FLAIR 3.6

1
Extending the Boundaries of Heat
Transfer by Brian Spalding The 13th International
Heat Transfer Conference August 16, 2006, Sydney,
Australia James P.Hartnett Lecture
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Abstract

• In keeping with Jim Hartnett's breadth
• of vision, and of his readiness to be
• controversial, this lecture questions
• some common assumptions about the
• subject of Heat Transfer.
• Specifically, it is argued that
• Heat Transfer and its effects is our
• proper field of study.

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Abstract

• 2. Among the not-to-be neglected effects are the
  resulting Stresses in Solids.
• 3. Numerical-Heat-Transfer techniques require
  corresponding extension to displacements and
  stresses, but without the needless complications
  of finite-element methodology.
• 4. CFD ( i.e. Computational Fluid dynamics )
  requires extension to SFT ( i.e.
  Solid-Fluid-Thermal analysis , for which its
  finite-volume methods are fully sufficient.

4
Abstract

• 4. Heat-exchanger designers should move from
  guess-the-flow-pattern to compute-the-flow-pattern
  methods.
• 5. But conventional (detailed-geometry) CFD
  techniques are inadequate for this only
  space-averaged formulations are practicable.
• 6. Still, data-input obstacles remain formidable.
  Heat-exchanger designers need software which can
• (a) understand formulae, and
• (b) accept data in the form of relations.

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Contents of this lecturePart1

• 1. What is 'Heat Transfer'?
• 1. The received view
• 2. Reasons for enlargement
• 3. Some details by way of example.
• 2. Extending numerical heat transfer
• 1. Conventional methods for heat conduction
• 2. Simple extensions to chemical reaction
• 3. Extensions to displacements in solids
• 4. The research opportunities
• 3. CFD to SFT
• 1. Essential ideas
• 2. A simple example
• 3.A choice to be made

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Contents of this lecturePart 2

• 4. How not to design heat exchangers
• 1. What the Handbooks Say
• 2. Can CFD assist?
• 3. Why conventional packages fail to satisfy
• 5. Improving the input procedures
• 1. Input of formulae
• 2. Input of relations
• 3. Optimization
• 6. Concluding remarks
• 7. Acknowledgements
• 8. References

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What is Heat Transfer?

• 1. What is Heat Transfer?
• 1.1 The received view
• The conventional answer to this question is given
  by the chapter headings in the popular textbooks
  they follow the century-old pattern set by
  Nusselt and Jakob in Germany.
• 1. conduction
• 2. convection
• 3. radiation
• then perhaps
• 4. melting and freezing.
• 5. boiling
• 6. condensation.

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What is Heat Transfer?

• But it need not have been so for
• the action-at-a-distance laws of radiation are
  unlike the close-contact laws of conduction and
  convectionthey might have been rtreated as
  belonging to optics and
• the phase-change topics (melting, freezing, etc)
  might have been left to thermodynamiciststhey
  concern more the effects of heat transfer than
  the process itself.
• Conversely, if some of the effects of heat
  transfer are to be included, why not others? for
  example
• ignition and extinction of flames? or
• stresses in solids?
• They are surely of sufficient practical
  importance.

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The argument

• The existing boundaries of the subject of Heat
  Transfer are historical rather than rational.
• In the 1960s we added Mass Transfer to our
  territory, as witness
• IJHMT, the Journal published by Robert Maxwell,
  of which AV Luikov, Jim Hartnett and I were
  editors at launch time.
• ICHMT, the Centre proposed by Naim Afgan and
  Zoran Zaric and created with help from Jim and
  me.
• I shall argue that it is time to extend the
  boundaries further, so as to cover
• HMT and its chemical and mechanical effects.

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Reasons for enlargement

• Reason 1
• Heat transfer is for engineers, who design
  equipment and this must both
• meet performance requirements, and
• ensure safety.
• They must therefore predict both the desired and
  the undesired consequences of their actions.
• Examples are
• chemical effects (explosions)and
• mechanical effects (distortions and fractures).

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Reasons for enlargement

• Reason 2
• The necessary additional ideas are few, namely
• that combustion phenomena result from
  temperature-dependent heat sources
• that thermal stresses occur when heated bodies
  are mechanically constrained
• That stress is proportional to strain (Hooke's
  Law)
• Heat-transfer engineers need not, however, become
  chemists or metallurgists
• they need just enough extra knowledge, but no
  more.

