King Abdulaziz University
Faculty of Engineering
Mechanical Engineering Department
Basics of Rating and Thermal
Design of Heat Exchangers
General notes prepared for the course
MEP 460: Design of Heat Exchangers
by
Abdul-Rahim A. Khaled, Professor
2014-2015
�سم ا� ا�ر�ن ا�رحيم
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(i)
Table of Contents
No. Topic Page
1 Revision 1
2 General Correlations for Internal Flow 8
3 Classifications of Heat Exchangers 16
4 Basic Equations for Heat Exchangers 27
5 Fouling of Heat Exchangers 45
6 Double Pipe Heat Exchangers (DPHXs) 54
7 Shell-and-Tube Heat Exchangers (STHEs) 65
8 Compact Heat Exchangers (Compact HXs) 86
9 Boiling 100
10 Condensation 109
11 The Gasketed-Plate Heat Exchangers 117
12 Condensers and Evaporators 133
13 References 146
�سم ا� ا�ر�ن ا�رحيم
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(1)
Internal Flow
General Information
Mass flow rate, m :
Cm Aum ,
CA : Flow area; mu : Mean flow velocity normal to cross-section
Mean bulk Temperature, Tm:
p
ACp
mcm
TdAucT C
Newton’s law of cooling for the Local Heat Flux, q
ms TThq
Reynolds number, ReD:
w
hmD P
mDuRe
4
Hydraulic diameter, Dh:
w
Ch P
AD
4 , wP : Wetted perimeter
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(2)
For circular pipe,
ihiwiC dD;dPP;dA 2
4
Onset of turbulence occurs at a critical Reynolds number of
2300cr,DRe
Fully turbulent conditions occurs when
00010,ReD
Fully developed flow
A) Hydrodynamically fully developed flow
Hydrodynamic Entry Length
Laminar: Dh,fd Re.Dx 050
Turbulent: 6010 Dx h,fd
Requirement for fully developed hydrodynamically flow condition:
0
h,fd
w
h,fd x
d
x
u
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(3)
B) Thermally fully developed flow
Thermal Entry Length
Laminar: PrRe.Dx Dt,fd 050
Turbulent: 6010 Dx t,fd
For laminar flow, how do hydrodynamic and thermal entry lengths compare for a gas?
And oil? A liquid metal?
Can a flow be developing hydrodynamically and be thermally fully-developed?
Requirement for thermally fully developed flow condition:
0
t,fdms
s
xTxT
x,rTxT
x
xfk
h
TT
kq
TT
rT
TT
TT
r ms
s
ms
rr
rrms
s i
i
xfh
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(4)
Calculation of mean bulk temperature
mpmmmpconv dTcmTdTTcmdq
Integrating from the tube inlet to outlet Lxx 0 : i,mo,mpconv TTcmq
Uniform Heat Flux ttanconsqs
PdxqdTcmdq smpconv
p
sm
cm
Pq
dx
dT
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(5)
Integrating from the tube inlet to outlet Lxx 0
mss
p
si,mo,m TThq;
cm
PLqTT
Uniform Surface Temperature ttanconsTs
dxTThPdTcmdq msmpconv
dxcm
hP
TT
dT
pms
m
Integrating from the tube inlet to outlet Lxx 0
L
pi,ms
o,ms hdxL
h;cm
PLhexp
TT
TT
0
1
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(6)
Uniform External Fluid Temperature ttanconsT
totpi,m
o,m
Rcmexp
TT
TT
1
oo
W
ii
totAh
RAh
R11
LdA ii ; LdA oo ;
Lk
ddlnR
tube
ioW
2
i,m
o,m
i,mo,m
tot
i,mo,mpconv
TT
TTln
TTTT
RTTcmq
1
Overall heat transfer coefficients U,U,U oi
ooii
totAUAUUA
R111
itube
ioi
oo
i
iii
o
tube
ioo
oo hk
ddlnd
hd
d
U;
hd
d
k
ddlnd
hU
1
2
111
2
11
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(7)
Problems
P1. Exhaust gases from a wire processing oven are discharged into a tall stack,
and the gas and stack surface temperatures at the outlet of the stack must be
estimated. Knowledge of the outlet gas temperature Tm,o is useful for
predicting the dispersion of effluents in the thermal plume, while knowledge
of the outlet stack surface temperature Ts,o indicates whether condensation
of the gas products will occur. The thin-walled, cylindrical stack is 0.5 m in
diameter and 6.0 m high. The exhaust gas flow rate is 0.5 kg/s, and the inlet
temperature is 600 C. Estimate the outlet gas and stack surface
temperatures if the convection heat transfer coefficients are
KmW.hi
2210 and KmW.ho
2913 . Take CT 4 and
kgKJc air,p 1104 .
P2: A hot fluid passes through a thin-walled tube of 10-mm diameter and 1-m
length, and a coolant at free stream temperature of 25 C is in cross flow
over the tube. When the flow rate is 18 kg/h and the inlet temperature is 85
C, the outlet temperature is 78 C. Assuming fully developed flow,
determine the outlet temperature if the flow rate is increased by a factor of
2. That is, the flow rate is 36 kg/h, with all other conditions the same.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(8)
General Correlations for Internal Flow
Friction factor for hydrodynamically fully developed flow
The pressure drop may be determined from knowledge of the friction
factor f, where,
22
mu
Ddxdpf
Fanning friction factor fa:
4ffa
Laminar flow in a circular tube:
D
a
D Ref;
Ref
1664
Turbulent flow in a smooth circular tube:
621053000641790
DD Re,.Reln.f
621053000283581
DDa Re,.Reln.f
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(9)
Turbulent flow in a roughened circular tube (e: surface roughness):
equationColebrook,
fRe
.
.
Delog.
f D
512
7302
110
aDa fRe
.
.
Delog.
f
2551
7304
110
equationHaaland,.
De
Re
.log.
f
.
D
111
1073
9681
1
111
1073
9663
1.
Da.
De
Re
.log.
f
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(10)
Pressure drop for fully developed flow from x=0 to x=L
210 ppLxpxpp
2
2
mu
D
Lfp
24
2
ma
u
D
Lfp
Pumping power requirement P
p
pmP
p : Pump total efficiency
Nusselt number for fully developed flow condition
Laminar flow in a circular tube
- Uniform surface heat flux sq : 364.k
hDNuD
- Uniform surface temperature sT : 663.k
hDNuD
Turbulent flow in a circular tube
200050105103
127121
10002
187121
10008
63
3221
3221
Pr.,Re
Prf.
PrRefNu
ncorrelatioGnielinski,Prf.
PrRefNu
D
a
DaD
DD
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(11)
Laminar flow in a noncircular tube
w
Ch P
AD
4
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(12)
Laminar flow in annulus region with insulated outer surface 0oq
ioo,h
o,ho
omi,soi DDD;k
DhNu;TThq
- Uniform surface heat flux iq
20893615237821
499382208172
oioi
oio
DD.DD.
DD..Nu
- Uniform surface temperature i,sT
2859854133811
517355590571
oioi
oio
DD.DD.
