Solid-fluid-thermal analysis of heat exchangers
Keynote Lecture at 2005 ASME Heat Transfer Conference
July 17-22, 2005, San Francisco, California
Traditional heat-exchanger design methods predict steady-state
uniform-property performance imperfectly; and
flow, heat transfer, chemical reaction and stresses in solids not at
Traditional CFD techniques, relying on body-fitting grids and
dubious turbulence models, handle only small-scale phenomena
such as few-tube sub-sections of tube banks.
Intermediate CFD methods, which replace tube-bank details by
space-averaged representations and
heat-transfer correlations, have been successfully used for
years; but they are little favoured by designers.
One reason is that heat-transfer correlations and other formulae
needed by designers are too numerous and varied to be supplied
with commercial codes; so users should provide Fortran
themselves; but they lack time or skill.
What has long been needed is software which will itself
The lecture exemplifies how such software has been applied to a
shell-and-tube heat exchanger.
It also shows how the stresses in the solid components of the heat exchanger can
be computed at the same time.
Contents of the lecture
- Early successes
- Obstacles to further progress
- A way forward
- The Requirements of a Heat-Exchanger-Design Method
- Geometrical input data
- Material-property data
- Thermal and mass-flow boundary conditions
- Empirical correlations
- Predicting the flow pattern and temperature distribution
- Three ways of satisfying the requirements
- Method 1: 'User-supplied sub-routines'
- Method 2: 'Automated sub-routine writing'
- Method 3: When the program understands formulae
- Practical Example
- The heat exchanger and computer code in question
- Distributions of velocity, temperature, pressure and related properties
- Distributions of Reynolds, Prandtl and Nusselt number
- Variations of heat-transfer coefficient
- How the input data were introduced
- Simultaneous calculation of stresses in solids
- A common misconception
- The truth of the matter
- Fluid-structure interaction examples
- Exemplification for the heat exchanger
- Concluding remarks
The space-averaged-CFD technique applied to heat exchangers was first
described than thirty years ago by Patankar and Spalding . They concluded:
"It therefore seems that a tool of considerable practical utility is in
At first their expectations appeared to be fulfilled: application to two-phase flows helped to
resolve difficulties encountered by the then growing nuclear-power industry.
Specifically, the shell-side steam-water mixture circulating in boilers,
heated by pressurized water from the nuclear reactor, caused tubes
to vibrate and baffles to corrode. Consequently, first US and German companies
finally EPRI, sponsored the development of flow-simulating computer programs.
The work was pioneering and did not always proceed
as rapidly as desired.
So one joker suggested that the name
adopted for the EPRI-sponsored code, URSULA, was an acronym for:
Urgently Required Solution Unacceptably Late Arriving.
Despite the implied criticism,
the work was successful; and it was followed by the development of
further computer codes for simulating steam condensers and cooling
Nevertheless, the heat-exchanger-design community has shown little
enthusiasm; and a recent
paper  on the subject concluded "very few applications can be found
of using CFD technique as a tool for heat-exchanger design optimization".
Instead, designers still prefer to use methods, for example those of
Tinker  or Bell , in which the flow patterns are guessed ,
The reasons are not entirely clear. However, that
they are in part psychological is suggested by the remarks of
J Taborek  in the Hemisphere Handbook of Heat Exchanger Design.
He there opines: "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".
The approach recommended here may be congenial; for it enables
designers to insert the same formulae, including Tinker-Bell
'correction factors', as they would supply to the 'hand-held calculators'
preferred by Taborek.
The method to be described can be applied to heat exchangers of all
types, to any participating fluids, and to any conditions of operation.
However, in order to focus on essentials, discussion will henceforth be
Such a heat exchanger is shown from the outside
here and in a sectioned view, but without the
The software package allows the various components to be moved, re-sized,
and viewed from various angles.
