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Title: FLAIR 3.6

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

  • 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. Heat-exchanger designers should move from
    guess-the-flow-pattern to compute-the-flow-pattern
  • 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.

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

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

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.

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
  • ignition and extinction of flames? or
  • stresses in solids?
  • They are surely of sufficient practical

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
  • I shall argue that it is time to extend the
    boundaries further, so as to cover
  • HMT and its chemical and mechanical effects.

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).

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
  • Heat-transfer engineers need not, however, become
    chemists or metallurgists
  • they need just enough extra knowledge, but no

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
  • They speak different languages and
    misunderstandings are frequent.

1.3 What heat-transfer engineers should know
about combustion
Flame-propagation speeds of fuel-air mixtures
vary thus
Experimental combustion data can then be
correlated thus
  • This is from the 1954 thesis of Barry Tall, my
    first Australian student

1.4 What heat-transfer engineers should know
about stress analysis
  • That the three material properties of importance
  • 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
  • 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'.

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
  • material properties (uniform)
  • but these conditions prevail so seldom that
    numerical methods are almost always used for
    calculating temperature distributions.

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

2.2 Numerical heat transfer with chemical reaction
  • I used the Schmidt method for calculating the
    speed of laminar flame propagation, 50 years ago.

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

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.

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.

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

Control-volume for vertical displacement v
First the Figure
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.

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.

1/4 of square beam with fluid in square hole
  • When the outer-wall temperature is raised

1/4 of square beam with fluid in square hole
  • When the inner-duct pressure is raised

1/4 of square beam with fluid in square hole
  • When both changes are made simultaneously.

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

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.
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
  • 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.

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

The additional features of the CFD equations
  • the dependent variables include the components of
  • 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.

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.

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,
  • 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.

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
  • 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!

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
  • The following images relate to the heat exchanger
    in question, with the radial dimension magnified

Concentric tube heat exchanger
  • 1. Pressures in the two fluids causing mechanical

Concentric tube heat exchanger
  • 2. The temperature distribution, causing thermal

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

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

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

Concentric tube heat exchanger
  • 6. circumferential-direction stresses

Concentric tube heat exchanger
  • 7. axial-direction stresses.

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
  • 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
  • Certainly, but with much greater difficulty so
    why bother?

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
  • 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.

Final examples
  • 1. distortions of a sea-bed structure by ocean

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

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.

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.

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.

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.

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.

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

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

Computed fluid property distributions
  • Material properties vary throughout and so must
    heat-transfer coefficients.

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

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

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.

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

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
  • But the software should also allow them to used
    calculated flow patterns, not out-dated guesses.

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
  • Mid-'90s codes contained self-programming
    features, to which users simply supplied formulae.

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
  • 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.

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
  • 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,

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

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'.

Attributes of objects the dialogue box for the
  • Each object has attributes, expressed as
    numbers, variables, relationships or file-names.

The size- and position dialogue box
  • Each object has also size and position which may
  • similarly expressed.

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

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)
  • 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

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
  • overall coefficientcoeU at bundle is
  • the heat fluxflux at bundle is coeu(temt-tems)
    ! temperature difference
  • These statements may be edited manually or
  • Doing so gives the engineer the freedom which he
    needs, and which the wretched mouse-prisoner can
    never enjoy.

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

A deeper-level script
  • This is because of lines in the set-up script
    like this
  • if oddevengt0 ! oddeven refers to baffle
  • baff1 setposition list wallthick/2.
  • else baff1 setposition list
    Xsize(parname)-wallthick/2. \ ysize(parname)/2.0
    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.

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
  • material properties to be assigned to the
  • 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.

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
  • 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

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
  • 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.

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
  • objects are best assembled via algebraic
    relations which packages must understand
  • enforced restriction to mouse-clicking can damage
    one's mental health..

Concluding Remarks, 2
  • These recommendations now appear to be such
    obvious commonsense as to be totally
  • 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 !!!!

  • The author gratefully acknowledges the assistance
  • 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

  • Regarding the subject of Heat Transfer
  • Bosch M, Ten 1936 "Die Waermeuebertragung, 3rd
    Ed", Springer, Berlin
  • Jakob M , 1949, Heat Transfer, John Wiley, New
  • 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.

  • Regarding ignition, propagation and extinction of
  • 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

  • Regarding numerical methods generally
  • Richardson LF ,1910, Trans Roy Soc A, vol 210, p
  • 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)

  • Regarding the finite-volume approach to
  • 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

  • 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

  • Regarding the use of formulae in heat-exchanger
  • 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

  • The End !!!
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