DD..Nu
Turbulent flow in a noncircular tube and in an annulus region
w
Ch
P
AD
4 ,
h
Ce
P
AD
4 ,
hmD
DuRe
h ,
k
hDNu e
De
wP : Wetted perimeter; hP : Heat transfer perimeter
200050105103
127121
10002
187121
10008
63
3221
3221
Pr.,Re
Prf.
PrRefNu
ncorrelatioGnielinski,Prf.
PrRefNu
h
h
h
D
a
Da
eD
D
eD
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(13)
Nusselt number for developing flows (Entry region effects)
Laminar flow in a circular tube
- Thermal Entry region
3204001
06680663
PrReLD..
PrReLD..Nu
D
DD
- Combined Entry region
14031
861
.
s
bDD
L
DPrRe.Nu
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(14)
Problems
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(15)
Classifications of Heat Exchangers
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(16)
Classifications according to transfer processes
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(17)
Classifications according to construction features
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(18)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(19)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(20)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(21)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(22)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(23)
Classifications according to surface compactness
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(24)
Classifications according to number of fluids
Heat exchangers with as many as 12 fluids streams have been used in
some chemical processes applications.
The design theory of three- and multi fluid heat exchangers is
algebraically very complex.
The present notes covers only design theory of two-fluid heat exchangers.
Classifications according to heat transfer mechanism
Classifications according to flow arrangements
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(25)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(26)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(27)
Basic Equations for Heat Exchangers
Heat Exchangers: Devices used to exchange thermal energy between at least two fluids.
They encompass a wide range of flow configurations.
Classifications of Heat exchangers based on flow arrangement
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(28)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(29)
The overall heat transfer coefficient
Bare circular clean tubes of Nt number of tubes
ii
W
ooiioo AhR
AhAUAUUA
11111
LNdA;LNdA tiitoo
LNk
ddlnR
ttube
ioW
2
ii
o
tube
ioo
oo hd
d
k
ddlnd
hU
1
2
11
itube
ioi
oo
i
i hk
ddlnd
hd
d
U
1
2
11
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(30)
Bare circular fouled tubes of Nt number of tubes
iii
fi
W
o
fo
ooiioo AhA
RR
A
R
AhAUAUUA
11111
cetanresisunitfoulingoutside:R fo
cetanresisunitfoulinginside:R fi
ii
ofi
i
o
tube
ioofo
oo hd
dR
d
d
k
ddlndR
hU
1
2
11
i
fi
tube
ioifo
o
i
oo
i
i hR
k
ddlndR
d
d
hd
d
U
1
2
11
Finned circular fouled tubes of Nt number of tubes (rectangular fins)
iiiii
fi
W
oo
fo
oooiioo AhA
RR
A
R
AhAUAUUA
11111
i
fi
fii
o
fo
fooA
A;
A
A 1111
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(31)
LNNHdA;LNNHdA tfifiiitfofooo 22
LNNHA;LNNHA tfiififitfoofofo 22
LNNdA;LNNdA tifiiuitofoouo
fiuiifouoo AAA;AAA
efficiencysurfaceinner,outer:, io
surfaceinner,outeronfinsof.no:N,N fifo
lengthfininner,outer:H,H fifo
thicknessfininner,outer:, fifo
tyconductivithermalfininner,outer:k,k i,fino,fin
efficiencythermalfininner,outer:, fifo
ii,fin
iifi
ii,fin
iifi
fi
oo,fin
oofo
oo,fin
oofo
fo
k
hH
k
hHtanh
;
k
hH
k
hHtanh
2
2
22
22
22
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(32)
iii
o
i
fi
i
o
ttube
ioo
o
fo
ooo hA
AR
A
A
LNk
ddlnAR
hU
1
2
11
iii
fi
ttube
ioi
o
fo
o
i
ooo
i
i h
R
LNk
ddlnAR
A
A
hA
A
U
1
2
11
Log Mean Temperature Difference (LMTD) method of analysis
Assumptions: a) Fully developed conditions, b) Constant cross-sectional areas, c) Constant
properties
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(33)
1) Counter Flow Heat Exchangers
21
12
21122112
ch
ch
chchoohhphhccpcc
TT
TTln
TTTTAUTTcmTTcmQ
phhpcc
oo
ch
ch
cmcmAUexp
TT
TT
11
21
12
2) Parallel Flow Heat Exchangers
11
22
11222112
ch
ch
chchoohhphhccpcc
TT
TTln
TTTTAUTTcmTTcmQ
phhpcc
oo
ch
ch
cmcmAUexp
TT
TT
11
11
22
3) Other Types Heat Exchangers
lmoohhphhccpcc TAUTTcmTTcmQ 2112
21
12
2112
ch
ch
chchcf,lmlm
TT
TTln
TTTTFTFT
1Ffactorcorrection:F
tarrangemenflow,
TT
TTP,
TT
TT
cm
cmRfF
ch
cc
cc
hh
h,ph
c,pc
11
12
12
21
efficiencyeTemperatur:P
ratiocapacityHeat:R
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(34)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(35)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(36)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(37)
The-NTU method of heat exchanger analysis
Assumptions: a) Fully developed conditions, b) Constant cross-sectional areas, c)
Constant properties
Definitions and relationships
maxmax
minr
min
oo
Q
Q;
C
CC;
C
AUNTU
UnitsTransferofNumber:NTU
hcmin C,CofMinimumC
hcmax C,CofMaximumC
phhhpccc cmC;cmC
flowfluidhot,coldofcapacitythermal:C,C hc
esseffectivenexchangerheat:
11 chminmax TTCQ
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(38)
2112 hhhccc TTCTTCQ
11
21
11
12
11 chmin
hhh
chmin
ccc
chmin TTC
TTC
TTC
TTC
TTC
Q
arragementflow,C,NTUf r
arragementflow,C,gNTU r
1
1
1
1
1
NTUnNTU
nNTUNTU
;n
Q
NTU
NTU
Cr
6
5
4
3
2
1
1
1
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(39)
Heat exchanger with condensing fluid
2
1
2112
ch
ch
chchoofghccpcc
TT
TTln
TTTTAUhmTTcmQ
001 rh C;C;.F
Heat exchanger with evaporating fluid
ch
ch
chchoohhphhfgc
TT
TTln
TTTTAUTTcmhmQ
1
2
1221
oo
r
AU
NTU
NTU
E
F
C
8
7
6
5
4
3
2
1
1
1
1
1
1
1
1
NTUnNTU
nNTUNTU
;n
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(40)
001 rc C;C;.F
Basic heat exchanger equation under variable Uo-coefficient
21
12
2112
ch
ch
chchom,o
TT
TTln
TTTTFAUQ
oA
o
o
m,o dAUA
U1
Linear variation of Uo-coefficient with A
2
21 ,o,o
m,o
UUU
Small variation of Uo-coefficient with A
2oom,o AAUU
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(41)
Heat exchanger rating calculations
Known quantities: Inlet temperatures, mass flow rates, outer surface area
1) Calculate the overall heat transfer coefficient Uo.
2) Calculate thermal capacities Cc and Ch.
3) Calculate Cmin, Cmax and Cr.
4) Calculate NTU.