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Reasons for enlargement

• Reason 3
• Not equipping the heat-transfer engineer with the
  necessary skills is
• at best, uneconomical, and
• at worst, dangerous.
• The alternative, calling in specialists is
  expensive, time-consuming, and sometimes too
  late.
• They speak different languages and
  misunderstandings are frequent.

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1.3 What heat-transfer engineers should know
about combustion
Flame-propagation speeds of fuel-air mixtures
vary thus
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Experimental combustion data can then be
correlated thus

• This is from the 1954 thesis of Barry Tall, my
  first Australian student

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1.4 What heat-transfer engineers should know
about stress analysis

• That the three material properties of importance
  are
• Young's modulus,
• Poisson's ratio,
• thermal expansion coefficient.
• That (a few) formulae exist for stresses and
  strains in solids when the boundary conditions
  are simple.
• Otherwise, numerical methods of calculation are
  available.
• These can be of the 'finite-difference' or
  'finite-volume' kinds, familiar from studies of
  heat conduction
• There is no need to learn the 'foreign language'
  associated with 'finite elements'.

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2. Extending Numerical Heat Transfer

• 2.1 Numerical methods for heat conduction
• Analytical formulae exist only for
  heat-conduction problems which are simple in
  respect of
• geometry (rectangular, cylindrical or spherical),
  
• boundary conditions (constant, or linear in
  temperature),
• material properties (uniform)
• but these conditions prevail so seldom that
  numerical methods are almost always used for
  calculating temperature distributions.

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Extending Numerical Heat Transfer
The figure and equation shown here will be
familiar to all users of such methods.
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How to solve the equations

• There is one such equation for every volume into
  which the space is divided.
• The complete set of equations is soluble by
  successive-substitution methods.
• Before we had computers, the graphical method
  pioneered by Ernst Schmidt was often used.
• It was laborious, but profoundly educative.
• I luckily encountered it early in my career as
  shown by the following reminiscence. It
  concerns one of the chemical effects of HMT,
  namely flame propagation.

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2.2 Numerical heat transfer with chemical reaction

• I used the Schmidt method for calculating the
  speed of laminar flame propagation, 50 years ago.

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Extending Numerical Heat Transfer

• The graphs on the left show successive
  temperature distributions after two bodies of hot
  (burned) and cold (unburned) gas are brought into
  contact

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Extending Numerical Heat Transfer

• The graph on the right shows the source
  (horizontal) versus temperature (vertical)
  function which represents (sufficient of) the
  laws of chemical reaction.

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Extending Numerical Heat Transfer

• When computers came along, of course, pencils and
  rulers were pushed aside but I am glad that I
  started work before then.
• I would want every student in my imagined "HMT
  and Its Effects" course to have 'flame ignition
  and propagation' as an obligatory homework item.

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2.3 Extension to displacements in solids

• The numerical methods used for heat-conduction
  problems can also be extended to the calculation
  of stresses and strains in solids.
• There are many ways of doing so but probably the
  simplest is to solve the equations for the
  displacement components.
• The Figure and Equation shown below are a little
  more complex than those for temperature but not
  much.

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Control-volume for vertical displacement v
First the Figure
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Extending Numerical Heat Transfer

• then the equation
• The slight complication of the displacement-compon
  ent problem is that there are three sets of
  equations ( for U, V and W) and they are linked
  together in special (but easily-formulated) ways.

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Solving the equations

• I now show some results of solving the equations
  by the same successive-substitution method as is
  used for heat conduction.
• It is applied to the case of a square-sectioned
  beam having a square hole, filled with fluid,
  along its axis.
• Contours and vectors of displacement are shown.

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1/4 of square beam with fluid in square hole

• When the outer-wall temperature is raised

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1/4 of square beam with fluid in square hole

• When the inner-duct pressure is raised

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1/4 of square beam with fluid in square hole

• When both changes are made simultaneously.

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Consequential stresses

• From the displacement fields may be deduced the
  distributions of the direct stresses in the
  horizontal direction...