- a baffled shell-and-tube heat-exchanger,
- single-phase non-reacting fluids,
- steady-state operation,
- thermal and pressure-drop performance; and
- longituginal stresses in the tubes.
Whatever the calculation technique,
the apparatus in question must first be described
in geometrical terms, including (for the simplest cases):
- inside shell diameter
- inside shell-nozzle diameter
- tube outside diameter
- tube-wall thickness
- tube-layout pitch
- tube-layout characteristic angle
- tube length
- baffle cut
- baffle spacing
- number of tubes
- number of tube passes
Specification must be made of:
However, for most materials, these properties are known to vary with
temperature; and this knowledge is expressed either by way of:
- the thermal conductivity of the tube material
- the thermal conductivities of the shell- and tube-side fluids
- the specific heats of both fluids
- the densities of both fluids, and
- the viscosities of both fluids.
- tables of numbers, or
- graphs of various kinds.
If graphs are in question, their content must be converted into formulae
tables before it can be communicated to a computer program.
when this has been done, the problem of using the information
remains; for the whole point of a heat exchanger is to change temperature;
and it is not
known in advance what temperatures will prevail at any chosen point within
the tubes or shell.
- a guessed 'average' temperature is taken, as in traditional heat-exchanger
- some means must be found of communicating to the computer program
the whole content of the formulae or tables, together with the instruction:
"YOU work out values of conductivity and density etc for each
The second is the main theme of the present paper.
Also needed, of course, are the (known):
The main task of performance prediction is to determine what will be the
(mass-flow-weighted average) temperatures of the shell- and tube-side fluids
at their outlets from the heat exchanger.
- mass-flow rate and temperature of the shell-side fluid in the inlet nozzle;
- mass-flow rate and temperature of the tube-side fluid in its inlet header.
a traditional CFD code could predict performance well.
- the geometry in question were extremely simple (e.g. with unbaffled shell
of large length/diameter, and one central tube),
- the flow were laminar, and
- the temperature variations were small,
This entails that,
if performance were to be predicted purely from CFD,
a very fine grid would have to be needed (see Prof. Sunden's lecture); and
the performance-prediction calculation would take more time
than any designer could afford to wait.
- industrial heat exchangers have very many tubes;
- baffles are present; and
- the flow is usually turbulent.
Moreover, for flow in tube banks, the
knowledge of turbulence
is still rudimentary; so the reliability of the
predictions far from one hundred per cent.
The only practical solution is therefore to
introduce additional information,
derived from such experimental data as can be found, concerning the rates of
heat and momentum transfer per unit area of solid-fluid interface.
information is usually expressed in the form of
mathematically-expressed relationships between the well-known
All these parameters involve the material properties listed in section 2.1.
- Nusselt or Stanton number, for the heat-transfer coefficient;
- Reynolds number, to characterize the state of the fluid, and
- Prandtl number, to characterize the relative ease of heat and mass transfer
in the fluid.
Therefore the use of empirical correlations still requires
the computer program to work out the
property values from the given formulae and the temperatures which it
finds at every point.
The outlet temperatures of the heat-exchanging fluids are the main
quantities which it is desired to predict; however, these depend on the
temperatures just upstream of the outlet; these just-upstream-of-outlet
temperatures depend on the temperatures upstream of them;
and so on.
Therefore, the whole temperature distribution has to be computed.
When the flow pattern is not one-dimensional, what point lies
'just upstream of' a given point is not obvious a priori;
to calculate the temperature distribution depends on ability to
calculate the whole three-dimensional flow distribution giving rise to it.
This therefore is what the computer program must additionally do, providing
incidentally further information needed by the designer:
the pressure losses suffered by the two streams.
Fortunately, computer programs (the so-called CFD codes) do exist for
computing both the flow fields and the temperature distributions
Although their accuracy depends on the fineness of
computational grid which is employed, and desirably fine grids do
increase computer times and therefore costs, the
requirements relating to shell-and-tube heat exchangers are usually
but only when the space-averaged approach is adopted.