5) Calculate the heat exchanger effectiveness using -NTU relationships.
6) Determine the heat transfer rate Q.
Heat exchanger design calculations using LMTD method
Known quantities: Inlet temperatures, mass flow rates, one outlet temperature
1) Calculate the heat transfer rate Q.
2) Calculate the unknown outlet temperature using the conservation of energy
principle.
3) Calculate cf,lmT .
4) Calculate the correction factor F.
5) Calculate the overall heat transfer coefficient Uo.
6) Determine Ao.
Heat exchanger design calculations using -NTU method
Known quantities: Inlet temperatures, mass flow rates, one outlet temperature
1) Calculate the heat transfer rate Q.
2) Calculate the unknown outlet temperature using the conservation of energy principle.
3) Calculate the overall heat transfer coefficient Uo.
4) Calculate thermal capacities Cc and Ch.
5) Calculate Cmin, Cmax and Cr.
6) Calculate the heat exchanger effectiveness .
7) Calculate the NTU using NTU- relationships.
8) Determine Ao.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(42)
Heat Exchanger Design Methodology
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(43)
Problems
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(44)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(45)
Fouling of Heat Exchangers
Fouling: It is accumulation of undesirable substances on a surface.
Examples on fouling
Deposit of cholesterol on the inner surface of the artery wall. This deposit results in
narrowing the blood flow cross-sectional area. Thus more pumping power is required
by the heart to circulate the blood.
Deposit of ashes on the tube surface which forms of a less thermally conducting layer
on the surface. Thus, heat transfer rate is reduced.
Disadvantages of fouling on heat exchanger operation
Reducing heat transfer rate due to the increased thermal resistance of the deposit
layer.
Increasing pumping power requirement due to narrowing of the flow passages.
Definitions
conditionfouledonbasedtcoefficientransferheatOverall:Uof
conditioncleanonbasedtcoefficientransferheatOverall:Uoc
ft
ocof
RUU
11
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(46)
factorfoulingTotal:R ft
tubecircularbare,d
dRRR
i
ofifoft
tubefinned,A
ARRR
i
o
i
fi
o
fo
ft
Design of heat exchangers based clean condition
lmococ TAUQ
Design of heat exchangers based fouled condition
lmofof TAUQ
Relationship between clean and fouled conditions based designs
lmococlmofof TAUTAU
ococofof AUAU
011 .RUU
U
A
Aftoc
of
oc
oc
of
Heat exchanger operation under fouled condition
A. Effect of fouling on pressure drop and pumping power
22
22f,m
if
ff
c,m
ic
cc
u
d
Lfp;
u
d
Lfp
fc ff
22
44iff,micc,mfc dudumm
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(47)
2
if
ic
c,m
f,m
d
d
u
u
01
5
.d
d
p
p
P
P
if
ic
c
f
c
f
B. Effect of fouling on flow rate
L
pdm;
L
pdm
f
iffc
icc
44
128128
fc pp
4
ic
if
c
f
d
d
m
m
C. Effect of fouling on heat transfer
f,lmooff TAUQ
c,lmoocc TAUQ
c,lm
f,lm
ftocc,lm
f,lm
oc
of
c
f
T
T
RUT
T
U
U
Q
Q
11
Cost of fouling on industrial sector
Increased capital cost (large pumps are required, large heat transfer area is required,
stand by heat exchangers are required).
Increased maintenance cost (to clean the deposits).
Loss of production cost (shutting down the plant for cleaning the heat exchangers).
Energy losses (Large electrical energy is required to operate the large pumps).
053251
251
5..
P
P
.d
d
c
f
if
ic
4096080
251
4..
m
m
.d
d
c
f
if
ic
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(48)
Categories of fouling
A. Particulate fouling: e.g. dust, ash.
B. Crystallization fouling: This arises due to presence of salts in the fluid.
C. Corrosion fouling: corrosive fluids may react with tube material producing corrosion
products.
D. Biofouling: e.g. bacteria, algae and molds.
E. Chemical reaction fouling: The tube surface can act as catalyst expediting
chemical reaction on the surface. e.g. polymerization.
Fundamental process of fouling
1. Initiation of the surface: e.g. removing of any protective layers.
2. Transport of undesirable substances: Mechanisms of this process are: a) mass
diffusion, b) Inertial impaction, c) Sedimentation, d) Thermophoresis (motion of
particles due to temperature gradients), d) Electrophoresis (motion of particles due to
electrical potential gradients).
3. Attachment: depends on adhering forces between the deposits and the surface.
4. Removal: removal mechanisms are: a) Dissolution (removal by ions), b) Erosion
(removal by small fouling masses), c) Spalling (removal by large fouling masses).
5. Aging: growing effect.
(Fouling is an extremely complex phenomenon)
Cleanliness Factor (CF) of the heat exchanger:
ftococ
of
RUU
UCF
1
1
designsTypical,.CF 850
Percent Over Surface (OS) of the heat exchanger:
%RU%A
AOS ftoc
oc
of1001100
designsTypical%,.OS 617
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(49)
TEMA values of fouling factors to be used in heat exchangers design
TEMA: Tubular Exchangers Manufacturers Association
Cleaning of heat exchanger can be started once the fouling factors reach TEMA
values shown in the next tables.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(50)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(51)
Prediction of fouling
Techniques to control fouling
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(52)
Problems
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(53)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(54)
Double Pipe Heat Exchangers (DPHXs)
DPHX consists of one set of pipes of smaller diameter (tubes) placed concentrically inside a
pipe of larger diameter (pipe or shell) with appropriate fittings to direct the flow
from one section to the next.
Annulus is the volume between the outer surface of the tubes and the inner surface of the
pipe.
DPHXs are used majorly for sensible cooling/heating processes.
DPHXs exist in industry in form of hairpin heat exchangers as shown in the figures below.
DPHXs can be arranged in series and parallel arrangements or combined arrangements.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(55)
Advantages of DPHXs: a) easy to be cleaned, b) easy to be maintained, c) fluids can be
gases or liquids, d) tubes may have fins on their inner surface,
outer surface or on both inner and outer surfaces (fins are
usually placed on the surface that has minimum convection heat
transfer coefficients).
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(56)
Disadvantages of DPHXs: a) bulky, b) have small heat transfer area per unit volume, c)
expensive per heat transfer area.
