Heat Exchangers
Heat exchange equipment
Heating and cooling are common in
food operations
•
•
•
•
•
•
•
Pasteurization
Blanching
Evaporation
Drying
Sterilization
Freezing
Extrusion
Heat
exchangers
Contact
type
Steam
infusion
Steam
injection
Plate
Non contact type
Tubular
Shell and
Tube
Scraped
Surface
HE classification: type of medium used
• Gas-Gas
• Liquid-Gas
• Liquid-liquid
HE classification: flow direction
• Countercurrent .
• Concurrent (parallel).
• Countercurrent is more used than concurrent
due to its higher efficiency.
Examples of heat exchangers
Shell and tube heat exchangers
PLATES Heat Exchangers
Plate thickness is 0.4 to 0.8 mm
Channel lengths are 2-3 meters
Plates are available in: Stainless Steel,
Titanium, Titanium-Palladium, Nickel
PLATES
Double tube heat exchangers
• One example of this type is the Double pipe
heat exchanger.
• In this type, the hot and cold fluid streams do
not come into direct contact with each other.
• They are separated by a tube wall or flat
plate.
Principle of Heat Exchanger
•
First Law of Thermodynamic: “Energy is conserved.”
0
0
0
0
dE


ˆ
ˆ
 .hin   m
 .hout   q
w
s  e
generated
 m
dt
out
 in

qh  m.h.C ph .Th
qc  m c .C pc .Tc
•Control Volume
in
out
COLD
HOT
Cross Section Area
 m .hˆ   m .hˆ
Thermal Boundary Layer
THERMAL
Region III: Solid –
Cold Liquid
Convection
BOUNDARY LAYER
Energy moves from hot fluid to
a surface by convection,
through the wall by conduction,
and then by convection from
the surface to the cold fluid.
NEWTON’S LAW OF
CCOLING
dqx  hc .Tow  Tc .dA
Th
Ti,wall

To,wall
Tc
Region I : Hot LiquidSolid Convection
Q hot
Q cold
NEWTON’S LAW OF
CCOLING
dqx  hh .Th  Tiw .dA
Region II : Conduction
Across Copper Wall
FOURIER’S LAW
dT
dqx  k.
dr
U = The Overall Heat Transfer Coefficient [W/m.K]
Region I : Hot Liquid –
Solid Convection
Region II : Conduction

Across Copper Wall
Region III : Solid – Cold
Liquid Convection
Th  Tc 
qx  hhot .Th  Tiw .A
qx 
qx
R1  R2  R3
1
A.R

qx  hc To,wall  Tc Ao

qx  U.A.Th  Tc 
U
kcopper .2L
(T  T )
ro
ln
ri
Th  Tiw 

To,wall  Ti ,wall
qx
hh .Ai
r 
qx . ln  o 
ri 


kcopper .2L
qx
To,wall  Tc 
hc .Ao


ro 
ln  


r
1
1
 i 

Th  Tc  qx 


hh .Ai k copper .2L hc .Ao 






 ro 
ro . ln  


r
r
1

 i 

U  o 
 hhot .ri
kcopper .ri
hcold 




1
r
r
i
o
+
Calculating U using Log Mean Temperature
Hot Stream :
 h .C ph .dTh
dqh  m
Cold Stream:
 c .C .dTc
dqc  m
d (T )  dTh  dTc
T  Th  Tc
c
p
dq  dqhot  dqcold
 dq  U .T .dA
 1
1 

d (T )  U .T .dA.

 m .C h m .C c 
c
p 
 h p

T2
T1

T2
T1
 dqh
dqc 

d (T ) 

 m .C h m .C c 
c
p 
 h p
 Th Tc  A2
d (T )
. dA
 U .

T
qc  A1
 qh
 1
d (T )
1
 U .

 m .C h m .C c
T
c
p
 h p
 A2
. dA
 A1

 T 
U . A.
Th  Tc    U .A Thin  Thout  Tcin  Tcout
ln  2   
q
q
 T1 

 
q  U .A
Log Mean Temperature

T2  T1
 T2 
ln 
 T 

1 

Log Mean Temperature evaluation
m h .C ph .T3  T6  m c .C pc .T7  T10 
T2  T1
TLn 
U

 T2 
A.TLn
A.TLn

ln 
 T1 
1
CON CURRENT FLOW
∆ T1
2
Wall
∆ T2
∆A
A
T10
T1
T4
T5
T2
T6
T3
T1  Thin  Tcin  T3  T7
T9
T8
T7
Para llel Flow
T2  Thout  Tcout  T6  T10
Log Mean Temperature evaluation
m h .C ph .T3  T6  m c .C pc .T7  T10 
T2  T1
TLn 
U