However, the heat-transfer and friction correlations require:
It follows that, even if the temperature variations were small enough not to
affect material properties, the need for the code to evaluate formulae from
values which varied from place to place would remain.
- not only material properties which vary with temperature according to formulae which must be
made known to the code; but also
- other quantities which can not be
specified a priori, namely the
three components of the shell-side velocity.
Thus the Reynolds Number
enters most pressure-drop and convective-heat-transfer formulae; and its
value depends on the local velocity, which varies with position in ways that
are not known at the start.
Moreover, the angle between the mean-flow direction and the tube axis is
probably important. It should appear in the formulae.
In summary, predicting the performance of shell-and-tube heat exchangers
necessitates use of a program which is not restricted, as conventional
design methods are, to the presumptions that:
- material properties can safely be based on guessed average temperatures,
- mass flow rates can be based on guessed average velocities and densities.
Of course, many CFD codes have some built-in correlation-evaluation
sequences, representing friction and heat-transfer; and they
also contain computer-coding modules which express the variation with
temperature and pressure of some properties of some
In principle, there is no limit to the extent to which these provisions can
be extended. But in practice, however much is provided, some users of the
- require different correlations
- want them at once;
- be unwilling to pay the code-developer to provide them.
From the earliest years of commercial CFD, therefore, developers have
allowed users to add coding modules of their own, usually in the form of
Fortran or C subroutines, which would supplement the built-in correlations
in the desired respect.
Users of the 1981 PHOENICS code, for example, will remember what clever
use some users made of the so-called 'GROUND-coding' facility, which
indeed many old-stagers continue to use. The paper by Stevanovich et al  is an excellent
example of the use of this technique for heat exchangers.
However, the proportion of CFD-code users with the necessary skills is
constantly diminishing; and few heat-exchanger designers
either possess or have the time to acquire them.
In order to enable PHOENICS users to benefit from the features of
'GROUND-coding' without themselves having to be familiar with either
Fortran or C, the so-called 'PLANT' feature was introduced in 1997.
This enabled the user to express his wishes by way of formulae, written in
accordance with prescribed rules; whereupon PHOENICS itself:
- interpreted the formulae;
- created corresponding Fortran subroutines;
- compiled them;
- re-built the executable; and
- carried out the required flow-simulating calculation.
This was a big step forward; and it did, at least potentially, satisfy
the 'formula-processing' requirement which has been pointed out above.
However, because it was not adequately presented to them, it did
not convert many heat-exchanger designers into CFD users.
Perhaps also the 'prescribed rules' were shaped by those thinking too much
of the Fortran to be written, and not sufficiently of the prospective user.
PLANT remains as a valuable feature of the current PHOENICS; but the
feature now to be described has rendered it almost redundant.
The new feature has the acronym "In-Form", standing for "Input (or Intake)
of Formulae". Its concept is very simple, namely:
- let the user, in language which he or she can easily understand, write the
formulae according to which he wants the solver to compute values of, say,
- let this be sent to the equation-solving module in the form of a character
- let the latter module first inspect and 'parse' all the strings which it
receives, converting them into settings of 'internal switches' which dictate
how the calculation shall be conducted; and then
- let the calculation proceed.
The formulae may provide CFD inputs of any kind, whether:
The formulae most relevant to heat-exchanger design are those which:
- initial values,
- sources and sinks,
- boundary conditions,
- numerical criteria.
- compute the local material properties in shell-side fluid,
tube-side fluid and metal, from the local temperatures and (if appropriate)
- compute the corresponding Reynolds and Prandtl numbers;
- compute the corresponding Nusselt or Stanton numbers and thence the local
heat-transfer and friction coefficients;
- compute the resulting local sources and sinks of heat and momentum, and
- supply these to the equations on which the solver operates.