DPHX cross sections; See next figures for various cross-sections
Pressure drop in single hairpin heat exchanger
o,Co
oo,m
i,Ci
ii,m
A
mu;
A
mu
2
24
2
i,m
ioutletinletS,bend
i
i,ai
uKKK
d
Lfp
2
24
2
o,m
ooutletinletS,bend
o,h
o,ao
uKKK
D
Lfp
025001 .K;.K;.K S,bendoutletinlet
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(57)
Pressure drop in NHP hairpin heat exchangers arranged in series
o,Co
oo,m
i,Ci
ii,m
A
mu;
A
mu
22
24
2
i,m
iioutletiinletHP
L,ibend
S,ibend
i
i,ai
uKKN
KK
d
Lfp
22
24
2
o,m
oooutletoinletHP
L,obend
S,obend
o,h
o,ao
uKKN
KK
D
Lfp
51025001 .K;.K;.K;.K L,o,ibendS,o,ibendo,ioutleto,iinlet
Thermal/hydraulic analysis of tubes with NHP=1
i,h
i,C
i,e
i,w
i,C
i,hP
AD;
P
AD
44
i
i,ei
D
i
i,hi,mi
Dk
DhNu;
DuRe
i,ei,h
Bare circular tubes of number Nt
tii,C NdA 2
4
tii,hi,w NdPP
LNdA tii 2
Finned circular tubes of number Nt (rectangular fins)
ti,fii,ftii,C NNHNdA
2
4
ti,fi,ftii,hi,w NNHNdPP 2
11
HPii NAA
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(58)
ii,fi,fti,fii,fiti,u HLNNA;NdLNA 22211
i,fi,fiti HNdLNA 221
Convection heat transfer coefficient inside tubes (hi)
Developing Laminar flow in a circular tube
- Thermal Entry region
i
ii,mi
d
duRe
i
320401
06680663
idi
idi
i
iid
PrReLd.
PrReLd..
k
dhNu
i
i
i
- Combined Entry region
14031
861
.
i,s
i,biid
i
iid
L
dPrRe.
k
dhNu i
i
Turbulent fully developed flow
200050105103
127121
10002
63
3221
iD
ii,a
iDi,a
D
Pr.,Re
Prf.
PrRefNu
i,h
i,h
i,e
tubesmooth;Re,.Reln.fi,hi,h DDi,a
621053000283581
tuberoughened;.
De
Re.
log.f
.
Di,a i,h
111
10 7396
631
Thermal/hydraulic analysis of annulus with NHP=1
o,h
o,C
o,e
o,w
o,C
o,hP
AD;
P
AD
44
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(59)
o
o,eo
D
o
o,ho,mo
Dk
DhNu;
DuRe
o,eo,h
Bare circular tubes of number Nt
toio,C NdDA 22
4
too,htoio,w NdP;NdDP
LNdA too 21
Finned circular tubes of number Nt (rectangular fins)
to,foo,ftoio,C NNHNdDA
22
4
to,fo,ftoo,hto,fo,ftoio,w NNHNdP;NNHNdDP 22
oo,fo,fto,foo,foto,u HLNNA;NdLNA 22211
o,fo,foto HNdLNA 221
Convection heat transfer coefficient outside tubes (ho)
Developing Laminar flow
- Thermal Entry region
32
0401
06680663
oDo,h
oDo,h
o
o,eoD
PrReLD.
PrReLD..
k
DhNu
o,h
o,h
o,e
- Combined Entry region
14031
861
.
o,s
o,bo,hoD
o
o,eoD
L
DPrRe.
k
DhNu o,h
o,e
11
HPoo NAA
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(60)
Turbulent fully developed flow
200050105103
127121
10002
63
3221
oD
oo,a
oDo,a
D
Pr.,Re
Prf.
PrRefNu
o,h
o,h
o,e
tubesmooth;Re,.Reln.fo,ho,h DDo,a
621053000283581
111
1073
9663
1.
Do,a.
De
Re
.log.
fo,h
Thermal analysis of NHP hairpin series heat exchangers
21
12
21122112
ch
ch
chchoohhphhccpcc
TT
TTln
TTTTAUTTcmTTcmQ
111
HPooHPoo NAA;NAA
Bare circular tubes
ii
ofi
i
o
tube
ioofo
oof hd
dR
d
d
k
ddlndR
hU
1
2
11
Circular tubes with fins on their outer surfaces
ii
o
fi
i
o
ttube
ioo
o
fo
ooof hA
AR
A
A
LNk
ddlnAR
hU
1
22
11
1
1
1
11
Circular tubes with fins on their inner surfaces
iii
o
i
fi
i
o
ttube
ioo
fo
oof hA
AR
A
A
LNk
ddlnAR
hU
1
22
11
1
1
1
11
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(61)
Finned circular tubes with fins on inner and outer surfaces
iii
o
i
fi
i
o
ttube
ioo
o
fo
ooof hA
AR
A
A
LNk
ddlnAR
hU
1
22
11
1
1
1
11
1
1
1
1 1111i
fi
fii
o
fo
fooA
A;
A
A
ii,fin
iifi
ii,fin
iifi
fi
oo,fin
oofo
oo,fin
oofo
fo
k
hH
k
hHtanh
;
k
hH
k
hHtanh
2
2
22
22
22
Design and operational features
DPHXs have four key design components:
1. Shell nozzles
2. Tube nozzles
3. Shell-to-tube closure
4. Return-bend housing
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(62)
Problems
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(63)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(64)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(65)
Shell-and-Tube Heat Exchangers (STHEs)
STHE basic components:
Tube bundle Shell Front end head Rear end head Baffles Tube sheets
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(66)
STHEs have larger heat transfer area per unit volume than double pipe heat exchangers.
STHEs can be used for large pressure applications.
STHEs are easier to be cleaned than many types of heat exchangers such as compact heat
exchangers.
TEMA Shell and end heads types
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(67)
ShellEShellF pp 8
ShellEShellG pp
ShellEShellJ pp 8
1
E-Shell: least expensive shell
E-Shell and 1P tubes: counter flow heat exchanger
F-Shell and 2P tubes: counter flow heat exchanger
J-Shell: can be used as shell side horizontal condenser
G-Shell, J-Shell and X-Shell: cross flow heat exchanger
Tubes covers 60% of the shell diameter of K-Shell
Tube bundle
They should accommodate thermal expansion.
They should furnish ease of cleaning.
They should provide least expensive construction.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(68)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(69)
Tubes and tube passes
Tube material: low carbon steel, low alloy steel, stainless steel, copper, admiralty,
cupronickel, inconel, alumnium (in form of alloys) or titanum.
Tube standards
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(70)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(71)
Tube layouts
PT: tube pitch; C: clearence; oT dPC
mmC 7 : cleaning requirment for square pitch
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(72)
Traingular pitch results in largest tube density inside the shell
51251 .d
P.
o
T : to avoid weak structurally tube sheets while enhancing heat
transfer
layouttube,P,N,d,DfN TPoimaxt
maxtN : Maximum tubes to be fit inside the shell – (Tube count)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(73)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(74)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(75)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(76)
Allocations of streams
The more seriously fouling fluid flows through the tubes.
The high pressure fluid flows through the tubes.
The corrosive fluid must flow through the tubes.
Fluids producing lower heat transfer coefficients flows on the shell side.
Baffle types and geometry
Baffles function
Supporting the tubes to prevent vibrations.
Diverting shell side fluid flow across the bundle to obtain higher convection heat
transfer coefficients.