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Consequential stresses

• and in the vertical direction.

Comparison with solutions made by the
finite-element code Elcut showed close
agreement, of course for the finite-volume and
finite-element methods solve the same
differential equations.
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2.4 The research opportunities

• The computer time needed for solving the 3
  displacement equations is more than 3 times that
  needed for the temperature equation. The reason
  is that the equations for the 3 displacement
  components are inter-linked.
• Naive sequential solution procedures may
  (depending on geometry) converge rather
  slowly.More refined procedures are needed, and
  are being developed but there is still much to
  do.
• Researchers seeking little-exploited territories
  may therefore find them here and the world still
  awaits compilation and publication of the
  definitive textbook.Why? The numerical-stress-ana
  lysis field was devastated in the 1960's by the
  finite-element tsunami. Recovery takes time.

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3. Extending Computational Fluid Dynamics to SFT

• 3.1 Essential Ideas
• When Numerical Heat Transfer concerns itself with
  convection as well as conduction, it becomes a
  part of CFD..
• This also came into existence in the late 1960s.
• It uses equations similar to those governing heat
  conduction, shown above, with additional
  features, namely

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The additional features of the CFD equations

• the dependent variables include the components of
  velocity
• the coefficients (aN, aS, etc). account for
  convective as well as diffusive interactions
  between adjacent control volumes
• the sources include pressure gradients, gravity,
  centrifugal and Coriolis forces and
• the effective transport properties vary with
  position over many orders of magnitude.
• The CFD equations is thus more complex than the
  thermal-stress problem yet satisfactory
  iterative solution procedures have been in
  widespread use since the early 1970s.

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Use of CFD procedures for solid-stress problems

• CFD solution procedures have been successfully
  applied to solid-stress problems. Both Steven
  Beale and I independently showed this in 1990, as
  did Demirdzic and Mustaferija soon after.
• Mark Cross's group at Greenwich University has
  also made significant use of such methods for
  fluid-solid-interaction problems.
• Since the fluids and the solids occupy
  geometrically separate volumes, a single computer
  program can predict the behaviour of both solids
  and fluids simultaneously.
• This possibility has not been widely exploited
  because of the popular misconception that
  solid-stress problems must be solved by
  finite-element methods.
• It is therefore high time that CFD should enlarge
  to become SFT, i.e. Solid-Fluid-Thermal.

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3.2 A simple example

• Let us consider a primitive counterflow heat
  exchanger, consisting of two concentric tubes.
• Let us also suppose that because of
• natural convection in the cross-stream plane, or
• non-uniformity of external surface temperature,
  or
• turbulence-promoting baffles within one or both
  of the tubes ,
• the distributions of temperature and pressure,
  and therefore also of stress and strain in the
  tubes, are not axisymmetrical.

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The concentric-tube heat exchanger

• How are the stresses and strains to be computed?
• Numerically, of course and, if (misguided !)
  common practice is followed, one computer code
  will be used for the fluids and another for the
  solids.
• Then means must be devised for transferring
  information between them.
• How much more convenient it will be to use one
  computer code for the whole job!

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Extending CFD to SFT

• A true SFT code can do just that by
• solving for velocities and pressure in the space
  occupied by fluid
• solving for displacements and strains in that
  occupied by solid
• solving simultaneously for temperature in both
  spaces.
• The following images relate to the heat exchanger
  in question, with the radial dimension magnified
  four-fold.

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Concentric tube heat exchanger

• 1. Pressures in the two fluids causing mechanical
  stresses

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Concentric tube heat exchanger

• 2. The temperature distribution, causing thermal
  stresses.

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Concentric tube heat exchanger

• The circumferential variation of temperature
  imposed on the outer surface has produced 3D
  variations of temperature, stress and strain, as
  follows

3. radial-direction strains (positive being
extensions, negative compressions)
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Concentric tube heat exchanger

• 4. circumferential-direction strains

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Concentric tube heat exchanger

• 5. radial-direction stresses (positive being
  tensile, and negative compressive)

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Concentric tube heat exchanger

• 6. circumferential-direction stresses

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Concentric tube heat exchanger

• 7. axial-direction stresses.