In-Form has many more capabilities than the heat-exchanger designer is
likely to need. Therefore only the few relevant ones will be illustrated
here, as follows:
- specific fluids may be introduced by statements such as:
tube_fluid is SAE_5W-30_engine_oil
which dictates use of a pre-existing set of formulae for density,
viscosity, specific heat and thermal conductivity;
- individual material properties can be set by such statements as:
property RHO1 at SHELL is CONST1+CONST2*TEM1+CONST3*TEM1^2
- RHO1 stands for density,
- TEM1 stands of temperature, and
- ^ is the symbol used for exponentiation;
- the local Reynolds number can be defined by a statement such as:
Stored var Reyn is TUBEDIAM*RHO1*AbsV/Visc
with 'Stored var' meaning 'compute and place in 3D store', and
AbsV and Visc signifying absolute velocity and viscosity;
- then Stanton Numbers can be specified by the statement:
Stored var STAN is CONST1*Reyn^CONST2*PRNO^CONST3
with PRNO meaning Prandtl number;
- whereafter a local heat-transfer coefficient can be specified by way
Stored var COEF is STAN*RHO1*CP1*ABSV
with CP1 meaning specific heat; and finally
- the heat source can be specified via:
Source of TEM1 is COEF*AREA(TMET-TEM1)
with TMET meaning metal temperature.
The relevance of these statements to heat-exchanger design should be
obvious; for they say (nearly) all that is to be said about how local heat
transfer from tube to fluid is to be calculated.
Once they have been typed into the input file, there is nothing further for
the designer to do than to wait (for a minute or two)
until the calculation has been completed.
A heat exchanger will be considered which has:
- a single tube pass,
- a shell of 4m length and 1m diameter with
- three baffles.
The shell-side fluid is water and the tube-side fluid SAE 5W-30 engine-oil ;
these enter at 10 and 60 degrees Celsius respectively.
The mass flow rates of both fluids are 100 kg/s.
Text-book formula, connecting Nusselt, Reynolds and Prandtl numbers, have
been adopted, with modifications made by the user, for the shell-side and tube-side heat transfer coefficients.
The computer code
The distributions of pressure, velocity and temperature of the two fluids
have been computed by the general-purpose CFD code, PHOENICS, without
activation of any heat-exchanger-specific special features.
Therefore any other CFD code equipped with a formula-understanding module
could have been used.
The results to be displayed
The computer runs of which the results will be presented have been chosen in
order to illustrate that:
- the variations in space of properties, flow patterns, Reynolds numbers,
Prandtl numbers, Nusselt numbers and heat-transfer coefficients, which are
neglected in conventional design methods, are rather large;
- it is however as easy to calculate, and to take account of, these
variations as it is to neglect them; and
- changing the formulae used,
the output required or
any other specification, and
- then observing the consequences, is a matter of minutes only.
The distributions are of course three-dimensional. However it is sufficient
for present purposes to consider the central plane only.
Results will be represented by way of vector and contour plots on this plane.
After presentation of the results, some of the formulae used for
generating them will be shown and discussed.
The velocity distribution in the shell, on the central plane is shown in
The shell-fluid inlet is at the bottom on the left, and its outlet at the top
on the right. The influences of the two baffles is clearly seen.
The temperature distributions in the shell- and tube-side fluids are shown
in Fig.2 and Fig. 3.
The latter conforms to that to be expected in an ideal
counter-flow heat-exchanger, but the former (understandably) does not.
The pressure distribution in the shell is shown in
Fig.4. It shows the
to-be-expected discontinuities caused by the baffles.
As has been emphasized above, the properties of most fluids depend upon
temperature. The variation of the viscosity of the tube-side fluid, for
example, is shown in Fig. 5.
Evidently (see scale on the right), it varies
by a factor of more than two.