Baffle types
Transverse baffles (Plate baffles, Rod baffles)
Longitudinal baffles.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(77)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(78)
Baffle window (single/others segmental):
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(79)
B : Baffle spacing WA : area of baffle window
Single segmental baffle %%D
HcutBaffle%
b
W 3010025
Other segmental baffle %D
AAcutBaffle
b
WW 10042
21
For strong structurally tube
sheets, less vibration, and
augmented heat transfer
6040 .D
B.
i
Basic design procedure of a heat exchanger
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(80)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(81)
Shell side pressure drop
140
2
2
1.
w,ooo,eo
ibooo
D
DNGfp
Square pitch:
o
oTo,e
d
dPD
44 22
Triangular pitch:
2
8434 22
o
oTo,e
d
dPD
T
oio,C
P
dBDA 1
o,C
oo
A
mG
1B
LNb ; bN : no. of baffles
oo Reln..expf 1905760
o
oo,e
o
GDRe
6101400 oRe
Tube side pressure drop (bare circular tubes)
P
tii,C
i,Ci
ii,m
N
NdA;
A
mu 2
4
; PN : no. of tube passes
P
i,m
i
i
i,ai Nu
d
Lfp
244
2
Convection heat transfer coefficient inside tubes (hi)
Developing Laminar flow in a circular tube
- Thermal Entry region
i
ii,mi
d
duRe
i
320401
06680663
idi
idi
i
iid
PrReLd.
PrReLd..
k
dhNu
i
i
i
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(82)
- Combined Entry region
14031
861
.
w,i
b,iiiid
i
ii
idL
dPrRe.
k
dhNu
Turbulent fully developed flow
200050105103
127121
10002
63
3221
iD
ii,a
iDi,a
D
Pr.,Re
Prf.
PrRefNu
i,h
i,h
i,e
tubesmooth;Re,.Reln.fi,hDi,hDi,a
621053000283581
tuberoughened,.
De
Re.
log.f
.
Di,a i,h
111
10 7396
631
Shell side heat transfer coefficient using Kern method
63
140
31
550
101102
360
o
oo,e
o
.
w,o
oo
.
o
oo,e
o
o,eo
GDRe
PrGD
.k
Dh
Square pitch:
o
oTo,e
d
dPD
44 22
Triangular pitch:
2
8434 22
o
oTo,e
d
dPD
T
oio,C
P
dBDA 1
o,C
oo
A
mG
%cutBaffle 25
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(83)
Thermal analysis of shell-and-tube heat exchangers
21
12
21122112
ch
ch
chchoohhphhccpcc
TT
TTln
TTTTFAUTTcmTTcmQ
Bare circular tubes
ii
ofi
i
o
tube
ioofo
oo hd
dR
d
d
k
ddlndR
hU
1
2
11
LNdA too
Finned circular tubes with fins on inner and outer surfaces
(rectangular fins)
iimLi
mLo
i
fi
mLi
mLo
ttube
iomLo
o
fo
ooo hA
AR
A
A
Nk
ddlnAR
hU
1
2
11
1
1
1
11
mLi
mLfi
fii
mLo
mLfo
fooA
A;
A
A
1
1
1
11111
ii,fin
iifi
ii,fin
iifi
fi
oo,fin
oofo
oo,fin
oofo
fo
k
hH
k
hHtanh
;
k
hH
k
hHtanh
2
2
22
22
22
ii,fi,fti,fii,fiti,u HLNNA;NdLNA 2
i,fi,fiti HNdLNA 2
oo,fo,fto,foo,foto,u HLNNA;NdLNA 2
o,fo,foto HNdLNA 2
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(84)
Problems
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(85)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(86)
Compact Heat Exchangers (Compact HXs)
Compact HXs is used for gas flow applications.
Compact HX types are: a) Plate-fin type, and b) Tube-fin type.
Compact HX has heat transfer surface area per unit volume larger than 700 m2/m
3.
32700 mmVAt
Microheat exchanger has heat transfer surface area per unit volume larger than
10000 m2/m
3.
3200010 mm,VAt
Compact HXs are used for gas to gas or liquid to gas heat exchangers.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(87)
Compact HXs applications: a) air conditioning condensers and evaporators, b)
automotive radiators, c) intercoolers of compressors.
Heat transfer enhancement techniques
Active techniques (requiring external power to enhance heat transfer), e.g. surface
vibration, acoustic techniques, using electrohydrodynamic or hydromagetic effects.
Passive techniques (do not require external power to enhance heat transfer), e.g.
using fins, twist tapes to gererate turbulence, surface roughness.
Heat transfer in compact heat exchangers
o,po
oo
cG
hSt:StnumbertontanS
o
o,ho
o
o
o,po
o
DGRe;
k
cPr
omin,
oomax,oo
A
mUG
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(88)
areaflowexternalimummin:A omin,
areatransferheatexternal:AA ot
areafrontalflowexternal:A o,fr
HWA o,fr
t
minho
A
ALD 4
3232
o
o,po
oooo,H Pr
cG
hPrStj
Important relationships
HWLV;A
A;
V
A
o,fr
omin,t
4 o,h
omin,
t D;LA
A
o,,o
o,fr
o
omin,
oo
U
A
m
A
mG 1
o
o,,o
o,fro
o
o
o,ho
o,h
U
A
mDGRe 144
Overall heat transfer coefficient
cmthicknessfin:o
1cmpitchfin:bo
t
o,f
oA
A
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(89)
ofoo 11
thicknesstube:tube
perimeterinnertube:Pi
perimeteroutertube:Po
Circular tube with fins on outer surface and no-fins on inner surface
ootube
io
o
ooo
io
oo
i
o
o hk
ddlnbd
h
b
d
d
U
1
21
11
1
11
Rectangular tube with fins only on outer surface
ootube
tube
o
oo
i
o
io
oo
i
o
o hk
b
P
P
h
b
P
P
U
1
1
11
1
11
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(90)
Thermal analysis of compact heat exchangers
21
12
21122112
ch
ch
chchtohhphhccpcc
TT
TTln
TTTTFAUTTcmTTcmQ
Gas-side pressure drop for compact heat exchangers
21
11
2
11
,o,oo
Tube-fin compact heat exchangers
11
2 2
121
1
2
,o
,o
o
,o
omin,
to
,o
oo
A
Af
Gp
Plate-fin compact heat exchangers
2
121
2
12
1
2
11212 ,o
,o
e
o
,o
omin,
to
o
oc
,o
oo k
A
Afk
Gp
tcoefficienlossncontractioinlet:kc
tcoefficienlossansionexpoulet:ke
Gas-side convection coefficient, ho, using different charts
The h-coefficient shown in the subsequent figures is the ho-coefficient.
The f-factor shown in the subsequent figures is the fo-factor.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(91)
rowsof.no:NL
rowpertubesof.noimummax:NT
inch.PL 8660
inch.PT 001
LLL PPNL 1
TTT PPNH 1
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(92)
rowsof.no:NL
rowpertubesof.noimummax:NT
inch.Df 8610
inch.PL 9000
inch.PT 9750
fLL DPNL 1
fTT DPNH 1
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(93)
rowsof.no:NL
rowpertubesof.noimummax:NT
inch.D f 1211
inch.PL 351
inch.P;inch.P B,TA,T 84812321
fLL DPNL 1
fTT DPNH 1
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(94)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(95)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(96)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(97)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(98)
Problems
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(99)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(100)
Boiling
Boiling is associated with transformation of liquid to vapor at a
solid/liquid interface due to convection heat transfer from the solid.
