Transcript A Compressed Air System

Outline
(1) Heat Exchanger Types
(2) Heat Exchanger Analysis Methods
• Overall Heat Transfer Coefficient
»fouling, enhanced surfaces
• LMTD Method
• Effectiveness-NTU Method
(3) Homework #4
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Introduction
• Heat exchangers are devices that provide the flow
of thermal energy between two or more fluids at
different temperatures.
• Used in wide range of applications
• Classified according to:
• Recuperators/Regenerators
• Transfer processes: direct and indirect contact
• Construction Geometry: tubes, plates, extended
surfaces
• Heat Transfer Mechanisms: single and two phase
• Flow arrangements: parallel, counter, cross-flow
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HX Classifications
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HX Classifications
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Heat Exchanger Types
Concentric tube (double piped)
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Heat Exchanger Types
Concentric tube (double piped)
• One pipe is placed concentrically within the
diameter of a larger pipe
• Parallel flow versus counter flow
Fluid B
Fluid A
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Heat Exchanger Types
Concentric tube (double piped)
• used when small heat transfer areas are
required (up to 50 m2)
• used with high P fluids
• easy to clean (fouling)
• bulky and expensive per unit heat transfer area
• Flexible, low installation cost, simple
construction.
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Heat Exchanger Types
Shell and Tube
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Heat Exchanger Types
Shell and Tube
• most versatile (used in process industries,
power stations, steam generators, AC and
refrigeration systems)
• large heat transfer area to volume/weight ratio
• easily cleaned
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Heat Exchanger Types
Compact Heat Exchangers
•
•
•
•
generally used in gas flow applications
surface density > 700 m2/m3
the surface area is increased by the use of fins
plate fin or tube fin geometry
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Heat Exchanger
Types
Compact Heat
Exchangers
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Heat Exchanger Types
Cross Flow
• finned versus unfinned
• mixed versus unmixed
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Heat Exchanger Types
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Heat Exchanger Types
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Heat Exchanger Applications
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Heat Exchanger Analysis
• Overall Heat Transfer Coefficient
• LMTD
• Effectiveness-NTU
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Overall Heat Transfer Coefficient
The overall coefficient is used to analyze heat exchangers. It contains the effect of hot and cold side
convection, conduction as well as fouling and fins.
Rf ,c
Rf ,h
1
1
1


 Rw 

UA (o hA)c (o A)c
(o A) h (o hA) h
Rf  foulingfactor
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Fouling Factors
Heat exchanger surfaces are subject to fouling by
fluid impurities, rust formation, or reactions
between the fluid and the wall.
Rf  foulingfactor
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Enhanced Surfaces
Fins are often added to the heat exchange surfaces
to enhance the heat transfer by increasing the
surface area. The overall surface efficiency is:
o  1 
Af
A
(1   f )
Q  o hA(Tb  T )
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Enhanced Surfaces
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Log-Mean Temperature Difference
Need to relate the total heat transfer rate to inlet and
outlet fluid temperatures. Apply energy balance:
Q  m h (ih,i  ih,o )  m h c p,h (Th,i  Th,o )
Q  m c (ic,i  ic,o )  m c c p,c (Tc,i  Tc,o )
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Log-Mean Temperature Difference
We can also relate the total heat transfer rate to the
temperature difference between the hot and cold
fluids.
let T  Th  Tc
Q  UATLM
The log mean temperature difference depends on the
heat exchanger configuration.
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LMTD Parallel-Flow HX
Apply energy balance:
Assume:
• insulated
• no axial conduction
• PE, KE negligible
• Cp constant
• U constant
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LMTD Parallel-Flow HX
dQ  m h c p,h dTh  Ch dTh
dQ  m c c p,c dTc  Cc dTc
dQ  UTdA
T  Th  Tc
Integrate to get :
T2  T1
Q  UA
ln(T2 / T1)
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LMTD Parallel-Flow HX
Q  UATLM
TLM
T2  T1

