Advances in thermal design of heat exchangers

Advances in Thermal Design of
Heat Exchangers
A Numerical Approach:
Direct-sizing, step-wise rating, and transients

Eric M Smith

John Wiley & Sons, Ltd

Professional

Advances in Thermal Design of Heat Exchangers: A Numerical Approach: Direct-sizing, step-wise
rating, and transients. Eric M. Smith
Copyright  2005 John Wiley & Sons, Ltd. ISBN: 0-470-01616-7


Advances in Thermal Design of Heat Exchangers


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Advances in Thermal Design of
Heat Exchangers
A Numerical Approach:
Direct-sizing, step-wise rating, and transients

Eric M Smith

John Wiley & Sons, Ltd

Professional


Copyright © 2005

Eric M. Smith

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This volume is dedicated to Dorothy my wife
for her unfailing kindness and understanding,
and to my three sons for their consistent support.


'If you can build hotter or colder than anyone else,
If you can build higher or faster than anyone else,
If you can build deeper or stronger than anyone else,
If...
Then, in principle, you can solve all the other problems in between.'
(Attributed to Sir Monty Finniston, FRS)


Contents
Preface

xxiii

Chapter 1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11

Classification
Class definition
Exclusions and extensions
Helical-tube, multi-start coil
Plate-fin exchangers
RODbaffle
Helically twisted flattened tube
Spirally wire-wrapped
Bayonet tube
Wire-woven heat exchangers
Porous matrix heat exchangers
Some possible applications

1

1
1
3
5
6
7
7
8
9
9
10

Chapter 2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10

Fundamentals
Simple temperature distributions
Log mean temperature difference
LMTD-Ntu rating problem
LMTD-Ntu sizing problem
Link between Ntu values and LMTD

The 'theta' methods
Effectiveness and number of transfer units
e-Ntu rating problem
e-Ntu sizing problem
Comparison of LMTD-Ntu
and e-Ntu approaches
Sizing when Q is not specified
Optimum temperature profiles in
contraflow
Optimum pressure losses in contraflow
Compactness and performance
Required values of Ntu in cryogenics
To dig deeper
Dimensionless groups

19
19
21
23
25
26
26
27
31
32

35
40
42
42

45
47

Steady-State Temperature Profiles
Linear temperature profiles in contraflow
General cases of contraflow and parallel flow

59
59
61

2.11
2.12
2.13
2.14
2.15
2.16
2.17
Chapter 3
3.1
3.2

33
34


viii

Contents

3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13

Condensation and evaporation
Longitudinal conduction in contraflow
Mean temperature difference in unmixed crossflow
Extension to two-pass unmixed crossflow
Involute-curved plate-fin exchangers
Longitudinal conduction in one-pass unmixed crossflow
Determined and undetermined crossflow
Possible optimization criteria
Cautionary remark about core pressure loss
Mean temperature difference in complex arrangements
Exergy destruction

66
67
74
79
82
83

90
92
92
93
94

Chapter 4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18

Direct-Sizing of Plate-Fin Exchangers
Exchanger lay-up
Plate-fin surface geometries
Flow-friction and heat-transfer correlations

Rating and direct-sizing design software
Direct-sizing of an unmixed crossflow exchanger
Concept of direct-sizing in contraflow
Direct-sizing of a contraflow exchanger
Best of rectangular and triangular ducts
Best small, plain rectangular duct
Fine-tuning of ROSF surfaces
Overview of surface performance
Headers and flow distribution
Multi-stream design (cryogenics)
Buffer zone or leakage plate 'sandwich'
Consistency in design methods
Geometry of rectangular offset strip fins
Compact fin surfaces generally
Conclusions

99
99
101
103
103
106
110
113
120
125
127
127
130
130

130
132
133
138
138

Chapter 5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11

Direct-Sizing of Helical-Tube Exchangers
Design framework
Consistent geometry
Simplified geometry
Thermal design
Completion of the design
Thermal design results for t/d = 1.346
Fine tuning
Design for curved tubes
Discussion
Part-load operation with by-pass control

Conclusions

143
143
145
151
153
159
162
163
168
172
174
174


Contents

ix

Chapter 6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9

6.10

Direct-Sizing of Bayonet-Tube Exchangers
Isothermal shell-side conditions
Evaporation
Condensation
Design illustration
Non-isothermal shell-side conditions
Special explicit case
Explicit solution
General numerical solutions
Pressure loss
Conclusions