The dimensionless parameters which feature in the calculation of heat-transfer
coefficients vary through the heat exchanger partly, because of temperature
variations and partly because of the non-uniformities of velocity.
distributions of Reynolds, Prandtl and Nusselt number calculated in the
present case are shown, for the shell- and tube-side fluids in turn, in
Fig. 10 and
In respect of Reynolds number, variations are greatest on the shell side;
the presence of the baffles accounts for this.
The consequential variation
of Nusselt number is correspondingly great, being highest near the edges of
the baffles and fifty times smaller in low-velocity regions, near the baffle
roots and in the corners opposite inlet and outlet.
From the Nusselt numbers, the computation of the corresponding shell- and
tube-side heat-transfer coefficients per unit volume of shell is an easy
step; and the overall heat-transfer coefficient, U, follows as their harmonic mean.
Their distributions are displayed in
The shell-side coefficients show wide variations but, their
effect on U is diminished by the fact
that the tube-side ones are the smaller; so the maximum U is
less than 50 % greater than the minimum U.
This observation might be thought to blunt somwhat the above criticism of conventional design methods;
but it does not truly do so.
The objection to conventional methods is not that
that they use a constant value of U for the whole heat exchanger; it is
that the means of determining that value are based on guesswork and not on
detailed analysis of the flow field.
The results displayed so far will have come as no surprise to any
heat-exchanger designer who has thought even superficially about what is
truly happening inside his equipment.
What may interest him more may be to
The ability of the computer program to understand easily-written formulae is
the key requirement.
- how easily they were obtained, and
- how quickly the effects of changes to the input can be investigated.
Examples of such formulae will now be presented,
starting with the following extract from the engineer's data-input file:
The lower-case words ('stored', 'var', 'is') tell the code that it must
compute some new variables everywhere within the 'virtual heat exchanger'
with which it is concerned.
- (stored var REY1 is DIAM*VABS/ENUL)
- (stored var PRN1 is CPS*RHO1*ENUL/COND)
- (stored var NUS1 is 0.2*REY1^0.6*PRN1^0.33)
- (stored var COE1 is AOVERV*NUS1*COND/DIAM)
- (stored var REY2 is DIAM*TUBVEL/ENU2)
- (stored var PRN2 is CPT*RHO2*ENU2/CON2)
- (stored var NUS2 is MAX(2.0,0.328*(REY2*PRN2)^0.33))
- (stored var COE2 is AOVERV*NUS2*CON2/DIAM)
- (stored var COEU is 1/(1/COE1+1/COE2))
- (stored var TEMM is (COE1*TEM2+COE2*TEM1)/(COE1+COE2))
The upper-case words have been chosen by the engineer, who appears to have
The engineer has also chosen the formulae, most of which are rather easy to
- REY1 an adequate name for 'Reynolds number of shell-side fluid',
- REY2 likewise for 'Reynolds number of tube-side fluid',
- PRN1, PRN2, NUS1 and NUS2 as adequate for their Prandtl and Nusselt
- that AOVERV will serve as 'area/volume',
- COE1, COE2 and COEU remind him of the shell-side, tube-side and overall
- and so on.
- 'DIAM*TUBVEL/ENUL' stands for 'diameter times tube-fluid velocity divided
by viscosity, i.e. the tube-side Reynolds number,
wherein the first two
variables (the code is clever enough to work out) are constants, whereas
the third must be computed for each location;
- 'NUS2 is MAX(2.0,0.328*(REY2*PRN2)^0.33)' represents a formula which some
text books recommend for pipe flow at modest Reynolds numbers, with a
lower limit of 2.0 inserted by the engineer for some reason of his own;
- '1/(1/COE1+1/COE2))' shows how the overall coefficient is to be computed
from the individual coefficients; and
- the formula for the tube-metal temperature, TEMM, shows that it is a
suitably-weighted mean of the fluid temperatures, all varying, like
the coefficients themselves, from place to place.
