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HEAT
TRANSFER
CHAPTER 11
Heat Exchangers
Heat Transfer
#1
Su Yongkang
School of Mechanical Engineering
Heat Exchangers, LMTD Method
Where we’ve been ……
• So far have focused on detailed heat transfer
analysis of specific conditions, such as external
heat transfer coefficient
Where we’re going:
• Investigate methods for larger system level
analysis that combine all these modes of heat
transfer in heat exchangers
Heat Transfer
#2
Su Yongkang
School of Mechanical Engineering
Heat Exchangers, LMTD Method
KEY POINTS THIS LECTURE
• Types of heat exchangers, advantages and
disadvantages
• Overall heat transfer coefficient, concept of
fouling factor
• Log mean temperature difference
• Application of LMTD to heat exchanger
analysis
• Text book sections: §11.1 – 11.3
Heat Transfer
#3
Su Yongkang
School of Mechanical Engineering
Heat Exchanger Types
TB ,out
TA,in
T A,out
TB ,in
TB ,in
T A,out
TA,in
TB ,out
TB ,out
T A,out
TA,in
Example:
TB ,in
Heat Transfer
#4
Su Yongkang
School of Mechanical Engineering
Heat Exchanger Types (Cont’d)
Shell and Tube:
(common in chemical process industry)
T A,out
TB ,in (shell side)
TA,in (tube side)
Shell and Tube:
TB ,out
TB ,in (shell side)
TA,in (tube side)
T A,out Shell and Tube:
TB ,out
TB ,in (shell side)
T A,out
Shell and Tube:
TB ,out
Heat Transfer
#5
T A,in
(tube side)
Su Yongkang
School of Mechanical Engineering
Heat Exchanger Types (Cont’d)
• Shell and Tube:
Heat Transfer
#6
Su Yongkang
School of Mechanical Engineering
Heat Exchanger Types (Cont’d)
Plate and Frame
• Series of plates with flow channels embossed in
them.
• The two fluids are guided through alternating
rows of the plates
• Advantages: __________________________
• Application pictured: Electrocoat paint in
automotive assembly plant
Heat Transfer
#7
Su Yongkang
School of Mechanical Engineering
Heat Exchanger Types (Cont’d)
Plate and Fin
• Dense array of plates that guide alternating
channels of fluids (typically air)
• Series of fins connect the plates and greatly
increase the heat transfer area
• Advantage: very large heat transfer surface area
per unit volume .
• One common application: Aircraft
environmental control systems
Heat Transfer
#8
Su Yongkang
School of Mechanical Engineering
Overall heat transfer coefficient for HX
• Recall from earlier the overall thermal resistance
concept:
1
1
1
UA U c Ac U h Ah
Rf ,c
Rf ,h
1
1
Rw
(o hA) c (o A) c
(o A) h (o hA) h
• Types of resistances involved with heat
exchangers (covered in previous sessions)
– Cold side internal convection
– Cold side fouling factor
– Conduction through wall
– Hot side external convection (smooth wall
or may involve fins)
TB ,out
– Hot side fouling factor
• Review how
these were
calculated
T A,out
TA,in
TB ,in
Heat Transfer
#9
Su Yongkang
School of Mechanical Engineering
Analysis of heat transfer
• Total heat transfer rate is found through energy
balance, regardless of the HX type or flow path
Thot ,in
Thot ,out
Tcold ,in
Tcold ,out
q
For hot fluid:
m c pT
m c p T dT
Energy balance:
E E
in
m h c p ,hTh m h c p ,h T dT h dqh
dqh m h c p ,h dTh
dqh Ch dTh
dq
• Define
m h c p ,h Ch
out
(Heat capacity rate for hot fluid)
For the cold fluid:
dqc Cc dTc
(Note: no minus sign “-” in this equation,
since heat flow in)
Heat Transfer
# 10
Su Yongkang
School of Mechanical Engineering
Analysis of heat transfer (Cont’d)
• Energy balance gives: dqc dqh dq
• For the entire flow length
dq Cc dTc Ch dTh
• A convenient way to compute the heat transfer is
