HEAT PROCESSES

1
HEAT PROCESSES
HP5
Heat transfer in ducts, fouling
Noncircular profiles and equivalent diameter of
pipe. Compact and plate heat exchangers.
Hydraulic and thermal analysis of chevron type
heat exchanger (H.Martin). Heat transfer
enhancement (static mixers, centrifugal forces,
Deans vortices). Flow invertors. Performance
criteria (PEC). Fouling (example crude oil
fouling - Polley model and diagrams).
Rudolf Žitný, Ústav procesní a zpracovatelské
techniky CVUT FS 2010
2
Noncircular ducts
HP5
Eliptical, rectangular ducts, channels with
longitudinal fins
Multiply connected regions (annular, tube bundle
in shell and tube exchanger)
3
Noncircular ducts
HP5
General cross section of a channel can be
characterized by equivalent hydraulic diameter
Dh, that is used in definition of Reynolds and
Nusselt numbers.
Cross section surface
Volume of channel
Surface of wall
Perimeter of cross section
At turbulent flows the same correlations for
pressure drop (friction factor) and heat transfer
(Nusselt number) can be used. Correlations for
circular pipe are usually used, however the cross
sections with sharp corners (triangles, cusped
ducts) lead to error up to 35 .
Equivalent diameter is used also in laminar
flows, but different correlations for different
cross sections must be used (from this point of
view the laminar regime is more
complicated). Modified definitions of equivalent
diameter exist for specific classes of cross
sections (e.g. average distance from the point of
maximum velocity in triangles, or square root of
the cross section area, see next slides).
4
Noncircular ducts-examples
HP5
Laminar flow pressure drop and asymptotic
Nusselt number (extremes)
Increased Nu and ?f when compared with circular
pipe
b
The value 96 corresponds to laminar flow and very
thin gap. Compare with ?fRe64 for circular pipe
a
Asymptotic Nu. The value 7.54 corresponds to a
narrow flat channel with the constant wall
temperature. Compare with the limiting value 3.66
for circular pipe.
Decreased Nu and ?f when compared with circular
pipe
Shah R.K., London A.I. Laminar flow forced
convection in ducts, Supplement 1 to Advances in
Heat transfer eds. Irvine, Hartnett, Academic
Press, N.Y. 1978, Referred by Rohsenow Handbook
of heat transfer, McGraw Hill, Boston, 1998
5
Friction factor f ?f/4
HP5
Warning There exist two different friction
factors for pressure drop calculation, be careful
whether you are using the correct one
f-Fanning friction factor
6
Parallel plate heat exchangers
HP5
Simultaneous development of temperature and
velocity profiles (laminar).
Both plates at constant temperature
WHAT IS CORRECT??? There are two different
correlations in two very respected books used by
thousands profesionals
You can found this correlation in VDI Warmeatlas
One plate is insulated
One plate is at constant temperature
Similar but different correlation in Rohsenows
book
7
Parallel plate heat exchangers
HP5
Have you noticed the basic difference between
correlations for circular tube and parallel
channel?
The difference is in the exponent of Gz (1/3 for
tube, 1/2 for planar channel)
8
Corrugated plates Heat exchangers
HP5
How to calculate pressure drop and heat transfer
coefficient in plate heat exchangers with
corrugated heat transfer walls?
9
Corrugated plates paper Martin Holger
HP5
Applications of CFD is rather demanding and not
very accurate.

• According to my opinion the best way how to
  calculate pressure drop and heat transfer in heat
  exchangers with corrugated plates is the
  semiempirical method described by Martin Holger
  in Chemical Engineering and Processing, 1996.
• Pay attention to the following features
• How to blend results for friction factors
  corresponding to different flow patterns
  (longitudinal and furrow flows)
• How to apply analogy between momentum and heat
  transfer (how to predict heat transfer from
  friction factors). Quite unique feature is the
  Leveque analogy.