How were the material properties calculated? Also by way of formulae drawn
from textbooks. Thus, the formulae for the properties of the engine-oil in
question were found in a book by K.Hagen  and translated thus into the
form understood by (at least) the PHOENICS computer code:
wherein POL4(TEM2,.....) signifies a fourth-power polynomial, the
coefficients in which are the numbers which follow the comma.
- (property RHO2 is 1052.3-0.6420*TEM2)
- (stored var CPT is 753.7+3.65*TEM2)
- (stored var CON2 is 0.1447-2.3073E-5*TEM2)
- (stored var ENU2 is 10.0^(POL4(TEM2,58.2987,-.53817,1.92827e-3, -3.16448E-6,1.97922E-9)-2)
Fortunately, many formulae are provided as items to be selected from a
library. Nevertheless, it is not difficult to translate a new formula into
'In-Form-speak': users are not confined to what is on the code-vendor's menu.
There are engineers who are unwilling to do more, when designing equipment,
than make selections, by way of mouse-clicks, from what so many have done
before that the code provider has had time and inducement to adopt as
Others however, more like those referred to in the above quote from J.Taborek,
will welcome the power which In-Form provides to "develop a 'feel' for the
Noting the considerable temperature differences between
the metal temperature and the tube-fluid temperature, a designer might wonder whether
he ought to multiply the relevant coefficient, as some textbooks recommend,
by the ratio (wall viscosity/ bulk viscosity) raised to the power 0.14).
He could set his doubts at rest in a few moments by introducing the following
lines into his input file
(by copying; God forbid that he should have to type it
(stored var ENUM is: 10.^(POL4(TEMM,58.2987,-.53817,1.92827e-3, -3.16448,E-6,1.97922E-9)-2)
so as to compute the viscosity of the engine-oil at the wall temperature, TEMM;
then he should modify the formula for coe2 so as to reflect the
viscosity-ratio effect, thus:
(stored var COE2 is (ENUM/ENU2)^0.14*AOVERV*NUS2*CON2/DIAM).
If he did this, he would learn, after inspecting the computed results, that
the total heat transferred would increase by only 0.5 %, so adding to his
stock of 'engineering feel'.
Alternatively, he might wish to know how the heat-transfer rate per unit
volume varied through the shell; then he could satisfy his curiosity by
writing the single line:
(stored var flux is COEU*(TEM2-TEM))
and, one minute later, view the results presented in
Comparing this with other images which he has seen before he will be able to
decide whether he is satisfied with the nearly-two-fold variation there
disclosed, or will seek by re-design to achieve greater uniformity.
Lastly, he might suddenly think: "What about fouling?" Then he has only to
insert one line in his input file such as:
(stored var FOUL is
.... whatever function of position and temperature he invents)
and to change the overall-coefficient line to:
(stored var COEU is 1/(1/COE1+1/COE2+FOUL))
The subsequent computer run will inform him of the consequences, both by
way of numbers and of graphical displays.
There is no limit to the easily-effected variations of input and output
which the In-Form facility allows; therefore, the main points having already
been made, no further examples will be presented.
5.1 A common misconception
It is widely believed that the problem of computing the stresses in solids differs
from that of calculating fluid flow so much that different methods
are needed for each problem.
In particular, it is often supposed that the so-called finite-element
method must be used for the solid-stress problem.
Both these beliefs are erroneous.
5.2 The truth of the matter
In fact, the differential equations governing displacements in solids
are very similar to (but simpler than) those governing velocities in fluids.
It is true that the displacements in the three coordinate directions are connected, via
Poisson's Ratio, in a manner of which velocities know nothing.
Further, equations for the three components of rotation must be solved in addition
However, the finite-volume methods employed in CFD codes are well able to solve these equations,
without any of the leftovers of pre-computer days (e.g. energy theorems and Galerkin weighting
procedures) which clutter the finite-element formulation.
One of the first to recognise this was Stephen Beale [Reference 8].