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Extending CFD to SFT

• Three questions
• 1. Are the predictions correct?
• Probably, because
• the code produces the analytically-derived exact
  solutions for all cases in which these exist
• the displacement equations, are, after all, very
  simple.
• 2. Did solving for stress and strain increase the
  computer time?
• Not noticeably. Calculating finite values of
  displacement is not much more expensive then
  setting velocities to zero and convergence of
  the velocity and pressure fields dictated how
  many iterations were needed.
• 3. Could the same result have been achieved by
  coupling a finite-volume and a finite-element
  code?
• Certainly, but with much greater difficulty so
  why bother?

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3.3 A choice to be made

• Which forms the better method for SFT?
  Finite-volume or finite-element?
• The printed version of the lecture discusses the
  question at length. Here I summarise thus
• The general-purpose SFT codes needed by
  heat-transfer engineers could be based on
  finite-element methods). But..
• The highly-demanding F part of SFT, is handled so
  much better by finite-volume methods than
  finite-element ones
• Why else did Ansys buy Fluent and CFX?,
• that the best SFT codes are likely to be
  FV-based.
• Early arguments that FE methods are better for
  awkward geometries lost their force more than
  twenty years ago.
• It is only mental and commercial inertia that
  keeps the finite-element juggernaut in motion.

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Final examples

• 1. distortions of a sea-bed structure by ocean
  waves,

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Final examples

• 2. flapping of a wing, courtesy of K Pericleous

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Part 2. How not to design heat exchangers

• 4.1 What the handbooks say
• AC Mueller, in Hartnett and Rohsenow's 'Handbook
  of Heat Transfer' states
• "Heat exchangers are designed by the usual
  equation q UAMTD"
• wherein
• U is the overall heat-transfer coefficient,
• A is the area of the heat-exchange surface, and
• MTD is the Mean Temperature Difference.
• The area, A, is fairly easy to estimate
  otherwise we can be sure only that
• U is not a constant, and that
• MTD can be determined only for simple flow
  patterns which never exist in practice.

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How not to design heat exchangers

• Ah! But thats why we have correction factors.
• Yes, we do and we have all seen, and perhaps
  used, such charts as this from Hartnett and
  Rohsenow but they based on unrealistic idealised
  flow patterns.

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How not to design heat exchangers

• The Tinker-Bell-Devore corrections
• Then there are allowances for leakages between
  baffles and shell , and for 'by-pass streams',
  based on experiments carried out long ago, at the
  University of Delaware and elsewhere.

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How not to design heat exchangers

• But the experiments are of course too few. Indeed
  to carry out enough experiments, and then to
  express their results as formulae, is an
  impossible task.
• Nowadays, few designers use the charts and
  correction formulae directly for they have been
  embodied in software which reduces labour.
• Alas, it also reduces the doubt which their users
  ought to maintain for the underlying concepts
  are based on fictions, not physics.

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4.2 Can CFD assist?

• Computational Fluid Dynamics is based on physics.
  Can CFD then be a better basis for heat-exchanger
  design? My answers are
• 1. Yes, in principle , but heat exchangers have
  many close-together solid-fluid interfaces
• 2. Therefore flow details can not be simulated.
• 3. However, the space-averaged (also called
  porous medium) approach works well, especially
  for 'difficult' equipment, e.g. power-station
  steam condensers and nuclear boilers.
• 4. Its lack of adoption by the heat-exchanger
  fraternity may have resulted from data-input
  difficulties, which are now being removed.
• Before turning to the difficulties, I show
  results from a recent study of a baffled
  shell-and-tube heat exchanger.

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Computed flow patterns

• The baffles produce a complex three-dimensional
  flow, different for each configuration.

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Computed temperature distributions

• No handbook 'correction factor' can represent
  temperature distributions like this.

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Computed fluid property distributions

• Material properties vary throughout and so must
  heat-transfer coefficients.

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Computed Nusselt numbers

• Note the wide variation of values of the
  dimensionless heat-transfer coefficient.

