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Heat Exchangers
A heat exchanger is used to exchange heat between twofluids of different temperatures, which are separated by a
solid wall.
Applications in heating and air conditioning, powerproduction, waste heat recovery, chemical processing,
food processing, sterilization in bio-processes.
Heat exchangers are classified according to flowarrangement and type of construction.
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HEX Classification According to Flow Arrangement
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double pipe heat exchanger
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Configuration of an induced-draft air-cooled
heat exchanger
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Task
Heat Exchanger Sizing
Given: inlet and outlet temperatures and flow rates of
the two fluids.
Find: Surface area of heat exchanger
Heat Exchanger Rating
Given: flow rates, inlet temperatures and surface area of
heat exchanger.Find: heat transfer rate, fluid outlet temperatures.
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Heat Exchanger Analysis
In a two-fluid heat exchanger, consider the hot and cold fluids separately:
)(
)(
,,,
,,,
icoccpcc
ohihhphh
TTcmq
TTcmq
lmTUAq and
The usual design goal is to determine the required area A for a heating
duty q
Need to determine U and Tlm
(1&2) (3)
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Tubular geometry
For the unfinned and clean tubular HEX, the
overall heat transfer coefficient is given by
1 1ln( / )1 1
2
o o i i
t o i
i i o o
U A U AR r r
h A kL h A
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Fouling
For the HEX whose walls are fouled by deposit
formation on both the inside and outside surfaces,
the total thermal resistance can be expressed as
Rw : wall resistance
Rf : fouling factor / unit fouling resistance
1 1 1 1 1fi fot w
o o i i i i i o o o
R RR R
UA U A U A h A A A h A
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U based on outside surface rea
U is usually based on the outer area. U based on
the outside surface area of the wall for an unfinned,tubular HEX is given by
If fins are present on the wall(s), fin efficiency andfin area should be considered in calculating U.
1
ln( )1 1o
o o o o ifi fo
i i i o
U
r r r r r R Rr h r k h
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Orders of Magnitude for h [w/m2K]
Gases (natural convection) 3-25
Engine oil (natural convection) 30-60
Flowing liquids (nonmetal) 100-10,000
Flowing liquid metals 5000-250,000
Film boiling 300-400
Dropwise condensation 60,000-120,000
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Tlm: 1. Parallel-Flow Heat Exchangers
where
lmTUAq
)/ln( 12
12
TT
TTTlm
ocoh
icih
TTT
TTT
,,2
,,1
T1 T2
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Tlm: 2. Counter-Flow Heat Exchangers
where
lmTUAq
)/ln( 12
12
TT
TTTlm
icoh
ocih
TTT
TTT
,,2
,,1
T1 T2
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Overall Heat Transfer Coefficient
For tubular heat exchangers we must take into account the conductionresistance in the wall and convection resistances of the fluids at the inner
and outer tube surfaces.
kL
DDR
AhR
AhUA
iocond
oo
cond
ii
2
)/ln(
111
where inner tube surface
outer tube surface LDA
LDA
oo
ii
(4)
ooii AUAUUA
111
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Example 1
A counterflow, concentric tube heat exchanger is used to cool the
lubricating oil for a large industrial gas turbine engine. The flow rate ofcooling water through the inner tube (Di=25 mm) is 0.2 kg/s, while the
flow rate of oil through the outer annulus (Do=45 mm) is 0.1 kg/s. The
oil and water enter at temperatures of 100 and 30C respectively. How
long must the tube be made if the outlet temperature of the oil is to be
60C?
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Heat Exchangers 15
Table 1 Nusselt number for fully developed
laminar low in an annulus with one surfaceisothermal and the other adiabatic
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Shell-and-Tube Heat Exchangers
Baffles are used to
establish a cross-flow and
to induce turbulent mixing
of the shell-side fluid, both
of which enhance
convection.
The number of tube and
shell passes may be variedOne Shell Pass and One Tube Pass
One Shell Pass,
Two Tube Passes
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Multipass and Cross-Flow Heat Exchangers
To account for complex flow conditions in multipass, shell and tubeand cross-flow heat exchangers, the log-mean temperature difference
can be modified:
CFlmlm TFT ,
where F=correction factor, to be determined from
the next figure in terms of parameters P & R .
: Logarithmic mean temperature
difference for counter flowCFlm
T,
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Correction Factor F
where t is the tube-
side fluid
temperature
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Heat Exchangers 19
Example
A shell-and-tube heat exchanger must be designed to heat 2.5 kg/s of water
from 15 to 85C. The heating is to be accomplished by passing hot engine
oil, which is available at 160C, through the shell side of the exchanger. The
oil is known to provide an average convection coefficient of ho=400 W/m2.K
on the outside of the tubes. Ten tubes pass the water through the shell.