5.3 Fluid-structure interaction examples
Results from an early study are shown below for a two-solid-material
block, heated by radiation from above, and cooled by a stream of air:
(1) velocity vectors,
(2) displacement vectors,
computed at the same time, and
(3) horizontal-direction stresses,
obtained by post-processing.
A bent beam
A beam bent by fluid forces is shown
Flow in a turn-around duct
One of the early arguments for preferring FE methods was that they
handled curved boundaries more easily.
But FV techniqes serve just as well, even when the grid is
cartesian, as shown here for flow in a
In this case there are heat sources in the solids, giving rise to these
Because of the unified-computational-mechanics technique, we are able
to compute simultaneously the velocity and displacement
Forces on an under-water structure
Finally, deflection is shown of a sea-bed structure, resulting from the
Here it is essential to be able to simulate solids and fluids at
the same time.
5.4 Exemplification for the heat exchanger
In order to illustrate these assertions, calculations have been performed for the longitudinal
stresses in the tubes of the present shell-and-tube heat exchanger.
Fig. 16 shows the results of the calculations in terms of vector diagrams.
Vectors of what?
The latter have been shifted to the right of the former for ease of display. However
PHOENICS specialists might recognise that the MUSES (Multiply-USed-Space) trick has been played,
whereby a double-size grid has been employed, with:
- The left half of the diagram shows vectors of shell-side-fluid velocity; and
- the right-half shows vectors of displacement in the tube metal.
- flows computed on the first grid,
- displacements computed on the second grid, and
- metal temperatures forced to be the same for both grids by In-Form statements.
Why do the displacement vectors have the distributions which have been shown? Because
of the arbitrarily-introduced fixings postulated for the tube ends within the shell.
The stressescan be deduced from the strains, which are themselves deduced by differentiating the displacements.
Fig. 17 shows contours of the stresses, of course in
the right-hand part of the display region.
The higher (compressive) stresses appear in the lower part of the shell, where the tube ends have been rigidly fixed.
The importance of Fig. 17 in the present context is that:
- the stresses were computed at the same time as the fluid flow and temperature distributions, by means of a single general-purposecomputer code;
- the additional computational effort was trivial;
- alternative (and more realistic) mechanical constraints can be introduced via user-written In-Form statements.
It should be stressed that the techniques employed can be applied
- when the heat exchanger is of any other configuration;
- when its operating conditions vary with time (e.g. when the
inlet mass-flow rates and/or temperatures vary in accordance with
- when either or both fluids are two- or multi-phase, In-Form being used to
introduce any of the complex formulae which are commonly used for the
design of such equipment ;
- when chemical reaction takes place within the tubes, for example in accordance with a
formula which depends not only on local temperature but also on the
changes in composition to which the reaction itself gives rise.
It is therefore argued that:
- the time has come for heat-exchanger
designers to exploit computational fluid dynamics with space-averaged
representations of heat-transfer and friction processes;
- they should consider calculating solid stresses at
the same time;
- specifically, the
difficulty of introducing the necessary empirical knowledge has been
removed by the formula-parsing capability;
- this enables the computer code to 'understand'
the formulae which designers are accustomed to use in their
thus all that formerly could be done only by specialists capable of
exploiting the 'user-subroutine' facility
can now be done by any flexibly-minded heat-transfer engineer.
The author gratefully acknowledges the assistance of Mr. Nikolay Pavitsky,
of CHAM's office in Moscow, Russia, in developing the In-Form facility
during the last five years.
- SV Patankar and DB Spalding "A calculation procedure for the
transient and steady behavior of shell and tube heat exchangers"
in "Heat exchangers: design and theory sourcebook"
edited by N Afgan and E Schluender, McGraw Hill 1974
- Z.Stevanovic, G Ilic, N Radojkovic, M Vukic, V Stefanovic and G Vukovic
"Design of shell and tube heat exchangers by using CFD technique - part one:
Facta Universitatis Series Mechanical Engineering vol 1 no 8, 2001,
- 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"
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The End !!!