from the mean temperature difference between
the hot and cold fluids
q UATm
T Th Tc
• Next:
Evaluation of Tm different for parallel and
counter flow
Heat Transfer
# 11
Su Yongkang
School of Mechanical Engineering
Analysis of parallel flow heat transfer
Parallel flow heat exchanger
• At any location along the heat exchanger
Thot ,in
Thot ,out
Tcold ,in
Tcold ,out
dq
dq UdA T
Define : T Th Tc so : dT dTh dTc
dq
Where: dqc m c c p,c dTc Cc dTc dTc
Cc
dqh m h c p,h dTh Ch dTh
• So:
-dT
dq UdA T
1
1
C h Cc
1
1 dT
UdA
C h Cc T
• Integrating from the inlet to the outlet
1
T2
1
UA
ln
T1
Ch Cc
Heat Transfer
Eq. 11.13
# 12
Su Yongkang
School of Mechanical Engineering
Analysis of parallel flow heat transfer (Cont’d)
• From the overall energy balance, total heat transfer:
q qh m h c p ,h Th,in Th,out qc m c c p ,c Tc ,out Tc ,in
so :
q C h Th,in Th,out and q Cc Tc ,out Tc ,in
thus:
q
q
Ch
and Cc
Th,in Th,out
Tc ,out Tc ,in
• Combining
Th,in Th,out Tc ,out Tc ,in
To
ln
UA
Ti
q
q
UA
Tin Tout
q
Eq. 11.14
q UATlm
• For parallel flow:
Tin Tout
Tlm
ln Tin / Tout
Heat Transfer
Tin Th,in Tc ,in
Tout Th,out Tc ,out
# 13
Su Yongkang
School of Mechanical Engineering
Analysis of parallel flow heat transfer (Cont’d)
• Temperature profile for parallel flow:
dTh
Ti
T
dq
To
dTc
In
Out
Fig 11.7
Heat Transfer
# 14
Su Yongkang
School of Mechanical Engineering
Analysis of counter flow heat transfer
• For counter flow:
Tin Tout
Tlm
ln Tin / Tout
Tin Th,in Tc ,out
Tout Th,out Tc ,in
• Temperature profile for counter flow:
Ti
dTh
T
Fig 11.8
dq
To
dTc
In
Out
Tlm, CF Tlm, PF
Heat Transfer
# 15
Su Yongkang
School of Mechanical Engineering
Typical use of the LMTD method:
Given:
• Need to cool a certain mass flow rate of fluid A
from TA,i to TA,o using the fluid B at TB,i
Find:
• Design / size the heat exchanger
Solution Method:
• Use the overall energy balance to find
q Ch Th
• Select the heat exchanger type (based on the
other project needs, available resources, size and
weight considerations, etc., etc.)
• Select tube diameters and types of heat transfer
surfaces (fins, no fins, etc.)
• Use A q / UTlm to determine the needed
heat exchanger heat transfer area ( length)
Heat Transfer
# 16
Su Yongkang
School of Mechanical Engineering
Special cases
• For a condensing vapor or Ch Cc
TCond
T
In
Out
x
• For an evaporating liquid or Ch Cc
T
TEvap
In
Out
x
• What if Ch = Cc in a counter-flow HX?
T
T1 T2
In
Heat Transfer
Out
x
# 17
Su Yongkang
School of Mechanical Engineering
Multipass and cross-flow heat exchangers
• The equations are the same.
dq Cc dTc Ch dTh
q UATlm
Tlm FTlm,CF
Tlm, CF
Tin Tout
ln Tin / Tout
Tin Th,in Tc ,out
Tout Th,out Tc ,in
Counter-flow conditions
To find F, please refer to the figures 11.10-13.
Heat Transfer
# 18
Su Yongkang
School of Mechanical Engineering
Typical Example
E11.1 ( textbook, pp619)
Heat Transfer
# 19
Su Yongkang
School of Mechanical Engineering
Heat Exchangers, LMTD Method
KEY POINTS THIS LECTURE
• Various types of heat exchangers that are
commonly used in industry and product designs.
Understanding of when to consider using each
type.
• Defined the fluid heat capacity:
Ch m
h c p,h
(Heat capacity rate for hot fluid)
• Log mean temperature difference introduced again
T Tin
TLMTD out
T
ln o
Ti
Parallel flow : Ti Th.i Tc,i Counter flow : Ti Th.i Tc,o
To Th.o Tc,o
To Th.o Tc,i
• Temperature distribution parallel vs. counterflow
Parallel
Counterflow
dTh
Ti
T
dq
Ti
To
T
dq
dTc
dTc
Heat Transfer
dTh
# 20
Su Yongkang
School of Mechanical Engineering
To