Each tube is thin walled, of diameter D=25 mm, and makes eight passes
through the shell. If the oil leaves the exchanger at 100C, what is the flow
rate? How long must the tubes be to accomplish the desired heating?
Eff ti N b f T f U it ( NTU)
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Effectiveness-Number of Transfer Units (e-NTU)for HEX Analysis
When exit temperatures are unknown, a trial anderror procedure may be needed. Instead, the
method of number of transfer units (NTU) based
on HEX effectiveness may be used.
The e - NTU method is based on the fact that theinlet or exit temperature differences of a heat
exchanger are a function of UA/Ch and Ch/Cc.
Where, Ch = (mCP)h and Cc =(mCP)c
The HEX heat transfer equations may be written
in dimensionless form resulting in some
dimensionless groups.
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Dimensionless groups
1. Heat capacity rate ratio: , C* 1
2. HEX heat transfer effectiveness:
eis the ratio of the actual heat transfer rate in a HEXto the thermodynamically limited maximum possibleheat transfer rate if an infinite heat transfer areawere available in a counter flow HEX.
min
max
CCC
max
Q
Qe
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The actual heat transfer is obtained either by the
energy given off by the hot fluid or the energyreceived by the cold fluid
If Ch> Cc, then (Th1-Th2) < (Tc2-Tc1)If Ch< Cc, then (Th1-Th2) > (Tc2-Tc1)
The above equations are valid for CF and PF.The fluid that might undergo the maximumtemperature difference is the fluid having theminimum heat capacity rate Cmin.
1 2 2 1( ) ( ) ( ) ( )p h h h p c c cQ mc T T mc T T
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Maximum heat transfer:
or
Therefore, HEX effectiveness can be written as
The above equation is valid for all heat
exchanger flow arrangements. The value of eranges between 0 and 1.
For a given e and Qmax, the actual HT rate is
Q =e(mcp)min(Th1-Tc1)
max 1 1( ) ( ) if p c h c c hQ mc T T C C
max 1 1( ) ( ) if p h h c h cQ mc T T C C
1 2 2 1
min 1 1 min 1 1
( ) ( )( ) ( )
h h h c c c
h c h c
C T T C T T C T T C T T
e
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3. Number of Transfer Units:
The third dimensionless number NTU shows the
nondimensional heat transfer size of the HEX
min min
1NTUA
AU UdAC C
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e-NTU Expressions for different types of HEX arrangements
Type of HEX e(NTU,C*) NTU(e,C*)
Counterflow
Parallel Flow
Cross flow, Cmin
mixed and Cmax
unmixed
Cross flow, Cmax
mixed and Cmin
unmixed
1 to 2 shell-and-
tube HEX
NTU1exp1NTU1exp1
CC
Ce
e
e
1
1ln
1
1NTU C
C
NTU1exp11
1
CC
e
C
C NTUexp1exp1e
NTUexp1exp11
C
C
e
2/121NTUexp1
2/121NTUexp1
2/1211
2
C
C
CC
e
CC
11ln
1
1NTU e
e 1ln1ln1
NTU C
C
C
C
e1ln1
1-lnNTU
2/1
2112
2/12112
ln2/12
1
1NTU
CC
CC
Ce
e
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Example 2.9
A two-pass tube, baffled single-pass shell, shell-and-tubeHEX is used as an oil cooler. Cooling water flows
through the tubes at 20oC at a flow rate of 4.082 kg/s.
Engine oil enters the shell side at a flow rate of 10 kg/s.
The inlet and outlet temperatures of oil are 90oC and60oC, respectively. Determine the surface area of the
HEX using both the LMTD and e-NTU methods, if the
overall heat transfer coefficient based on the outside tube
area is 262 W/m2K. The specific heats of water and oil
are 4179 J/kgK and 2118 J/kgK, respectively.
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Heat Exchanger Sizing
If inlet temperatures, one of the outlettemperatures and mass flow rates are known, we
can use LMTD method for sizing problem:
1. Calculate Q and the unknown temperature
2. Calculate LMTD and obtain F if necessary
3. Calculate U
4. Determine A from A=Q/(UFTlm,cf)
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Heat Exchanger Rating
For an available heat exchanger (size, massflow rates, inlet temperatures and materials areknown) using e-NTU method we can rate theheat exchanger:
1. Calculate C*=Cmin/Cmax and NTU=UA/Cmin2. Determine e from appropriate charts ore-NTU
equations
3. Calculate Q=e Cmin(Th1-Tc1)
4. Calculate outlet temperatures
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Sizing Using e-NTU method1. Calculate e using Cmin, Cmax and temperatures2. Calculate C*=Cmin/Cmax
3. Calculate U
4. Determine NTU from charts or equations5. When NTU is known calculate heat transfer area
from A=(CminNTU)/U