Transcript Document 7845459

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
Rf ,c
Rf ,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  UATm
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 : dT  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:
-dT
dq  UdA T 
1
1

C h Cc
 1
1  dT
 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  UATlm
• 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 / UTlm 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  UATlm
Tlm  FTlm,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