Agitation of the liquid by vapor bubbles is one mechanism that provides
for large convection coefficients and hence large heat fluxes at low-to-
moderate surface-to-fluid temperature differences.
Special form of Newton’s law of cooling:
esatss ThTThq
liquidofetemperatursaturation:Tsat
etemperaturexcess:TTT satse
Special cases
Pool boiling
Liquid motion is due to natural convection and bubble-induced mixing.
Forced convection boiling
Fluid motion is induced by external means, as well as by bubble-induced
mixing.
Saturated boiling
Liquid temperature is slightly higher than saturation temperature.
Subcooled boiling
Liquid temperature is less than saturation temperature.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(101)
The boiling curve
Reveals range of conditions associated with saturated pool boiling on es Tq
plot.
Free convection boiling atm@water,CTe 15
- Little vapor formation
- Liquid motion is due principally to single-phase natural convection.
Onset of Nucleate Boiling - ONB atm@water,CTe 15
Nucleate boiling atm@water,CTC e 1305
Isolated vapor bubbles atm@water,CTC e 1105
- Liquid motion is strongly influenced by nucleation of bubbles at the surface.
- h and sq increase sharply with increasing eT .
- Heat transfer is principally due to contact of liquid with the surface (single-phase
convection) and not to vaporization.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(102)
Jets and columns atm@water,CTC e 13010
- Increasing number of nucleation sites causes bubble interactions and coalescence
into jets and slugs.
- Liquid/surface contact is impaired.
- sq continues to increase with eT but h begins to decrease.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(103)
Critical Heat Flux - CHF, atm@water,CTq emax 130
- Maximum attainable heat flux in nucleate boiling.
- 21 mMWqmax for water at atmospheric pressure.
Potential burnout for power - Controlled heating - An increase in beyond maxq causes the surface to be blanketed by vapor, and the
surface temperature can spontaneously achieve a value that potentially exceeds its
melting point for water at atmospheric pressure CTe
1000 .
- If the surface survives the temperature shock, conditions are characterized by film
boiling.
Film boiling atm@water,CTe 1120
- Heat transfer is by conduction and radiation across the vapor blanket.
- A reduction in sq follows the cooling curve continuously to the Leidenfrost point
corresponding to the minimum heat flux minq for film boiling.
- A reduction in sq below minq causes an abrupt reduction in surface temperature
to the nucleate boiling regime.
Transition boiling for temperature - Controlled heating - Characterized by a continuous decay of sq (from maxq to minq ) with increasing
eT .
- Surface conditions oscillate between nucleate and film boiling, but portion of
surface experiencing film boiling increases with eT .
- Also termed unstable or partial film boiling.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(104)
Pool boiling correlations
Nucleate boiling
- Rohsenow Correlation
fgsvn
lfgf,s
eL,p
f
vLfgLs hAm
PrhC
Tcghq
321
L Dynamic visocity of liquid phase
fgh Enyhalpy of vaporization
g Gravitional acceleration
L Density of liquid phase
v Density of vapor phase
f Surface tension
L,pc Specific heat of liquid phase
LPr Prandtl number of liquid phase
n,C f,s Surface/fluid combination
- Critical heat flux of Zuber
fgsmaxv
v
vLf
vfgmaxs hAmg
Chq
41
2
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(105)
1310.C Horizontal cylinder or sphere
1490.C Large horizontal plate
Film boiling
fgvsatsss hmTTAhq
313434 hhhh radconv
radconvradconv hhifhhh 4
3
413
satsvv
fgvL
v
conv
TTk
DhgC
k
DhNu
620.C Horizontal cylinder DLAs
670.C Sphere 2DAs
satsv,pfgfg TTc.hh 80
sats
satsrad
TT
TTh
44
ttanconsBoltzmannStefan:KmW. 42810675
Correlation for boiling inside tubes
fg
sAC
hm
Dxq
m
uXdAX C
X : Mean vapor mass fraction at a given section
f,s
.
.
fgC
s..
.
v
l
sp
GXhAm
qFrfXX.
h
h 80
70
640160
10
1 11058166830
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(106)
f,s
.
.
fgC
s..
.
v
l
sp
GXhAm
q.FrfXX.
h
h 80
70
080720
450
2 1266711361
gDAmFr lC
2
01.Frf Vertical tubes
01.Frf Horizontal tubes with 040.Fr
30632 .Fr.Frf Horizontal tubes with 040.Fr
40
80
0230 .
i
.
l
l,ml
i
spPr
Du.
k
Dh
21 h,hMAXh
800 .X
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(107)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(108)
Problems
P1 A long, 1-mm-diameter wire passes an electrical current dissipating 3150
W/m and reaches a surface temperature of 126 C when submerged in water
at 1 atm. What is the boiling heat transfer coefficient? Estimate the value of
the correlation coefficient Cs,f.
P2 A nickel-coated heater element with a thickness of 15 mm and a thermal
conductivity of 50 W/mK is exposed to saturated water at atmospheric
pressure. A thermocouple is attached to the back surface, which is well
insulated. Measurements at a particular operating condition yield an
electrical power dissipation in the heater element of 6.950x107 W/m
3 and a
temperature of To= 266.4 C.
(a) From the foregoing data, calculate the surface temperature, Ts, and the
heat flux at the exposed surface.
(b) Using the surface heat flux determined in part (a), estimate the surface
temperature by applying an appropriate boiling correlation.
P3 A 1-mm-diameter horizontal platinum wire of emissivity 0.25 is operated in
saturated water at 1-atm pressure. What is the surface heat flux if the surface
temperature is 800 K?
P4 Copper tubes 25 mm in diameter and 0.75 m long are used to boil saturated
water at 1 atm. (a) If the tubes are operated at 75% of the critical heat flux,
how many tubes are needed to provide a vapor production rate of 750 kg/h?
What is the corresponding tube surface temperature?
P5 A vertical steel tube carries water at a pressure of 10 bars. Saturated liquid
water is pumped into the =0.1-m diameter tube at its bottom end (x =0) with
a mean velocity of um=0.05 m/s. The tube is exposed to combusting
pulverized coal, providing a uniform heat flux of qs=100,000 W/m2.
(a) Determine the tube wall temperature and the quality of the flowing water
at x =15 m. Assume Gs, f=1.
(b) Determine the tube wall temperature at a location beyond x=15 m where
single-phase flow of the vapor exists at a mean temperature of Tsat.
Assume the vapor at this location is also at a pressure of 10 bars.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(109)
Condensation
Heat transfer to a surface occurs by condensation when the surface temperature
is less than the saturation temperature of an adjoining vapor.
Film condensation
Entire surface is covered by the condensate, which flows continuously
from the surface and provides a resistance to heat transfer between the
vapor and the surface.
Thermal resistance is reduced through use of short vertical surfaces and
horizontal cylinders.
Characteristic of clean, uncontaminated surfaces.
Dropwise condensation
Surface is covered by drops ranging from a few micrometers to
agglomerations visible to the ordinary eyes.
Thermal resistance is greatly reduced due to absence of a continuous film.