177
177
178
189
190
191
194
196
199
201
204

Chapter 7
7.1
7.2
7.3

7.4
7.5
7.6
7.7
7.8
7.9
7.10
7.11
7.12
7.13
7.14
7.15
7.16
7.17

Direct-Sizing of RODbaffle Exchangers
Design framework
Configuration of the RODbaffle exchanger
Approach to direct-sizing
Flow areas
Characteristic dimensions
Design correlations
Reynolds numbers
Heat transfer
Pressure loss tube-side
Pressure loss shell-side
Direct-sizing
Tube-bundle diameter
Practical design
Generalized correlations

Recommendations
Other shell-and-tube designs
Conclusions

207
207
208
208
209
209
210
211
211
213
214
215
217
217
220
222
222
224

Chapter 8

Exergy Loss and Pressure Loss

229

Exergy loss

Objective
Historical development
Exergy change for any flow process
Exergy loss for any heat exchangers
Contraflow exchangers
Dependence of exergy loss number on absolute
temperature level
Performance of cryogenic plant
Allowing for leakage
Commercial considerations
Conclusions

229
229
230
231
233
234

8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.10

236
238
240
242
242


x

Contents

Pressure loss
Control of flow distribution
Header design
Minimizing effects of flow maldistribution
Embedded heat exchangers
Pumping power

243
243
244
250
251
253

Chapter 9
9.1
9.2
9.3
9.4

9.5
9.6

Transients in Heat Exchangers
Review of solution methods - contraflow
Contraflow with finite differences
Further considerations
Engineering applications - contraflow
Review of solution methods - crossflow
Engineering applications - crossflow

257
257
259
265
266
267
268

Chapter 10
10.1
10.2
10.3
10.4
10.5

Single-Blow Test Methods
Features of the test method
Choice of theoretical model
Analytical and physical assumptions

Simple theory
Relative accuracy of outlet response curves
in experimentation
Conclusions on test methods
Practical considerations
Solution by finite differences
Regenerators

275
275
276
277
278

8.11
8.12
8.13
8.14
8.15

10.6
10.7
10.8
10.9
Chapter 11
11.1
11.2
11.3
11.4
11.5

11.6
11.7
11.8
Chapter 12
12.1
12.2
12.3

Heat Exchangers in Cryogenic Plant
Background
Liquefaction concepts and components
Liquefaction of nitrogen
Hydrogen liquefaction plant
Preliminary direct-sizing of multi-stream
heat exchangers
Step-wise rating of multi-stream heat exchangers
Future commercial applications
Conclusions
Heat Transfer and Flow Friction
in Two-Phase Flow
With and without phase change
Two-phase flow regimes
Two-phase pressure loss

284
287
287
289
290
297

297
298
307
313
314
317
321
322
325
325
326
327


Contents

12.4
12.5
12.6
12.7
12.8
Appendix A
A. 1
A.2
A.3
Appendix B
B.I
B.2
B.3
B.4

B.5
B.6
B.7
B.8

Two-phase heat-transfer correlations
Two-phase design of a double-tube exchanger
Discussion
Aspects of air conditioning
Rate processes
Transient Equations with Longitudinal
Conduction and Wall Thermal Storage
Mass flow and temperature transients in contraflow
Summarized development of transient equations
for contraflow
Computational approach
Algorithms And Schematic Source Listings
Algorithms for mean temperature distribution in
one-pass unmixed crossflow
Schematic source listing for direct-sizing
of compact one-pass crossflow exchanger
Schematic source listing for direct-sizing
of compact contraflow exchanger
Parameters for rectangular offset strip fins
Longitudinal conduction in contraflow
Spline-fitting of data
Extrapolation of data
Finite-difference solution schemes for
transients

Supplement to Appendix B - Transient Algorithms
Appendix C

xi

331
333
336
340
343
349
349
352
355

361
361
364
365
366
370
375
376
377
383

Optimization of Rectangular Offset Strip,
Plate-Fin Surfaces
Fine-tuning of rectangular offset strip fins
Trend curves