 T2 
A.TLn
A.TLn

ln 
 T1 
COUNTER CURRENT FLOW
1
2
T3
T4
T6
T1
T6
Wall
T7
T2
T8
T9
T10
A
T10
T1
T4
T2
T5
T3
T6
T7
T8
Counter - Current Flow
T9
T1  Thin  Tcout  T3  T7
T2  Thout  Tcin  T6  T10
Heat Exchangers:
The Effectiveness – NTU Method
General Considerations
• Computational Features/Limitations of the LMTD
(log mean Temperature difference) Method:
 The LMTD method may be applied to design problems for
which the fluid flow rates and inlet temperatures, as well as
a desired outlet temperature, are prescribed.
For a specified H.E. type, the required size (surface area), as well as the other
outlet temperature, are readily determined.
 If the LMTD method is used in performing calculations for which
both outlet temperatures must be determined from knowledge of the
inlet temperatures, the solution procedure is iterative.
 For both design and performance calculations, the effectiveness-NTU
method (Number of Transfer Units) may be used without iteration.
Definitions
• Heat exchanger effectiveness, 𝓔 ( ratio between actual and max heat transfer) :

q
qmax
0   1
Fluid Heat Capacity Rates

Ch  mh c p ,h

Cc  mc c p,c
New Definitions:
Cmin  min( Ch , Cc )
qmax  Cmin * (Th ,i  Tc ,i )
Max possible
heat transfer
• Maximum possible heat rate:
qmax  Cmin Th,i  Tc,i 
Cmin
Ch if Ch  Cc
 or

Cc if Cc  Ch
 Why is Cmin and not Cmax used in the definition of qmax?
to include maximum feasible heat transfer among the working fluids
during calculation
 Will the fluid characterized by Cmin or Cmax experience the largest possible
temperature change through the HX?
Heat exchanger effectiveness

q
qmax

Ch * (Th,i  Th,o )
Cmin * (Th,i  Tc ,i )

Cc * (Tc ,o  Tc ,i )
Cmin * (Th,i  Tc ,i )
q   * Cmin * (Th ,i  Tc ,i )
Number of Transfer Units, NTU:
UA
NTU 
Cmin
q  with  NTU
 A dimensionless parameter whose magnitude
influences H.E. performance:
Effectiveness – NTU Method
Cmin
  f ( NTU ,
)
Cmax
C min
C max
𝓔
UA
NTU 
Cmin
NTU
Effectiveness – NTU Method
For Parallel Flow with Cmin = Ch

(Th ,i  Th ,o )
(Th ,i  Tc ,i )

Cmin mh c p ,h (Tc ,o  Tc ,i )
 

 Cr
Cmax m c
(Th,i  Tc ,i )
c p ,c
1  exp[  NTU (1  Cr )]

1  Cr
Effectiveness – NTU Method
For Parallel Flow with Cmin = Ch
1  exp[  NTU (1  Cr )]

1  Cr
ln[ 1   (1  Cr )]
NTU  
1  Cr
Effectiveness – NTU Method
For Counterflow with Cr = Cmin/Cmax
1  exp[  NTU (1  Cr )]

1  Cr exp[  NTU (1  Cr )]
Cr  1
NTU

1  NTU
Cr  1
Effectiveness – NTU Method
For Counter-flow with Cr = Cmin/Cmax
1
 1
NTU 
ln(
)
Cr  1 Cr  1
NTU 

1 
Cr  1
Cr  1
• Design Calculations:
NTU  f   , Cmin / Cmax 
 Relations  Table 11.4 or Figs. 11.14 - 11.19
• For all heat exchangers,
  with  Cr
• For Cr = 0, (phase change: condensation or evaporation)
a single   NTU relation applies
  1  exp   NTU 
or
NTU  1n 1   
• Performance Calculations:
  f  NTU , Cmin / Cmax 

Cr
 Relations  Table 11.3 or Figs. 11.14 - 11.19
Effectiveness – NTU Method
Graphical Representations of Equations in Tables 11.3 & 11.4
Effectiveness – NTU Method
Effectiveness – NTU Method
Heat exchanger selection.
• Thermal performance analysis (NTUs) for
co- & counter-current exchangers.
• Multi-pass exchangers (S&T).
• Condensation & boiling.
• Radiation.
General Procedure
• Must calculate heat duty
• Minimise cost subject to constraints
– fluid inlet and outlet temperatures
– allowable pressure drops
– compatibility of materials (corrosion) and fluids
(direct/indirect contact)
– maintenance (repairs)
– availability (can we get it easily?)
– sensitivity to other conditions
General Considerations
•
•
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•
•
•
•
•
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Design pressures
Design temperatures
Heat duty / size range
Fluid type / compatibility
Boiling/condensation (“quality”)
Temperature driving forces
Allowable pressure drops
Fouling tendency
Space limitations
Fundamentals of Heat and Mass Transfer
THEODORE L. BERGMAN, FRANK P. INCROPERA, ADRIENNE S.
LAVINE, DAVID P. DEWITT
http://books.google.com.sa/books?hl=ar&lr=&id=vvyIoXEywMoC&oi=fnd&pg=PR21&dq=table+11.3+heat+exchanger+effectiveness+relations&ots=8HqjQScVI8&sig=eA2YjAcHwA8A1lsCFT6RNEU8hY&safe=on&redir_esc=y#v=onepage&q=table%2011.3%20heat%20exchanger%20effectiveness%20relations&f=false