ∆x
q
ˆ
xx
q
ˆ
ϩ∆x
∆x
xx
Figure 1.2 Differential volume element used in derivation of conduction equation.
HEAT CONDUCTION 1/7
of strength

and taking the limit as x →0 yields:
ρc
∂T
∂t
=−
∂
ˆ
q
x
∂x
+
˙
q
Using Fourier’s law as given by Equation (1.5), the balance equation becomes:
ρc
∂T
∂t
=
∂
∂x

k ∂T
∂x

+
˙
q
When conduction occurs in all three coordinate directions, the balance equation contains y- and
z-derivatives analogous to the x-derivative. The balance equation then becomes:
ρc

written as:
ρc
k
∂T
∂t
=
∂
2
T
∂x
2
+
∂
2
T
∂y
2
+
∂
2
T
∂z
2
+
˙
q
k
(1.12)
or
1

∂x

+
∂
∂y

k
∂T
∂y

+
∂
∂z

k
∂T
∂z

+
˙
q
The components of the heat flux vector,
→
ˆ
q ,are:
ˆ
q
x
=−k
∂T

∂T
∂r

+
1
r
2
∂
∂φ

k
∂T
∂φ

+
∂
∂z

k
∂T
∂z

+
˙
q
The components of
→
ˆ
q are:
ˆ

ρ c
∂T
∂ t
=
1
r
2
∂
∂r

kr
2
∂T
∂r

+
1
r
2
sin θ
∂
∂θ

k sin θ
∂T
∂θ

+
1
r

r
∂T
∂θ
;
ˆ
q
φ
=−
k
r sin θ
∂T
∂φ
The use of the conduction equation is illustrated in the following examples.
Example 1.2
Apply the conduction equation to the situation illustrated in Figure 1.1.
Solution
In order to make the mathematics conform to the physical situation, the following conditions are
imposed:
(1) Conduction only in x-direction ⇒ T =T(x), so
∂T
∂y
=
∂T
∂z
=0
(2) No heat source ⇒
˙
q =0
(3) Steady state ⇒
∂T

(1) At x =0 T =T
1
(2) At x =BT=T
2
The first boundary condition gives T
1
=C
2
and the second then gives:
T
2
= C
1
B + T
1
1/10 HEAT CONDUCTION
Solving for C
1
we find:
C
1
=
T
2
− T
1
B
The heat flux is obtained from Fourier’s law:
ˆ
q

kA(T
1
− T
2
)
B
Since this is the same as Equation (1.1), we conclude that the mathematics are consistent with the
experimental results.
Example 1.3
Apply the conduction equation to the situation illustrated in Figure 1.1, but let k =a +bT, where a
and b are constants.
Solution
Conditions 1–3 of the previous example are imposed. The conduction equation then becomes:
0 =
d
dx

k
dT
dx

Integrating once gives:
k
dT
dx
= C
1
The variables can now be separated and a second integration performed. Substituting for k,we
have:
(a + bT )dT = C

B
+
b
2B
(T
2
2
− T
2
1
)