10
Corrugated plates paper Martin Holger
HP5
The first problem how to define equivalent
hydraulic diameter?
D plate distance
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Corrugated plates paper Martin Holger
HP5
Friction factor correlation
Heat transfer (generalised Leveque)
Brave idea to apply Leveque concept also at
turbulent flows!
12
Corrugated plates paper Martin Holger
HP5
Few more details about Friction factor correlation
Functions ?0 ?1 are defined separately for
laminar and turbulent regime
Flow along walleys (like in a straight pipe)
Flow in a wavy channel, characterized by
separation of vortices at down and up-hills
Few more details on Heat transfer (generalised
Leveque)
L is the distance between two crossings (and not
the length of plate). This distance is quite
small so that the thermal boundary layer is thin
enough to fulfill the Leveques assumption (it is
assumed that the boundary layer is restored at
each crossing)
Is it really Leveque? Yes, because at laminar
flow ?Reconstant
Leveque analogy is discussed in paper Martin
H.The generalized Leveque equation and its
practical use for the prediction of heat and mass
transfer rates from pressure drop,
Chem.Eng.Science, 57 (2002), pp.3217-3223
13
HT enhancement
HP5
Dalí
14
HT enhancement
HP5

• How to increase heat transfer coefficient at
  internal channel flows (in pipes)?
• Artificial wall roughness, porous wall
• Fins, grooves, dimples
• Inserts (static mixers, twisted tape, wire mesh,
  invertors)
• Centrifugal forces (coiled tubes, bends)
• Vibration, ultrasound, nanoparticles

