Heat Transfer Su Yongkang
School of Mechanical Engineering
# 1
HEAT TRANSFER
CHAPTER 11
Heat Exchangers
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 2
Heat Exchangers,NTU-? Method
Where we’ve been ……
Analysis of heat exchangers using log mean
temperature difference (LMTD)
Where we’re going,
Computation of heat exchanger performance
compared to the theoretical maximum possible
for the flow conditions and HX type and size.
L M T D
i
o
ino u t TUA
T
T
TTUAq
ln
dqiT? oT?
hdT
cdT
T?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 3
Heat Exchangers,NTU-? Method
KEY POINTS THIS LECTURE
Concept of heat exchanger effectiveness,?
based on the ratio of fluid heat capacity,C.
Concept of heat exchanger Number of Transfer
Units,NTU
Application of NTU-? method to predict the
performance of a given heat exchanger
Text book sections,§ 11.4 – 11.5
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 4
For a condensing vapor
For an evaporating liquid
What if Ch = Cc in a counterflow HX?
Recall earlier discussion
ch CCo r
x
T
In Out
x
T
In Out
ch CCo r
x
T
In Out
21 TT
CondT
EvapT
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 5
Heat exchanger effectiveness
Maximum possible heat transfer rate for any
given inlet temperatures and flow rates occurs in
a infinitely long counterflow HX
)(,an d
Ti n l et f l u i dh o t r e ac h w o u l df l u i d C o l d
If
,,m a x icihc
h,ic,ohc
TTCq
T,t h en,TCC
T
outhT,
incT,
outc
inh
T
T
,
,?
Length of heat exchanger
)(,an d
Ti n l et f l u i d c o l dr e ac h w o u l df l u i dH o t
If
,,m a x icihh
c,ih,ohc
TTCq
T,t h en,TCC
L
)(,,m i nm a x icih TTCq
Maximum T?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 6
Heat exchanger effectiveness (Cont’d)
Define,Heat exchanger effectiveness,?
Actual heat transfer,q,can be determined from
simple energy balance
Thus:
If the heat exchanger effectiveness were known,
then the actual heat transferred could be found
from:
inco u tcco u thinhh
inco u tccpcco u thinhhphh
TTCTTCqso
TTcmqTTcmqq
,,,,
,,,,,,
,
,,m i n
,,
,,m i n
,,
m a x
icih
icocc
icih
ohihh
TTC
TTC
OR
TTC
TTC
q
q
m a xq
q
m a xqq
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 7
Number of Transfer Units
Define,Number of Transfer Units,NTU
NTU depends on both the heat exchanger design
(UA) and the operating conditions (Cmin).
Define,Capacity Ratio,Cr
Effectiveness is a function of capacity ratio and
the NTU
Relationships between?,NTU and Cr can be
computed,
Tables 11.3 and 11.4
and Figures 11.14 – 11.19 in textbook
1 C /CC C rm a xm i nr
rCN T Uf,
m inC
UANT U?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 8
NTU -? Tables
Parallel
flow
Counter
flow
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 9
Summary of Solution Method
Typical scenario for using?-NTU method:
Given:
Find:
Solution method:
1,Determine UA for this heat exchanger
1,Find
2,Find
2,Calculate
3,Determine? from tabulated formulas or
plots
4,Compute actual heat transfer
5,Find outlet temperatures from
g e o m e t ry HX,,,,,,chincinh mmTT
qTT o u tco u th,,,,
icih TTCqq,,m inm a x
m
q
an d,
m
q
,c
,,
,h
,,
cp
icoc
hp
ihoh
c
TT
c
TT
rhc CCC,,
Aa n dU
m in/ CUAN T U?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 10
Calculation Methodology
Performance calculation,
Given:
Find:
Solution method,NTU
Design problems:
Given:
Find:
Solution method,LMTD
g e o m e t ry HX,,,,,,chincinh mmTT
qTT o u tco u th,,,,
)( o r,,,,,,,,o u tco u thchincinh TTmmTT
A q,),( o r,,outhoutc TT
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 11
Example #1
Situation:
Light lubricating oil (cp=2090 J/kg-K) is cooled
with water in a small heat exchanger,
Oil flow = 0.5 kg/s,inlet T = 375 K
Water flow = 0.2 kg/s,inlet T = 280 K
Part 1:
If desired outlet temperature of the oil is 350 K,
and you know the estimated overall heat
transfer coefficient,U = 250 W/m2-K,from
manufacturer’s data for this type of HX
Find,Required heat transfer area for a parallel
flow HX and compare to the area needed for a
counter flow HX.