Optimization graphs
Manglik & Bergles correlations

405
405
407
408
409

Appendix D
D.I
D.2

Performance Data for RODbaffle Exchangers
Further heat-transfer and flow-friction data
Baffle-ring by-pass

411
411
414

Appendix E

Proving the Single-Blow Test Method - Theory
and Experimentation
Analytical approach using Laplace transforms

419
419

C.I
C.2
C.3
C.4

E.I


xii

Contents

E.2
E.3

Numerical evaluation of Laplace outlet response
Experimental test equipment

420
423

Most Efficient Temperature Difference
in Contraflow
Calculus of variations
Optimum temperature profiles

425
425
426

Appendix G
G.I
G.2
G.3

Physical Properties of Materials and Fluids
Sources of data
Fluids
Solids

429
429
429
431

Appendix H
H.I
H.2
H.3

Source Books on Heat Exchangers
Texts in chronological order
Exchanger types not already covered
Fouling - some recent literature

433
433
439
442

Appendix I
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9

Creep Life of Thick Tubes
Applications
Fundamental equations
Early work on thick tubes
Equivalence of stress systems
Fail-safe and safe-life
Constitutive equations for creep
Clarke's creep curves
Further and recent developments
Acknowledgements

443
443
443
445
446
447
447
449

451
451

Appendix J
J. 1
J.2
J.3
J.4
J.5

Compact Surface Selection for Sizing Optimization
Acceptable flow velocities
Overview of surface performance
Design problem
Exchanger optimization
Possible surface geometries

455
455
455
458
466
467

Appendix K
K.I
K.2
K.3

Continuum Equations

Laws of continuum mechanics
Coupled continuum theory
De-coupling the balance of energy equation

469
469
473
474

Appendix L
L.I
L.2

Suggested Further Research
Sinusoidal-lenticular surfaces
Steady-state crossflow

477
477
478

Appendix F
F. 1
F.2


Contents
L.3
L.4
Appendix M

Notation
Commentary
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Appendix A
Appendix I
Index

xiii

Header design
Transients in contraflow

478
479

Conversion Factors

483

Fundamentals

Steady-state temperature profiles
Direct-sizing of plate-fin exchangers
Direct-sizing of helical-tube exchangers
Direct-sizing of bayonet-tube exchangers
Direct-sizing of RODbaffle exchangers
Exergy loss and pressure loss
Transients in heat exchangers
Single-blow test methods
Heat exchangers in cryogenic plant
Heat transfer and flow friction in two-phase flow
Transient equations with longitudinal conduction and
wall thermal storage
Creep life of thick tubes

487
487
488
489
490
491
493
494
495
496
497
498
499
500
501

503


XIV

THERMAL DESIGN ROADMAP
(outline guide for contraflow)
DIRECT-SIZING
(minimum input data required)
INPUT DATA
contraflow
Qduty

OPTIMAL TEMPERATURE DISTRIBUTION
Grassman & Kopp
exergy constraint -—- — const.

Ntu VALUES
{find Th2 Tci}

LMTD-nT
approach

approach

EXCHANGER TYPE
Plate-fin
Helical-tube
RODbaffle
MEAN PHYSICAL PROPERTIES

specific heats
absolute viscosities
thermal conductivities


XV

APPLY LMTD

UxS =

Qduty
LMTD

COMPACT PLATE-FIN GEOMETRIES
heat-transfer correlations
flow-friction correlations

FIXED GEOMETRIES
K&L correlations 1
L&S correlations |
range of validity J

=spline-fits=>-

VARIABLE GEOMETRIES
( M&B correlations
I (ROSF variable)
[ range of validity

DIRECT-SIZING
block heat exchanger
equivalent plate with half-height surfaces
optimal pressure loss
exergy constraint

but preferably design with Ma < 0.1

FOR RANGE OF Re VALUES FOR SIDE-1
GENERATE
heat-transfer curve
pressure-loss curve, Side-1
pressure-loss curve, Side-2

FIXED GEOMETRIES
coincidence of
Ap curves unlikely

VARIABLE GEOMETRIES
coincidence of
Ap curves possible


XVI

NEAR-OPTIMUM EXCHANGER
estimated cross-section and length

LONGITUDINAL CONDUCTION
(reduced performance in most exchangers)

STEADY-STATE TEMPERATURE PROFILES
three simultaneous partial differential equations