15
HT enhancement
HP5
Heat transfer augmentation (Nu increase
desirable effect) is usually accompanied by
pressure drop increase (undesirable effect).
There exist many different PEC (Performance
Evaluation Criteria) characterising efficiency of
considered modification (only those giving PECgt1
should be used) . The most frequently used
This PEC follows from comparison of the two
identical pipes (the same diameter and length),
one pipe is empty (Fanning friction factor f0)
the second one is modified by inserts, fins,
(higher f). So that the pumping power will be the
same the flowrate in the augmented pipe (fgtf0)
must be decreased
Assuming the same temperature approach ?T in the
both pipes, the thermal power is proportional to
the Nu and the PEC can be interpreted as
Proof!
Comparison of thermal powers for the same pumping
power, the same flow rates but different lengths
Proof!
16
HT enhancement wall
HP5
Heat transfer can be increased by a modification
of wall such that the heat transfer surface is
extended (fins, dimples), and the thermal
boundary layer is disrupted (for example by
vortices generated at protrusions or
dimples). Only a little bit controversial
enhancement by dimples will be presented in next
slides.
17
HT enhancement dimpled wall
HP5
H. Lienhart et al. / Int. J. Heat and Fluid Flow
29 (2008) 783791
Drag reduction by dimples? A complementary
experimental/numerical investigation
18
HT enhancement inserts
HP5
Inserts (static mixers, twisted tape) extend heat
transfer surface (as far as a good thermal
contact with pipe wall is ensured) and generate
secondary flows diminishing thermal boundary
layer. Inserts are effective first of all in
laminar flow regime (PEC is highest at low Re),
but heat transfer enhancement in turbulent regime
is also significant. Wire coils disrupt thermal
boundary layer (suitable for laminar flows), wire
mesh affects the main flow and is effective in
turbulent flows. Advantage Tiny wire at wall has
only small effect upon pressure drop. What is
surprising inserts usually suppress fouling!
19
HT enhancement SM Kenics
HP5
Static mixers (Kenics, Sulzer,Helax,) serve for
mixing of liquids but also for the heat transfer
intensification.
Standard solution consists in filling the whole
tube by SM elements (tight arrangement). For
Kenics SM the heat transfer at laminar flows is
increased as (see Joshi, Nigam, Cibulski)
Compare with empty pipe (Leveque)
On the other hand, the tube filled by SM elements
exhibits higher pressure drop (friction factor)
Question f, f0 represent Fanning or the Darcy
Weissbach friction factor?
Answer Fanning (see empty tube)
20
HT enhancement twisted tape
HP5
International Communications in Heat and Mass
Transfer 38 (2011) 348352
21
HT twisted tape wire coil
HP5
Lieke Wang, Bengt Sundén Performance comparison
of some tube inserts  International
Communications in Heat and Mass Transfer, Volume
29, Issue 1, January 2002, Pages 45-56
Twisted tape (laminar/transition/turbulent)
Swirl number
Wire coil (laminar/transition/turbulent)
22
HT centrifugal forces
HP5
Centrifugal forces in coiled pipes (spirals,
helically coiled pipes) create secondary flows
similar to vortices induced e.g. by a twisted
tape. Local effect of centrifugal forces and
secondary flow appear also in bends (for example
U-tube acts as a partial flow inverter).
Advantage Increased Nu is not accompanied by
too large pressure drop increase. Positive effect
is significant reduction of fouling (spiral heat
exchangers are suitable for dirty fluids, fibrous
pulps,). Residence time characteristics are
improved (residence times of fluid particles
moving at axis of pipe and in vicinity of wall
are not so different as in a straight pipe).
Disadvantage Effect of centrifugal forces
disappears at creeping flow, therefore this
technique cannot be applied for highly viscous
liquids (Relt10)
Dean, W.R., Note on the motion of fluid in a
curved pipe, Phil.Mag.Ser.7, vol.4, no.4, pp.208,
1927.
23
HT centrifugal forces
HP5
Some trivial facts
u
Centrifugal force acting on particle of mass m
Fc2mu2/Dc
Dc
m
Force acting on plate with cross section D x
1 Fi?ur2D
ur
D
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HT enhancement coiled pipe
HP5
Centrifugal forces generate two counter-rotating
vortices (secondary flow). Characteristic
velocity of circulation ur (transversal velocity)
can be estimated from balance of equilibrium
force Fc and inertial force Fd
Intertial force related to unit length of pipe
(dynamic pressure acts on area D)
centrifugal force on unit length of pipe (acting
on volume in the whole cross section)
From the force equilibrium follows the ratio
between radial and axial velocity
This is only brief derivation showing principles
Thermal boundary layer and penetration depth
?
Mori a Nakayama (1965)
See also M.M. Mandal et al. / Chemical
Engineering Science 65 (2010) 9991007
25
HT enhancement coiled pipe
HP5
Have you noticed similarity between Deans and
Swirl number?
26
Flow inversion
HP5
Flow inversion transfers overheated fluid from
wall to axis
Partial flow inversion in bends
27
Flow inversion in a bend paper Zitny
HP5
Zitny R, Luong TCT, Strasak P, et al. Heat
Transfer Enhancement and RTD in Pipes with Flow
Inversion. Heat Transfer Engineering, Vol. 25
(2004), pp. 67-79
Centrifugal forces in a bend generate secondary
flows and the flow inversion (counter-rotating
vortices transfer fluid particles from pipe axis
toward wall)
Secondary vortex
Centrifugal force
28
Flow inversion in a bend
HP5
Optimum flow inversion causes half-rotation of
the secondary vortex and this situation is
achieved at about Re.?100 (laminar flow)
29
Flow inverter paper Zitny
HP5
Zitny R, Thi C.T.L, Sestak J Heat Transfer
Enhancement in a Pipe Using a Flow Inverter. Heat
Transfer Engineering, Vol. 30 (2009), pp. 952-960
inverter
Hot center, cold wall
Incoming stream is mechanically subdivided into
the central and the wall region and mutually
exchanged
30
Flow inverter
HP5
In case of Relt10 centrifugal forces are not
strong enough to generate secondary flows and
flow inversion. Mechanical subdivision operates
also at Reltlt1.
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Flow inverter
HP5
Performance Evaluation Criterion
32
Extended surfaces
HP5
Previous analysis was concentrated upon the heat
transfer enhancement by increasing heat transfer
coefficient. Inserts or modifications of pipe
walls increases at the same time the heat
transfer surface, however this additional surface
can be fully accounted for only if the thermal
resistance of inserts or fins is negligible.
Dalí
33
Extended surfaces (fins)
HP5
Compact heat exchanger
Plate and fin
Tw
?
x
In the case that the thermal resistance of walls
is zero (infinitely large thermal conductivity of
fins) the surface of fins can be added to the
heat transfer surface and
In the case that thermal resistance of fins
cannot be neglected the heat transfer surface
must be reduced
Efficiency of fin ?fin can be calculated from
temperature profile T(x) in a fin, determined by
Fourier equation
2-because the fin is heated from both sides
completed by boundary conditions
34
Extended surfaces (fins)
HP5
Solution of previous equation yields temperature
profile along the height of fin
Efficiency of fin is calculated from temperature
gradient at the heel of fin (the gradient
determines heat flux at the heel)
I1,K1 are modified Bessel functions
In a similar way the efficiency of circular fin
can be derived
where ? are dimensionless radii
35
Extended surfaces (fins)
HP5
Example Calculate efficiency of rectangular fin
of constant thickness 1mm, height H20mm made
from stainless steel for heat transfer
coefficient 3000 W/m2/K Result ?0.16 If the
same fin will be from aluminium, the efficiency
increases to ?0.54
36
Fouling
HP5
Formation of deposits on heat transfer surface
increases thermal resistance (and pressure
drop) Precipitation Corrosion Chemical
deposits Biochemical deposits Solidification
Photographs from paper Khalil RanjbarEffect of
flow induced corrosion and erosion on failure of
a tubular heat exchanger. Materials and Design 31
(2010) 613619
There are many ways how to mitigate fouling
addition of tiny particles (nano, pulps),
sonication, pulsating electrical field,
turbulisation of flow (e.g. wire mesh usually
mitigates fouling)
S.N. Kazi, G.G. Duffy, X.D. Chen Fouling
mitigation of heat exchangers with natural
fibres. Applied Thermal Engineering 50 (2013)
1142-1148
Y.I. Cho, B.G. Choi Validation of an electronic
anti-fouling technology in a single-tube HE. Int.
J. Heat and Mass Transfer. 42 (1999), 1491-1499
37
Fouling
HP5