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Space-averaged CFD is needed and its available

• In Summary
• Hand-book methods of heat-exchanger design make
  assumptions about
• uniformity of properties
• uniformity of heat-transfer coefficient
• existence of idealised flow patterns
• calculability therefrom of the mean temperature
• difference.
• Every physics-based numerical simulation of
  practical heat exchangers shows that the
  assumptions are wrong.
• The numerical simulations also rest on
  assumptions but these, being local rather than
  global, are far more reliable.
• The computer time needed for calculating rather
  than presuming the flow and temperature
  distributions is trivial,
• Heat-exchanger-design software should therefore
  embody physics-based space-averaged CFD flow
  simulations.

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4.3 Why conventional packages fail to satisfy

• 1.CFD specialists distrust conventional
  heat-exchanger-design packages because the
  packages lack physics.
• 2. Some experienced heat-exchanger designers
  distrust them for other reasons. Thus, J Taborek
  5 in the Hemisphere Handbook of Heat Exchanger
  Design, states
• "Only if calculations are performed manually
  will the engineer develop a 'feel' for the design
  process as compared to the impersonal 'black box'
  calculations of a computer program".
• 3. The package designers seem to distrust their
  users they treat them as capable only of making
  selections by mouse-clicks on tick boxes.

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The mouses revenge

• Being restricted to the choices provided by the
  package designer is indeed to be a prisoner of
  the mouse, in fact rather like this

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Heat exchanger design is for men not mice

• Engineers who prefer 'manual calculation do so
  because they like to decide for themselves what
  formulae for
• heat-transfer coefficients
• pressure-drop coefficients
• fouling factors
• etc.
• are to be used in the various parts to exchanger.
  
• What is needed is software which respects their
  experience, and enables them to use it, freeing
  them from the constraints which mouse-click codes
  impose.
• But the software should also allow them to used
  calculated flow patterns, not out-dated guesses.

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5. Improving the input procedures

• 5.1 Input of formulae the history
• Early '80s CFD codes contained built-in modules
  for calculating, say
• viscosity from temperature, pressure and
  composition of fluids
• Nusselt from Reynolds and Prandtl numbers for
  specific geometries.
• There were never enough of these so provision
  was made for users to add their own Fortran or C
  coding.
• Mid-'90s codes contained self-programming
  features, to which users simply supplied formulae.

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Input of formulae

• The latest codes react to formulae directly
• If the user writes lines like Nusselt is
  0.023Reynolds0.8Prandtl0.33the computer
  code works out for itself what to do.
• The formulae can be of arbitrary complexity.
• Therefore anyone who can write a formula can "do
  CFD".
• Input of formulae was reported at the 2005 ASME
  Summer Heat Transfer Conference in San Francisco.
  I therefore turn to a newer development the
  input of relations.

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5.2 Input of relations

• The main steps in setting up a heat-exchanger
  simulation are
• a. assemble all component objects (shell,
  nozzles, headers, baffles, tubes, etc)
• b. specify their proper dimensions and positions
  
• c. assign the property formulae to the various
  solids and fluids
• d. select the heat-transfer and friction formulae
  to be used
• e. assign the inlet flows and temperatures, and
  any other relevant thermal, or mechanical
  conditions
• f. let the computer work out the consequential 3D
  temperature distributions (and stresses) as
  functions of time.
• I shall now show some parts of the process,
  conducted by way of the relational input module,
  PRELUDE.

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Shell-and-tube heat-exchanger in PRELUDE

• Objects, position, size and attributes
• The shell-and-tube exchanger (one half only)
  might, in the course of assembly, look like this

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The family of objects

• It is a collection of inter-linked objects,
  having names on the left of this picture which
  shows them linked as 'parent' and 'child'.

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Attributes of objects the dialogue box for the
shell

• Each object has attributes, expressed as
  numbers, variables, relationships or file-names.

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The size- and position dialogue box

• Each object has also size and position which may
  be
• similarly expressed.

70
Further details of the relational-input module

• Attributes, position and size may be
• created by a generic shell-and-tube
  heat-exchanger script or
• read in from a particular shell-and-tube
  heat-exchanger file (e.g. one of those which the
  desiner has used before) or
• entered interactively.
• As soon as any value or relationship is changed
  interactively, all consequential changes, for all
  objects, are made, and seen, at once.
• At the end of the interactive session, all
  positions, sizes and attributes, including
  relations, are saved, into a file, for later
  re-use.