(

hot fluid ... balance of energy }
solid wall... balance of energy \
cold fluid... balance of energy J

LMTD REDUCTION
(allowing for longitudinal conduction)

KROEGER SOLUTION
equal water equivalents

GENERAL SOLUTION
unequal water equivalents

| analytical solution
I greatest conduction

f numerical solution 1
1 Crank-Nicholson I

APPLY CORRECTION TO DIRECT-SIZING LMTD
leading to
CONSERVATIVE DIRECT-SIZING DESIGN
with mean thermophysical values
accurate cross-section and length
OPTIMIZED DESIGN

vary local surface geometries
until Ap curves coincide


XVII

STEP-WISE RATING
(using cross-section from direct-sizing)
AWKWARD CONDITIONS
arbitrary temperature profiles
physical properties varying along length
FOR TEMPERATURE RANGE OF EXCHANGER
spline-fit thermophysical data
for interpolation
SECTION-WISE DESIGN
assume equal temperature intervals for one fluid
and use enthalpy balance to calculate
corresponding temperatures for other fluid
LMTD AND MEAN TEMPERATURES AT EACH SECTION
thermophysical properties for each section
using spline-fitted data
CALCULATE SURFACE AREA AND LENGTH
for each section
CALCULATE PRESSURE LOSS FOR EACH FLUID
for each section
SUM LENGTHS AND PRESSURE LOSSES
to obtain final step-wise design

MULTI-STREAM DESIGN
(refer to specialist papers for cross-conduction and near-optimization)

XVIII

TRANSIENTS
(for known steady-state design)
COMBINED MASS FLOW AND TEMPERATURE TRANSIENTS
temperature-dependent physical properties
seven simultaneous partial differential equations
hot fluid

balance of mass
balance of linear momentum
balance of energy

solid wall — balance of energy
balance of energy
cold fluid

balance of linear momentum
balance of mass

FINITE-DIFFERENCE SOLUTION
solve sequentially by finite differences
two pairs of outer equations for density and velocity
three simultaneous central equations for temperature field
DELAYED ENTRY TO INDIVIDUAL CHANNELS
AND CROSS-CONDUCTION EFFECTS
(refer to specialist papers)

In general, finite-difference schemes were preferred for both steady-state
analysis, and for transients, as temperature-dependent physical properties
could then most easily be accommodated.


About the Author
Eric Smith is a Fellow of both the Institution of Mechanical Engineers and of the
American Society of Mechanical Engineers, and is also a Member of the Institute
of Refrigeration. He received his BSc and PhD degrees from the University of
Glasgow. His early research on the strength of high-temperature materials was complemented by an interest in heat transfer.
His early career included a total of 5 years in civil nuclear engineering
research at C.A. Parsons & Co. Ltd of Newcastle upon Tyne and at the Institut
fur Reaktor Bauelemente, Kernreaktor Kernforschungszentrum, Karlsruhe. The
next 20 years involved teaching and research to post-graduate level in Mechanical
Engineering at the University of Newcastle upon Tyne.
Dr Smith has published with IMechE, ASME, and ASTM, and has presented
papers at international and national level. He has represented the UK at a Nato
AGARD Special Technical Meeting in Washington DC, and was retained as an
expert witness by Norton Rose of London on behalf of shipbuilders Harland and
Wolff of Belfast.
Following short periods in Defence Consultancy in the UK, and teaching engineering in Hong Kong, he returned to the UK to pursue his interests in long-range
engineering.


The Book
All material presented in this volume has been computed from scratch by the author,
and a number of new points of understanding have been uncovered. Specifically and
illustratively:
• Alternative Effectiveness -Ntu and LMTD-Ntu approaches to design are
shown to be equivalent in finding terminal temperatures or Ntu values.

• Recommended Ntu performance limits for parallel flow, crossflow, and contraflow designs have been established, permitting appropriate choice for duty.
• With the LMTD-Ntu approach, longitudinal conduction can be approximated
by calculating the LMTD reduction factor in contraflow sizing.
• The application of direct-sizing to three different types of heat exchanger is
presented in some detail, and matching of local surface geometries prior to
direct sizing is explored.
• An unambiguous measure of specific thermal performance is defined, applicable to all types of exchanger.
• Exergy loss number is defined, and its relation to quality of heat exchange and
absolute temperature level of operation developed. Elimination of pressure
losses in headers, and the proper way of evaluating pumping power are
presented.
• Methods are set out for predicting full transients in contraflow allowing for
temperature-dependent physical properties. The single-blow method for determining heat-transfer and flow-friction correlations is outlined.
• Aspects of design for cryogenic and two-phase flow problems are examined.
• Numerical methods are emphasized throughout, starting from the controlling
differential equations and building towards understanding of thermal design
at every level.