• Fouling evolution
• Induction period
• Negative fouling (e.g. promoted nucleate boiling,
  heat transfer increased)
• Linear fouling (constant rate of deposits
  formation, thermal resistance increases)
• Falling fouling (decreasing rate of fouling
  formation)
• Asymptotic fouling (zero rate)

38
Fouling fouling rate models
HP5
Chemical fouling of oil products (Ebert Panchal
model)
Deposits as a product of chemical reaction with
activation energy E
Rate of deposits removal proportional to wall
shear stress
The production rate is proportional to the volume
of reaction zone overheated thermal boundary
layer of thickness ?
B.L. Yeap, D.I. Wilson, G.T. Polley, S.J. Pugh
Mitigation of Crude Oil Refinery Heat Exchanger
Fouling Through Retrofits Based on
Thermo-Hydraulic Fouling Models Chemical
Engineering Research and Design, Volume 82, Issue
1, January 2004, Pages 53-71 G. T. Polley, D. I.
Wilson, B. L. Yeap, S. J. Pugh Evaluation of
laboratory crude oil threshold fouling data for
application to refinery pre-heat trains Applied
Thermal Engineering, Volume 22, Issue 7, May
2002, Pages 777-788 W.A. Ebert, C.B. Panchal,
Analysis of Exxon crude slipstream coking data,
in C.B. Panchal, et al. (Eds.), Fouling
Mitigation of Industrial Heat-Exchange Equipment,
Begell House, 1997, pp. 451460.
39
Fouling fouling rate models
HP5
Asymptotic fouling is characterized by
and from the Ebert Panchal fouling model follows
the value of critical wall shear stress ensuring
zero fouling rate
This criterion is used for heat exchanger design
by Poddar diagrams. See next slide
40
Fouling fouling rate models
HP5
G.T. Polley et al. Use of crude oil fouling
threshold data in heat exchanger design. Applied
Thermal Engineering 22 (2002) 763776 T.K.
Poddar, G.T. Polley, Optimising the design of
shell-and-tube heat exchangers, Chemical
Engineering Progress (September) (2000).
Problem specification Calculate number of tubes
and length of ST HE for given thermal duty
(power), flowrates in shell and tubes, maximum
pressure drops in shell and tubes.
Region of design parameters (L,n) satisfying
constraints on duty and pressure drop (in this
case is limiting the shell side)
Poddar diagram
Optimum design 600 tubes in bundle, length 3.2 m
Unpleasant situation-for the optimum design
parameters a fouling in tubes can be expected
41
HP5
42
EXAM
HP5
Noncircular channels Concept of equivalent
diameter (Dh is used in definition Nu and Re)
43
What is important (at least for exam)
HP5
Heat transfer and thermal boundary layer
thermal boundary layer grows faster at a plate
than at the wall of pipe
tube (Léveque)
plate channel
Parallel plate channel
constant temperature of both plates
44
What is important (at least for exam)
HP5
Corrugated plates (chevron HE)
Fanning friction factor f (denoted as ? in
original paper by H.Martin) is calculated from
correlation as a function of chevron angle and
Reynolds number.
Generalised Léveque correlation is based upon
analogy between momentum and heat transfer. Nu is
calculated from friction factor (take into
account that fReconst at laminar flow regime)
This correlation holds at laminar and turbulent
flow regime!
45
What is important (at least for exam)
HP5

• Inserts in pipes and centrifugal forces (heat
  transfer enhancement)
• static mixers (enhanced Leveque
  )
• twisted tape (Nu depends upon swirl number
  )
• helical coils (Nu depends upon Dean number
  )

Extended heat transfer surface (fins)
The effective heat transfer surface of fins must
be reduced by where H is height, b is thickness
of fin and Biot number is
46
What is important (at least for exam)
HP5
Fouling in pipes (Ebert Panchal 3 parametric
model ?,?,E-activation energy, the model assumes
that rate of deposits formation is proportional
to the volume of overheated fluid inside
turbulent thermal boundary layer, see Dittus
Boelter correlation NuRe0.8Pr1/3)