KT inoil 375,?
KT inoil 350,?
KT inwa ter 280,?
,?outwaterT
Solution Method?
LMTD
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 12
Example (Cont’d)
Solution,Part 1:
For parallel flow,
For counter flow,
KT inoil 375,?
KT inoil 350,?
KT inwa ter 280,?
,?outwaterT
KKgJcKT cpc,/4 1 8 1,295,
/
a n d
,,
,,
cicoc
ohihh
CqTT
TTCq
W26125
)350375(20905.0
K311
)41812.0/(26125280
63)39/95l n ( 3995/lnT PFl m,
outin
outin
TT
TT
95 inT 39 outT
64 inT 70 outT
67)70/64l n ( 7064/lnT CFl m,
outin
outin
TT
TT
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 13
Example (Cont’d)
Solution,Part 1 (Cont’d):
Now,compute the required area
Parallel flow
Counter flow
Part 2:
Use?-NTU method to determine the required
NTU and heat transfer area for parallel and
counter flow
Solution Method?
66.1)/(, PFlmPF TUqA
56.1)/(, CFlmCF TUqA
2m
2m
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 14
Example (Cont’d)
Solution,Part 2:
To determine the minimum heat capacity rate,
Then
The effectiveness is
KKgJcKT cpc,/4 1 8 1,295,
KWC h /104520905.0
m i n/2.8 3 64 1 8 12.0 CKWC C
7 9 4 4 0)2 8 03 7 5(2.8 3 6
)(,,m i nm a x
icih TTCq
26125,, ohihh TTCq
33.07 9 4 4 0/2 6 1 2 5/ m a x qq?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 15
Example (Cont’d)
Solution,Part 2:
With
It follows from Figure 11.14 and 11.15 that
8.01 0 4 5 2.8 3 6
m a x
m i n
C
C
55.0?PFN T U 5.0?CFN T U
84.1/m i n UN T UCA PFPF
67.1/m i n UN T UCA CFCF
2m
2m
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 16
Example #2
The oil in an engine is cooled by air in a
cross-flow heat exchanger where both fluids
are unmixed,Atmospheric air enters at 303K
and 0.53 kg/s,Oil at 0.026 kg/s enters at 348K
and flows through a tube of 10-mm diameter,
Assuming fully developed flow and constant
wall heat flux,estimate the oil-side heat
transfer coefficient,If the overall convection
coefficient is 53 W/m2.K and the total heat
transfer area is 1m2,determine the
effectiveness,What is the exit temperature of
the oil?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 17
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 18
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 19
Heat Exchangers,NTU-? Method
KEY POINTS THIS LESSON
Defined heat exchanger effectiveness,?
Defined term Number of Transfer Units,NTU
Defined the Capacity Ratio,Cr
Identified methods
to determine relation
between?,NTU
and Cr
(Table formulas
or charts)
icih TTCqw h e r e q
q
,,m inm a x
m a x
,
m in
N TU CUA?
1 C C r
m a x
m inr CC
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 20
Appendix
The maximum possible heat transfer rate.
From the energy conservation,
If the fluid having the larger heat capacity rate
were to experience the maximum possible
temperature change,the other fluid would
experience a larger temperature change.
That is:
If and
)(,,m i nm a x icih TTCq
)(,,m a xm a x icih TTCq
)()(,,,,ohihhicocc TTCTTC
cCC?m a x ihoc TT,,?