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How the relations and formulae appear in the file

• Here, in italics, are the some of the relations
  governing 'bundle'. Although they have their own
  vocabulary, it is easy to learn, and use.
• position and sizexmid(bundle)
  Xmidcoord(SHELL) ymid(bundle) Ymidcoord(SHELL)
  zmin(bundle) Zmaxcoord(HEAD1) radius(bundle)
  inradius
• shapedisk bundle ! Disk is an object type
  bundle is one of them
• shell-side heat-transfer coefficientnuss at
  bundle is 0.2reys0.6prns0.33) ! shell-side
  Nucoes at bundle is aovervnusscond/diam) ! and
  coeff.

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Formulae for Reynolds, Prandtl Nusselt numbers

• tube-side coefficient reyt at bundle is
  diamtubvel/enut ! tube-side Re prnt at bundle
  is cptrho2enu2/cont ! and Pr nust at bundle is
  max(2.0,0.328(reytprnt)0.33) ! and Nucoet at
  bundle is aovervnustcont/diam) ! and
  coefficient
• overall coefficientcoeU at bundle is
  1/(1/coes1/coet)
• the heat fluxflux at bundle is coeu(temt-tems)
  ! temperature difference
• These statements may be edited manually or
  interactively.
• Doing so gives the engineer the freedom which he
  needs, and which the wretched mouse-prisoner can
  never enjoy.

73
Co-ordinated changes

• Changing the number of baffles
• When the user changes the baffle number from 3 to
  4, they jump into their new positions at once
  and the outlet nozzle moves from the top to the
  bottom, as seen here

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A deeper-level script

• This is because of lines in the set-up script
  like this
• if oddevengt0 ! oddeven refers to baffle
  number
• baff1 setposition list wallthick/2.
  ysize(parname)/2.0\ic(Zmincoord(d2)-Zmaxcoord
  (d1))/nmax
• else baff1 setposition list
  Xsize(parname)-wallthick/2. \ ysize(parname)/2.0
  ic(Zmincoord(d2)-Zmaxcoord(d1))/nmax
  baff1 setzrot 180.
• Heat-exchanger designers would NOT be expected to
  look at such details but their
  computer-specialist colleagues could do so, if
  some new functionality were required.

75
A common difficulty concerned with re-use

• Most CFD packages have graphical user interfaces
  which enable
• flow-simulation scenarios to be set up
• objects to be brought in from solid-modelling
  packages
• material properties to be assigned to the
  objects
• boundary conditions to be attached to them and
• computation-controlling settings to be made.
• Many also allow for the data-input files to be
  stored and re-used.
• However, when re-use involves changing the
  numbers, materials, sizes, shapes or positions of
  the objects, the labour required for the second
  scenario is nearly as great as for the first.

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The advantage of relational input modules

• A code equipped with a relational input module
  greatly reduces that labour for it remembers why
  the objects in the first scenario were placed
  where they were, recording these in its 'Book of
  Rules'
• Then, unless instructed otherwise, it will apply
  the same rules for the second scenario as were
  laid down for the first.
• For example, if the shell-length of a heat
  exchanger is increased, the headers will move
  appropriately further apart.
• Any desired relationship can be built in,
  including those linking geometric with thermal or
  computational conditions.
• Relational input modules are especially useful
  for handling SFT problems, in which objects,
  their supports and their applied loads must move
  together.

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5.3 Optimization

• Finally, for completeness, I mention that the
  designer's true task is not 'merely' that of
  predicting the performance of a prescribed heat
  exchanger.
• What is needed is the ability to determine the
  dimensions and configuration of the best-possible
  heat-exchanger for the prescribed duty, with
  prescribed constraints.
• Provided that a parameterised input procedure is
  available, of the PRELUDE kind, computers can be
  instructed systematically to search for the
  optimal parameter set.
• This is rarely done at present but it can and
  should become the norm.

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6. Concluding Remarks, 1

• In remembrance of Jim Hartnett, I have sought to
  be controversial, having asserted that
• the territory of 'Heat Transfer' should be
  enlarged so as to include more of its 'Effects'
• CFD should become SFT
• inclusion of stress analysis is best done without
  finite elements
• heat-exchanger design should be based on physics,
  not fiction
• software packages should allow input of arbitrary
  formulae
• objects are best assembled via algebraic
  relations which packages must understand
• enforced restriction to mouse-clicking can damage
  one's mental health..

