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CBE 150A – Transport Spring Semester 2014

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CBE 150A – Transport Spring Semester 2014
Temperature Driving Force
Concentric Pipe Heat Exchangers
CBE 150A – Transport
Spring Semester 2014
Concentric Pipe Heat Exchange
Goals:
By the end of today’s lecture, you should be able to:
 Write the heat transfer rate equation and the fluid enthalpy balances for
concentric pipe heat exchangers.
 Describe the temperature profiles and calculate the true mean ∆T for
parallel and countercurrent flow exchangers.
 Use the heat transfer rate equation and the fluid enthalpy balances to
make design calculations for concentric pipe heat exchangers.
CBE 150A – Transport
Spring Semester 2014
Concentric pipe (double pipe) heat exchangers
Heat exchangers are used to transfer heat from a hot fluid to a
cold fluid.
Concentric pipe heat exchangers are the simplest and most easily
analyzed configuration.
CBE 150A – Transport
Spring Semester 2014
Consider a typical concentric pipe heat exchanger:
t1
T1
T2
t2
Temperature Driving Force - DTlm
T = hot side fluid
CBE 150A – Transport
Q = UA DTlm
t = cold side fluid
Spring Semester 2014
Temperature driving force derivation
Assumptions:
(1)
(2)
(3)
(4)
Ui is constant
(Cp)hot and (Cp)cold are constant
heat loss to the surroundings is negligible
flow is steady state and parallel
The overall heat transfer coefficient (U) does change with temperature, but the
change is gradual. Thus, this assumption will hold for moderate temperature
ranges.
CBE 150A – Transport
Spring Semester 2014
Differential form of the steady-state heat balance:
dQ  U (Thot  tcold )  Di dL
1
 Di dL  dA
2
dQ  m hotCphot dThot  m cold Cpcold dtcold
3
m hotCphot (T  T2 )  m cold Cpcold (t  t1 )
4
(m Cp) cold
T  T2 
(t  t1 )
(m Cp) hot
5
CBE 150A – Transport
Spring Semester 2014
Using Eqns 1 and 3 and substituting Eqn 5 for T:


(mCp) cold
dQ  (m Cp) cold dt  U T2 
(t  t1 )  t   Di dL
(mCp) hot


U Di dL
 (m Cp)cold  
T2 
(m Cp) cold
(m Cp) hot
6
dt
 (m Cp) cold 
t1  
 1 t

(
m
Cp
)
hot


7
Using solution for general form of integral and integrating
between 0 and L and t1 and t2 yields:
dt
1

 a1  b1t b1 ln( a1  b1t )
UA
1

(m Cp) cold  (m Cp) cold

 (m Cp) hot
CBE 150A – Transport

 (m Cp) cold  
(m Cp) cold

T

t

 1 t 2 
 2
1


(
m
Cp
)
(
m
Cp
)
hot
hot

 
ln 
 
 (m Cp) cold  
(m Cp) cold
 1  T2 
t1  
 1 t1 


(
m
Cp
)
(
m
Cp
)

hot
hot
 

 
8
Spring Semester 2014
Expand and simplify:
UA
1
T t

ln 1 2
(m Cp) cold  (m Cp) cold 
T2  t1

1
 (m Cp) 
hot 

9
Substitute for (mCp) terms using Eqn 4:
UA
(m Cp) cold



 T1  t 2
1

 ln
(
T

T
)
  1 T2  t1
 1 2
(t 2  t1 )  
 
UA
t 2  t1
T t

ln 1 2
(m Cp) cold (T1  t 2 )  (T2  t1 ) T2  t1
(m Cp) cold 
CBE 150A – Transport
Q
(t 2  t1 )
10
11
12
Spring Semester 2014
Thus, the true mean DT for a parallel flow concentric pipe
heat exchanger is the log-mean temperature difference at
the two ends of the exchanger,
DTTM  DTLM
CBE 150A – Transport
(T1  t2 )  (T2  t1 )

(T1  t2 )
ln
(T2  t1 )
[13]
Spring Semester 2014
Also, regardless of the exchanger design, if a phase change occurs, such as
condensation or boiling (and the liquid is not subcooled or superheated), then:
(Th)in = (Th)out
and
or
(Tc)in = (Tc)out
DTTM = DTLM
Therefore, for concentric pipe heat exchangers and pure fluid condensers
or evaporators,
DTTM = DTLM.
As we will find out later, this is NOT the case for shell-and-tube heat
exchangers.
CBE 150A – Transport
Spring Semester 2014
Film Coefficient
Recall: Sieder-Tate equation for flow in pipes:
 DG 
 hD 


  0.023
 k 
  
0.8
 Cp 


 k 
N Nu  0.023NRe NPr
0.8
CBE 150A – Transport
0.333
  
 
 w 
0.14
0.14
0.333
Spring Semester 2014
Tubing Dimensions (BWG)
CBE 150A – Transport
Spring Semester 2014
Example Problem
Benzene is cooled from 141 F to 79 F in the inner pipe of a double-pipe
exchanger. Cooling water flows counter-currently to the benzene, entering the
jacket at 65 F and leaving at 75 F. The exchanger consists of an inner pipe of
7/8 inch BWG 16 copper tubing jacketed with a 1.5 inch Schedule 40 steel
pipe. The linear velocity of the benzene is 5 ft/sec. Neglect the resistance of
the wall and any scale on the pipe surfaces. Assume the L/D of both pipes is >
150.
Compute:
a) Both the inside and outside film coefficients.
b) The overall coefficient based on the outside area of the inner pipe.
c) The LMTD
CBE 150A – Transport
Spring Semester 2014
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