))(/()(,,,,icihhcohih TTCCTT
)()(,,,,icihohih TTTT
ocicoh TTT,,, impossible
School of Mechanical Engineering
# 1
HEAT TRANSFER
CHAPTER 11
Heat Exchangers
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 2
Heat Exchangers,NTU-? Method
Where we’ve been ……
Analysis of heat exchangers using log mean
temperature difference (LMTD)
Where we’re going,
Computation of heat exchanger performance
compared to the theoretical maximum possible
for the flow conditions and HX type and size.
L M T D
i
o
ino u t TUA
T
T
TTUAq
ln
dqiT? oT?
hdT
cdT
T?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 3
Heat Exchangers,NTU-? Method
KEY POINTS THIS LECTURE
Concept of heat exchanger effectiveness,?
based on the ratio of fluid heat capacity,C.
Concept of heat exchanger Number of Transfer
Units,NTU
Application of NTU-? method to predict the
performance of a given heat exchanger
Text book sections,§ 11.4 – 11.5
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 4
For a condensing vapor
For an evaporating liquid
What if Ch = Cc in a counterflow HX?
Recall earlier discussion
ch CCo r
x
T
In Out
x
T
In Out
ch CCo r
x
T
In Out
21 TT
CondT
EvapT
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 5
Heat exchanger effectiveness
Maximum possible heat transfer rate for any
given inlet temperatures and flow rates occurs in
a infinitely long counterflow HX
)(,an d
Ti n l et f l u i dh o t r e ac h w o u l df l u i d C o l d
If
,,m a x icihc
h,ic,ohc
TTCq
T,t h en,TCC
T
outhT,
incT,
outc
inh
T
T
,
,?
Length of heat exchanger
)(,an d
Ti n l et f l u i d c o l dr e ac h w o u l df l u i dH o t
If
,,m a x icihh
c,ih,ohc
TTCq
T,t h en,TCC
L
)(,,m i nm a x icih TTCq
Maximum T?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 6
Heat exchanger effectiveness (Cont’d)
Define,Heat exchanger effectiveness,?
Actual heat transfer,q,can be determined from
simple energy balance
Thus:
If the heat exchanger effectiveness were known,
then the actual heat transferred could be found
from:
inco u tcco u thinhh
inco u tccpcco u thinhhphh
TTCTTCqso
TTcmqTTcmqq
,,,,
,,,,,,
,
,,m i n
,,
,,m i n
,,
m a x
icih
icocc
icih
ohihh
TTC
TTC
OR
TTC
TTC
q
q
m a xq
q
m a xqq
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 7
Number of Transfer Units
Define,Number of Transfer Units,NTU
NTU depends on both the heat exchanger design
(UA) and the operating conditions (Cmin).
Define,Capacity Ratio,Cr
Effectiveness is a function of capacity ratio and
the NTU
Relationships between?,NTU and Cr can be
computed,
Tables 11.3 and 11.4
and Figures 11.14 – 11.19 in textbook
1 C /CC C rm a xm i nr
rCN T Uf,
m inC
UANT U?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 8
NTU -? Tables
Parallel
flow
Counter
flow
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 9
Summary of Solution Method
Typical scenario for using?-NTU method:
Given:
Find:
Solution method:
1,Determine UA for this heat exchanger
1,Find
2,Find
2,Calculate
3,Determine? from tabulated formulas or
plots
4,Compute actual heat transfer
5,Find outlet temperatures from
g e o m e t ry HX,,,,,,chincinh mmTT
qTT o u tco u th,,,,
icih TTCqq,,m inm a x
m
q
an d,
m
q
,c
,,
,h
,,
cp
icoc
hp
ihoh
c
TT
c
TT
rhc CCC,,
Aa n dU
m in/ CUAN T U?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 10
Calculation Methodology
Performance calculation,
Given:
Find:
Solution method,NTU
Design problems:
Given:
Find:
Solution method,LMTD
g e o m e t ry HX,,,,,,chincinh mmTT
qTT o u tco u th,,,,
)( o r,,,,,,,,o u tco u thchincinh TTmmTT
A q,),( o r,,outhoutc TT
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 11
Example #1
Situation:
Light lubricating oil (cp=2090 J/kg-K) is cooled
with water in a small heat exchanger,
Oil flow = 0.5 kg/s,inlet T = 375 K
Water flow = 0.2 kg/s,inlet T = 280 K
Part 1:
If desired outlet temperature of the oil is 350 K,
and you know the estimated overall heat
transfer coefficient,U = 250 W/m2-K,from
manufacturer’s data for this type of HX
Find,Required heat transfer area for a parallel
flow HX and compare to the area needed for a
counter flow HX.