Preface
'I would like to extend the way in which you may think
about the design of heat exchangers...'
(author, 10th International Heat Transfer Conference,
Brighton 1994)

Purpose of this work
The primary objective in any engineering design process has to be the elimination of
uncertainties. In thermal design of heat exchangers there are presently many stages
in which assumptions in mathematical solution of the design problem are being
made. Accumulation of these assumptions (e.g. use of mean values) may introduce

variations in design as large as the uncertainties introduced in heat-transfer and flowfriction correlations. The designer needs to understand where these inaccuracies
may arise, and strive to eliminate as many sources of error as possible by choosing
design configurations that avoid such problems at source.
This book is set at research graduate and professional level in clean technologies,
and is designed as a reference text. Theory is explained simply, so that the reader can
develop his/her own approach to solution of problems. The text is not intended as a
collection of heat-transfer and pressure-loss correlations, although a fair amount of
such material has been included.
Historical development of the subject
Up until the early 1940s virtually all papers employ 'mean temperature difference'
as the design parameter, a good collection being found in the two reference volumes
by Jakob (1949, 1957). Around 1942 the method of designing contra-parallel-flow
heat exchangers was effectively changed by London & Seban (1980) from using
LMTD to using the s-Ntu approach, partly on the grounds that the LMTD approach
did not give explicit results in some elementary cases, and partly because the
concept of 'effectiveness' provided a measure of the approach to ultimate performance of the exchanger.
The consequence has been that since 1942 many important papers have concentrated on expressing results in terms of effectiveness in preference to mean temperature difference, which in this author's view has not been entirely beneficial,
particularly in the case of variable thermophysical properties (Soyars, 1992), and in
the case of crossflow. The separate concepts of mean temperature difference and of
effectiveness both have useful roles to play in assessing the performance of heat
exchangers and should be used in combination.


xxiv

Preface

The present treatment shows that:
• The LMTD-Ntu approach is fully explicit in finding terminal temperatures in
contraflow and parallel flow, and contains expressions for 'energy' and 'rate'

processes (... iteration cannot be avoided when only inlet temperatures and
LMTD are known and outlet temperatures are required).
• Effectiveness may be a measure of performance for entropy loss, but exergy
loss number is essential in cryogenics. Aiming for minimum entropy generation in contraflow leads to temperature profiles with a pinch point at the
hot end, while aiming for least exergy loss in contraflow leads to temperature
profiles with a pinch point at the cold end.
• Exchanger comparisons are best made using the specific performance parameter

where Sref is the reference surface.
The case of unmixed-unmixed two-pass crossflow is examined in some detail.
The very comprehensive analytical paper by Baclic (1990) which examines 72 possible configurations for two-pass crossflow, concentrates on presenting results in
terms of effectiveness alone. However, understanding has been lost in not computing
temperature sheets, and for accurate design the assumption of equal mass flowrate at
inlet to each channel should be replaced by the assumption of equal pressure loss in
each flow channel. Dow's (1950) approach for designing headers with zero pressure
loss allows concentration on core pressure loss.
Direct-sizing methods
'Sizing' methods have traditionally posed more problems than 'rating' methods.
Guessing one principal dimension of the exchanger may be necessary before the performance of the core can be compared with design requirements. For the class of
heat exchangers in which 'local' geometry of the heat-transfer surface is fully representative of the whole geometry, guessing is no longer necessary. Methods of directsizing go straight to the dimensions of the heat exchanger core, while satisfying all
thermal performance constraints.
Design approaches for contraflow
Data

Rating

Direct sizing

Given

block size
L x W xH

thermal duty
Q, dPh, dPc

Inlet values

mh, Ch, Th\
mc, Cc, TC2

mh, Ch, Thi
mc, Cc, Tc2

Find

thermal duty

block size


Preface

xxv

In direct-sizing, the design approach is limited to that class of heat exchangers in
which 'local geometry' is fully representative of the complete heat exchange surface
and which provide core layouts which eliminate/minimize parasitic losses due to
flow leakage and by-pass flows, typically those described by Tinker1 (1951, Part I,
Fig. 6).