79
Concluding Remarks, 2

• These recommendations now appear to be such
  obvious commonsense as to be totally
  non-controversial.
• Sorry, Jim!
• But probably I have not explained my meaning well
  enough for some of you so you may disagree with
  what you think that I said.
• Perhaps that will produce controversy after all.
• !!!! Thank you for your attention !!!!

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Acknowledgements

• The author gratefully acknowledges the assistance
  of
• Dr Valeriy Artemov of the Moscow Power
  Engineering Institute in developing and testing
  the SFT technique,
• Dr Elena Pankova of the Moscow Baumann Institute
  in the preparation of diagrams,
• Dr Geoff Michel of CHAM in developing PRELUDE,
  the 'relational input module and of
• My sons Peter and Jeremy in Power-Pointing this
  lecture,

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References

• Regarding the subject of Heat Transfer
• Bosch M, Ten 1936 "Die Waermeuebertragung, 3rd
  Ed", Springer, Berlin
• Jakob M , 1949, Heat Transfer, John Wiley, New
  York
• Ganic, E, Rohsenow, W. M. and Hartnett, JP (Eds),
  1973, Handbook of Heat Transfer Fundamentals,
  McGraw Hill.
• Rohsenow, WM and Hartnett, JP (Eds), 1973,
  Handbook of Heat Transfer, McGraw Hill.

82
References

• Regarding ignition, propagation and extinction of
  flames
• Botha JP and Spalding DB, 1954, Proc Poy Soc A
  vol 225 pp 71-96
• Spalding DB and Tall BS, 1954, vol 5 p 195
• Spalding DB 1955, "Some Fundamentals of
  Combustion", Butterworths, London

83
References

• Regarding numerical methods generally
• Richardson LF ,1910, Trans Roy Soc A, vol 210, p
  307
• Schmidt, E, 1924, "On the application of the
  calculus of finite differences to technical
  heating and cooling problems", August Foeppl
  Festschrift, Springer
• Minkowicz, W M, Sparrow, E, Schneider, G E and
  Pletcher, R H, (Eds), 1988, Handbook of Numerical
  Heat Transfer, John Wiley
• Patankar SV, Spalding DB, "A calculation
  procedure for heat, mass and momentum transfer in
  three-dimensional parabolic flows" Int J Heat
  Mass Transfer vol 15 p 1787 (1972)

84
References

• Regarding the finite-volume approach to
  stress-analysis
• Spalding, D B, 1993. Simulation of Fluid Flow,
  Heat Transfer and Solid Deformation
  Simultaneously, NAFEMS Conference no 4, Brighton.
  
• Demirdzic, I. and Muzaferija, S., 1994,
  Finite-Volume Method for Stress Analysis in
  Complex Domains, Int J for Numerical Methods in
  Engineering vol 37, pp 3751-3766.
• Bailey C, Cross M, Lai C-H, 1995, "A
  finite-volume procedure for solving the elastic
  stress-strain equations on an unstructured
  mesh."Int. J. Num. Meth. in Eng. vol 38,1757-1776

85
References

• Regarding the currently-used methods of
  heat-exchanger design
• Devore, A., 1961, Try this simplified method for
  rating baffled exchangers, Pet. Refiner, vol 40,
  p 221.
• T Tinker J. Heat Transfer vol 80 pp 36-52 1958
• KJ Bell "Final report of the cooperative research
  program on shell-and-tube heat exchangers"
  University of Delaware Exp.Sta.Bull. 5 1993
• J Taborek "Recommended method principles and
  limitations" in "Hemisphere Handbook of Heat
  Exchanger Design" ed. by GF Hewitt, Hemisphere,
  New York 1983

86
References

• Regarding the use of formulae in heat-exchanger
  design
• Spalding DB 2005 "Solid-fluid-thermal analysis of
  heat exchangers", ASME Summer Heat Transfer
  Conference, San Francisco
• Regarding the use of relational input procedures
• Michel GM and Spalding DB 2006 "PRELUDE User
  Guide", unpublished

87

• The End !!!