KT inoil 375,?
KT inoil 350,?
KT inwa ter 280,?
,?outwaterT
Solution Method?
LMTD
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 12
Example (Cont’d)
Solution,Part 1:
For parallel flow,
For counter flow,
KT inoil 375,?
KT inoil 350,?
KT inwa ter 280,?
,?outwaterT
KKgJcKT cpc,/4 1 8 1,295,
/
a n d
,,
,,
cicoc
ohihh
CqTT
TTCq
W26125
)350375(20905.0
K311
)41812.0/(26125280
63)39/95l n ( 3995/lnT PFl m,
outin
outin
TT
TT
95 inT 39 outT
64 inT 70 outT
67)70/64l n ( 7064/lnT CFl m,
outin
outin
TT
TT
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 13
Example (Cont’d)
Solution,Part 1 (Cont’d):
Now,compute the required area
Parallel flow
Counter flow
Part 2:
Use?-NTU method to determine the required
NTU and heat transfer area for parallel and
counter flow
Solution Method?
66.1)/(, PFlmPF TUqA
56.1)/(, CFlmCF TUqA
2m
2m
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 14
Example (Cont’d)
Solution,Part 2:
To determine the minimum heat capacity rate,
Then
The effectiveness is
KKgJcKT cpc,/4 1 8 1,295,
KWC h /104520905.0
m i n/2.8 3 64 1 8 12.0 CKWC C
7 9 4 4 0)2 8 03 7 5(2.8 3 6
)(,,m i nm a x
icih TTCq
26125,, ohihh TTCq
33.07 9 4 4 0/2 6 1 2 5/ m a x qq?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 15
Example (Cont’d)
Solution,Part 2:
With
It follows from Figure 11.14 and 11.15 that
8.01 0 4 5 2.8 3 6
m a x
m i n
C
C
55.0?PFN T U 5.0?CFN T U
84.1/m i n UN T UCA PFPF
67.1/m i n UN T UCA CFCF
2m
2m
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 16
Example #2
The oil in an engine is cooled by air in a
cross-flow heat exchanger where both fluids
are unmixed,Atmospheric air enters at 303K
and 0.53 kg/s,Oil at 0.026 kg/s enters at 348K
and flows through a tube of 10-mm diameter,
Assuming fully developed flow and constant
wall heat flux,estimate the oil-side heat
transfer coefficient,If the overall convection
coefficient is 53 W/m2.K and the total heat
transfer area is 1m2,determine the
effectiveness,What is the exit temperature of
the oil?
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 17
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 18
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 19
Heat Exchangers,NTU-? Method
KEY POINTS THIS LESSON
Defined heat exchanger effectiveness,?
Defined term Number of Transfer Units,NTU
Defined the Capacity Ratio,Cr
Identified methods
to determine relation
between?,NTU
and Cr
(Table formulas
or charts)
icih TTCqw h e r e q
q
,,m inm a x
m a x
,
m in
N TU CUA?
1 C C r
m a x
m inr CC
Heat Transfer Su Yongkang
School of Mechanical Engineering
# 20
Appendix
The maximum possible heat transfer rate.
From the energy conservation,
If the fluid having the larger heat capacity rate
were to experience the maximum possible
temperature change,the other fluid would
experience a larger temperature change.
That is:
If and
)(,,m i nm a x icih TTCq
)(,,m a xm a x icih TTCq
)()(,,,,ohihhicocc TTCTTC
cCC?m a x ihoc TT,,?
))(/()(,,,,icihhcohih TTCCTT
)()(,,,,icihohih TTTT
ocicoh TTT,,, impossible