The concept can be applied to such different designs as:
compact plate-fin exchangers
helical-tube, multi-start coil exchangers
platen-type heat exchangers
RODbaffle shell-and-tube exchangers
lamella heat exchangers
flattened and helically twisted tubes
printed-circuit heat exchangers
HELIXCHANGERs
As all terminal temperatures may be determined in advance of direct-sizing, the
necessary input data for complete sizing take the following form:
exchanger duty (Q)
mean temperature difference for heat exchange (A0m)
'local' geometry on both sides
mass flowrates of both fluids (m)
physical properties for both fluids at mean bulk temperature (Pr, C, 17, A)
allowable pressure loss data (AP, P, Tbuik, Rgas)
physical properties of material of construction (A, p, C)
For the selected geometry, the standard procedure is to evaluate heat-transfer performance over the range of valid Reynolds numbers for both sides of the exchanger.
This provides a heat-transfer curve. Pressure-loss performance is similarly evaluated
for both sides over the same range of valid Reynolds numbers, providing two separate pressure-loss curves. Both pressure-loss curves will intersect the heat-transfer
curve, and the intersection furthest to the right provides the initial design point.
In cases where heat-transfer and pressure-loss correlations are suitable a fully
algebraic solution may be possible - as with the helical-tube, multi-start coil heat
exchanger. More often a numerical approach is preferred because the interpolating
cubic spline-fit provides more accurate temperature-dependent physical properties
plus heat-transfer and flow-friction coefficients, with the special advantage that
spline-fits cannot be extrapolated outside the range of their validity.
Longitudinal and cross-conduction
Techniques for estimating longitudinal conduction effects in both contraflow and

crossflow exchangers are described. Longitudinal conduction reduces exchanger
performance, and the design approach is to calculate and apply the reduction in
mean temperature difference.


xxvi

Preface

With multi-stream and crossflow exchangers, an additional problem exists,
caused by fluids flowing in the same direction having different temperature profiles
along the length of the exchanger. Cross-conduction effects may then have to be
taken into account.
Step-wise rating
When changes in thermophysical properties are significant, and it is not desired to go
to full transient analysis, it may be appropriate to design by step-wise rating. To start
this process an initial cross-section of the exchanger is required, and direct-sizing
can be helpful in providing the start-up information. By using temperaturedependent physical properties, and evaluating LMTD for each section, the design
can be made more accurate. Step-wise rating is the intermediate stage between
design assessment using mean values and full numerical prediction of transient
performance of a design.
Transient response
In contraflow exchangers which experience transient temperature disturbances,
longitudinal conduction terms appear in the set of seven simultaneous partial differential equations. As the Mach number in heat exchangers is normally less than
(Ma = 0.1) it becomes practicable to separate the problem into solution of mass
flowrate and temperature-field disturbances.
A full numerical study of transients in a two-stream contraflow exchanger
involves preparation of interpolating cubic spline-fits for both heat-transfer and
flow-friction data against Reynolds number, and for all temperature-dependent
physical parameters. At least 50 stations along the length of a contraflow exchanger

are desirable.
Single-blow testing
To measure heat-transfer and flow-friction performance of heat exchanger surfaces
the contraflow transient equations are simplified to the point where they become the
Single-Blow Transient Test Equations. This method of obtaining data for heattransfer and flow-friction correlations is well established as reliable, providing
that assumptions in the mathematical analysis are correctly matched to the experimental method.
Arbitrary inlet temperature disturbances and longitudinal conduction effects in a
matrix involve deeper analytical theory than presented in this text. A subset of the
full transient equations, combined with a numerical approach is one way forward.
The extraction of dimensionless numbers from governing differential equations is
covered in outline, to reveal the extent of their limitations when incorporated in
heat-transfer and flow-friction correlations. Rayleigh's empirical approach and
Buckingham's 7r-method are not included as they are readily available elsewhere.
linker's work on baffle losses in shell-and-tube exchangers has been reproduced in textbooks
and papers since Me Adams (1954).