Surface coatings may be applied to inhibit wetting and stimulate dropwise
condensation.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(110)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(111)
General correlations for film condensation on vertical surface
fgLssatsL hmTTAhq
ssatl,pfgfg TTc.hh 680
312 gh
TTLkP
lfgl
ssatl
Wavy free laminar region 815.P
41
312
9430 P.k
ghNu
l
lLL
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(112)
Wavy laminar region 2530815 P.
820
312
8906801 .
l
lLL .P.
Pk
ghNu
Turbulent region 012530 .Pr;P l
3421
312
895302401
l
l
lLL PrP.
Pk
ghNu
l Dynamic visocity of liquid phase
l kinematic visocity of liquid phase
fgh Enyhalpy of vaporization
l,pc Specific heat of liquid phase
g Gravitional acceleration
L Surface length along g-direction
lk Thermal conductivity of liquid phase
Lm Condensate mass flow rate at bottom section
A Surface area
Lh Average convection heat transfer coefficent
Correlations for film condensation on radial systems
fglssatsN,D hmTTAhq
ssatl,pfgfg TTc.hh 680
Single smooth sphere and single horizontal tube (N=1)
413
ssatll
fgvll
l
DD
TTk
DhgC
k
DhNu
7290.C Horizontal tube DLAs
8260.C sphere 2DAs
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(113)
Vertical tier of N horizontal tubes
n
DN,D Nhh
41n Analytical value, assuming continuous film between smooth tubes
61n Experimental value, due to dripping between smooth tubes
061 n Experimental value, finned or ribbed tubes
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(114)
Correlation for film condensation in horizontal tube
(a) Small vapor mass flow rate
00035,Du
Rev
v,mv
i,v
ssatl,pfgfg TTc.hh 3750
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(115)
413
550
ssatll
fgvll
l
DD
TTk
Dhg.
k
DhNu
(b) Large vapor mass flow rate
890
4080 22210230
.
tt
.
i
.
l,D
l
DD
X
.PrRe.
k
DhNu
m
mX;
D
XmRe v
l
l,D
14
1050901
.
v
l
.
l
v
.
ttX
XX:parameterMartinelli
Correlation for dropwise steam condensation on copper surfaces
ssatsdc TTAhq
CTC,T,h satsatdc
10022204410451
CT,KmW,h satdc
100510255 2
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(116)
Problems
P1 Saturated steam at 1 atm condenses on the outer surface of a vertical, 100-
mm-diameter pipe 1 m long, having a uniform surface temperature of 94 C.
Estimate the total condensation rate and the heat transfer rate to the pipe.
P2 The condenser of a steam power plant consists of a square (in-line) array of
625 tubes, each of 25-mm diameter. Consider conditions for which saturated
steam at 0.105 bars condenses on the outer surface of each tube, while a
tube wall temperature of 17 C is maintained by the flow of cooling water
through the tubes. What is the rate of heat transfer to the water per unit
length of the tube array? What is the corresponding condensation rate?
P3 The condenser of a steam power plant consists of AISI 302 stainless steel
tubes (ks=15 W/m.K), each of outer and inner diameters do=30 mm and
di=26 mm, respectively. Saturated steam at 0.135 bar condenses on the
outer surface of a tube, while water at a mean temperature of Tm=290 K is in
fully developed flow through the tube. For a water flow rate iside the tube of
0.25 kg/s, what is the outer surface temperature Ts,o of the tube and the rates
of heat transfer and steam condensation per unit tube length? As a first
estimate, you may evaluate the properties of the liquid film at the saturation
temperature. If one wishes to increase the transfer rates, what is the limiting
factor that should be addressed?
P4 Refrigerant R-22 with a mass flow rate of 8.75x10-3
kg/s is condensed inside
a 7-mm-diameter tube. Annular flow is observed. The saturation
temperature of the pressurized refrigerant is Tsat=45 C, and the wall
temperature is Ts=40 C. Vapor properties are v=77 kg/m3 and v=15x10
-6
N.s/m2. Determine the heat transfer coefficient and the heat transfer and
condensation rates per unit length at a quality of X=0.5.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(117)
The Gasketed-Plate Heat Exchangers
Gasketed Plate Heat Exchangers (G-P HXs) were introduced mainly for the
food industry because of their ease of cleaning.
G-P HXs design becomes well identified in 1960s with the development of
more effective plate geometries, assemblies, and improved gasket materials.
G-P HXs can be used as an alternative to tube-and-shell type heat
exchangers for low-and medium-pressure liquid-to-liquid heat trasfer
applications.
Unlike to common design of heat exchangers, manufactrures of G-P HXs
have developed their own computerized design procedures applicable to the
exchangers they market.
Main Components
G-P HX components are the plate (the heat transfer solid surface) and the
frame.
Elements of the frame: fixed plate, compression plate, pressing equipment,
and connecting ports.
Elements of the heat transfer soild surface: series of plates, parts for fluid
entry and exit in the four corners.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(118)
The Plate Pack
Packing the plates make the holes at the corners to form continuous tunnels
or mainfolds.
The plate pack is tightnend by means of either a mechanical or hydraulic
tightening device.
The passages formed between the plates and corner ports are arranged so
that the two heat transfer media can flow through alternate channels, always
in counter-current flow.
The warmer medium will give some of its thermal energy through the thin
plate wall to the colder medium on the other side.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(119)
The medium are led into similar hole-tunels as in the inlets at the other end
of the plate package and are then discharged from the heat exchanger.
Several hundereds of plates can be stacked in a single frame which are held
together by the bolts that hold the stack in compression.
The two sides of the plate heat exchanger are normaly of identical
hydrodynamic characteristics.
The plate is a sheet of metal precison-pressed into a corrugated pattern.
The largest single plate is the order of 4.3 m heigh x 1.1 m wide.
The heat transfer area for a single plate lies in the range 0.01-3.6 m2.
The plate thickness ranges between 0.5 and 1.2 mm.
The plates are spaced with nominal gaps of 2.5-5.0 mm.
The hydraulic diameters for the flow channels ranges between 4-10 mm.
The fluid should be equally distributed over the full width of the plate. This
requires the minmum length/width ratio of the order of 1.8.
Leakage from the channels between the plates to the surrounding
atmosphere is prevented by the gasketing around the exterior of the plate.
The number and size of the plates are determined by the flow rate, physical
properties of the fluids, pressure drop, and the temperature requirements.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(120)
The Plate Types
Wide types of corrugated plates are available including chevron and
washboard types.
The most used type is the chevron type.
In washboard type, turbulence is promoted by continuously altering flow
direction and fluid's velocity.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(121)
In chevron type, adjacent plates are assembled such that the flow in the
channels provides swirling motion to the fluids.
The Chevron angle () varies between the extremes of about 65 and 25.
The Chevron angle () determines the pressure drop and heat transfer
characteristics of the plate.
The chevron angle () is reversed on adjacent plates so that when plates are
clamped together, the corrugations provide numerous contact points.
Because of the many supporting contact points, the plates can be made from
very thin material, usually 0.6 mm.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(122)
Main Advantages
Flexibility of design through a variety of plate sizes and passes
arrangements.
Easily accessible heat transfer area, allowing changes in configuration to
suit changes in processes requirements through changes in the number of
plates.
Efficient heat transfer; high heat transfer coefficients for both fluids because
of turbulence and a small hydraulic diameter.
Very compact (large heat transfer area/volume ratio yet 2500 m2 of surface
area is available in a single unit), and low in weight.
Only the plate edges are exposed to the atmosphere, no insulation is
required as heat losses are negligible.
Inter-mixing of the two fluids cannot occur under gasket failure.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(123)
Plate units exhibit low fouling characteristics due to high turbulence and
low residence time. The transition to turbulence occurs at low Reynolds
number of 10 to 400.
More than two fluids may be processed in a single unit.
Less expensive than tubular heat exchangers if the tubes are made from
stainless steel.
Performance limits
The gaskets impose restriction on operating temperatures (160C-250C).
The gaskets impose restriction on operating pressures (25-30 bar).
The gaskets impose restriction on nature of fluids that can be handled.
The upper size of the G-P HX is limited by the presses available to stamp
out the plates from the sheet metal.
G-P HXs with sizes larger than 1500 m2 are not normally available.
It is possible to have a maximum design pressure of up to 2.5 MPa;
normally, the design pressure is around 1.0 MPa.
Operating temperatures are limited by the availability of suitable gasket
materials.
G-P HXs are not suitable for air coolers or gas-to-gas applications.
Velocities lower than 0.1 m/s are not used in plate heat exchangers.
High viscous fluids are not preferred to be used in G-P HXs.
Specially designed G-P HXs are now available for duties involving
evaporation and condensation systems.
Passes and Flow Arrangements
The term "pass" refers to a group of channels in which the flow is in the
same direction.
Single pass arrangement can be of U- and Z-arrangement types.
The U-arrangement: all four ports in this arrangement will be on the fixed-
head plate. This permits disassembly of the heat exchanger for cleaning or
repair without disturbing any external piping. The flow distribution for this
arrangement is less uniform than the Z-arrangement.
The Multipass arrangement: consists of passes connected in series.
Arrangements abbreviation is written as:
pN of 1st fluid no. of channels for 1st fluid/ pN of 2nd fluid no. of channels for 2nd fluid
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(124)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(125)
Applications
G-P HXs are used in chemical, pharmaceutical, hygiene products,
biochemical processing, food, and dairy industries as they can meet health
and sanitation requirements.
G-P HXs are mainly used as liquid-to-liquid turbulent flow HXs.
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(126)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(127)
Fouling of G-P HXs
G-P HXs have less fouling than tubular heat exchangers because of the
following reasons:
High turbulence maintains solids in suspension.
Velocity profiles across a plate are uniform with almost absent zones of
low velocities.
The plate surfaces are generally smooth and can be further electro-
polished.
Deposit of corrosion products are absent because of low corrosion rates.
The high film coefficients maintain a moderately low metal wall
temperature. This helps preventing crystallization growth.
The plates can be easily cleaned.
Heat Transfer and Pressure Drop Calculations
Surface enlargement factor ,
lengthojectedPr
lengthDeveloped , 251151 .. .
pA
A
1
1 ;
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(128)
1A : Actual effective area provided by manufacturer;
pA1 : The projected plate area;
wpp LLA 1 ; pvp DLL ; phw DLL ;
vL : The vertical ports distance;
wL : The horizontal ports distance.
The mean channel spacing b :
tpb ;
p : The plate pitch; t : the plate thickness
The compressed plate pact length cL , t
c
N
Lp , tN : total number of
plates.
The hydraulic diameter of the channel hD :
b
Lb
bLD
w
wh
2
2
4
;
hcDG
Re ;
wcp
cbLN
mG
;
cpN : Number of channels per pass;
p
tcp
N
NN
2
1 , pN : number of passes
Convection HT Coefficients Correlation:
170
31
.
w
bnh
h PrReCk
hD
The frictional pressure drop cp :
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(129)
1702
24
.
w
bc
h
pv
c
G
D
NLfp
,
m
p
Re
Kf
The port pressure drop pp :
241
2p
pp
GN.p ,
42p
pD
mG
.
The total pressure drop tp :
pct ppp .
The overall heat transfer coefficient:
whcc k
t
hhU
111;
fcfh
whcf
RRk
t
hhU
111
Required Heat Duty, eA is the total developed area for all thermally
effective plates 2tN :
2112 hhhpcccpr TTcmTTcmQ ;
cf,lmeff TFAUQ ;
2
1
21
T
Tln
TTT cf,lm
;
121 ch TTT ; 212 ch TTT
The safety factor of the design sC ,
r
f
sQ
QC
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(130)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(131)
Problems
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(132)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(133)
Condensers and Evaporators
Horizontal shell side condensers
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(134)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(135)
Horizontal tube side condensers
Vertical shell side condensers
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(136)
Vertical tube side condensers
1. Vertical in-tube down flow condenser
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(137)
2. Reflux condenser
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(138)
Air cooled condensers
Direct contact condensers
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(139)
Failure of condenser operation
1. The tubes may be more fouled than expected – a problem not unique
to condensers.
2. The condensate may not be drained properly, causing tubes to be
flooded. This could mean that the condensate outlet is too small or too
high.
3. Venting of non-condensable gases may be inadequate.
4. The condenser was designed on the basis of end temperatures without
noticing that design duty would involve a temperature cross in the
middle of the range.
5. Flooding limits have been exceeded for condensers with backflow of
liquid against upward vapor flow.
6. Excessive fogging may be occurring. This can be problem when
condensing high molecular weight vapors in the presence of non-
condensable gases.
7. Severe maldistribution in parallel condensing paths is possible,
particularly with vacuum operation. This occurs because there can be
two flow rates which satisfy the imposed pressure drop.
Condensers for refrigeration and air conditioning
1. Water-cooled condensers
Horizontal shell-and-tube
Vertical shell-and-tube
Shell-and-coil
Double pipe
2. Air-cooled condensers
3. Evaporative condensers
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(140)
Evaporative condensers
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(141)
Evaporators for refrigeration and air conditioning
Water cooling evaporators (Chillers)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(142)
Air cooling evaporators (Air coolers)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(143)
Standards for evaporators and condensers
Air-conditioning and Refrigerating Institute (ARI) Standards
American Society for Heating, Refrigerating and Air-Conditioning
Engineers (ASHRAE) Standards
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(144)
Problems
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(145)
Basics of Rating and Thermal Design of HXs. Prof. A.-R.A. Khaled
(146)
References
[1] F. P. Incorpera, D. P. DeWitt, T. L. Bergman, A. S. Lavine, “Fundamentals
of Heat and Mass Transfer-6th
Edition”, John Wiley, 2006, New York.
[2] F. P. Incorpera, D. P. DeWitt, T. L. Bergman, A. S. Lavine, “Fundamentals
of Heat and Mass Transfer-7th
Edition”, John Wiley, New, 2011, New York.
[3] R. K. Shah, D. P. Sekulic, Fundamental of Heat Exchanger Design, John
Wiley, 2003, New York.
[4] S. Kaka, H. Liu, Heat Exchangers: Selection, Rating, and Thermal Design,
CRC Press, 2002, Florida.