ln(T2 / T1)
Wherefor P arallelFlow :
T1  Th,1  Tc,1  Th,i  Tc,i
T2  Th, 2  Tc,2  Th,o  Tc,o
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LMTD Counter-Flow HX
Tlm,CF > Tlm,PF
FOR SAME U:
ACF < APF
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LMTD Counter-Flow HX
Q  UATLM
T2  T1
TLM 
ln(T2 / T1)
Wherefor CounterFlow :
T1  Th,1  Tc,1  Th, i  Tc, o
T2  Th,2  Tc,2  Th, o  Tc, i
Tlm,CF > Tlm,PF FOR SAME U: ACF < APF
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LMTD- Multi-Pass and Cross-Flow
Apply a correction factor to obtain LMTD
Q  UATLM
TLM  FTLM ,CF
t: Tube Side
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LMTD Method
SIZING PROBLEMS:
• Calculate Q and the unknown outlet
temperature.
• Calculate DTlm and obtain the correction factor
(F) if necessary
• Calculate the overall heat transfer coefficient.
• Determine A.
The LMTD method is not as easy to use for
performance analysis….
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The Effectiveness-NTU Method
• If the inlet temperatures are unknown then
the LMTD method requires iteration.
• Preferable to use the e-NTU method under
these conditions.
• Define Qmax
for Cc < Ch
Qmax = Cc(Th,i - Tc,i)
for Ch < Cc
Qmax = Ch(Th,i - Tc,i)
or
Qmax = Cmin(Th,i - Tc,i)
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The Effectiveness-NTU Method
• Now define the heat exchanger effectiveness, e.
e
q
qmax

Ch (Th,i  Th,o )
Cmin (Th,i  Tc,i )

Cc (Tc,o  Tc,i )
Cmin (Th,i  Tc,i )
• The effectiveness is by definition between 0 & 1
• The actual heat transfer rate is:
Q = eCmin(Th,i - Tc,i)
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The Effectiveness-NTU Method
• For any heat exchanger:
e  f(NTU,Cmin/Cmax)
• NTU (number of transfer units) designates the
nondimensional heat transfer size of the heat
exchanger:
UA
NTU 
Cmin
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The Effectiveness-NTU Method
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The Effectiveness-NTU Method
PERFORMANCE ANALYSIS
• Calculate the capacity ratio Cr = Cmin/Cmax and NTU =
UA/Cmin from input data
• Determine the effectiveness from the appropriate charts
or e-NTU equations for the given heat exchanger and
specified flow arrangement.
• When e is known, calculate the total heat transfer rate
• Calculate the outlet temperature.
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The Effectiveness-NTU Method
SIZING ANALYSIS
• When the outlet and inlet temperatures are known,
calculate e.
• Calculate the capacity ratio Cr = Cmin/Cmax
• Calculate the overall heat transfer coefficient, U
• When e and C and the flow arrangement are known,
determine NTU from the e-NTU equations.
• When NTU is known, calculate the total heat transfer
surface area.
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Homework Number 4
COMPLETE PARTs 1&2 BEFORE CLASS ON THURSDAY. WE
WILL USE CLASS/LAB TIME ON Tuesday TO WORK ON
PARTS 3 and 4.
Part 1:
Review Chapter 11 of Incropera and Dewitt. Work through Example
Problems 11.3, 11.4, 11.5.
Part 2:
To ventilate a factory building, 5 kg/s of factory air at a temperature of
27 oC is exhausted and an identical flow rate of outdoor air at a
temperature of -12 oC is introduced to take its place. To recover some of
the heat of the exhaust air, heat exchangers are placed in the exhaust and
ventilation air ducts and 2 kg/s of ethylene glycol is pumped between
the two heat exchangers. The UA value of both of these crossflow heat
exchangers is 6.33 kW/K. What is the temperature of the air entering
the factory?
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Homework Number 4
Part 3:
Calculate the UA value for the cross flow heat exchanger specified
above. The heat exchanger is 1m high by 1 m wide by 1 m long (in
flow direction) and contains a tube bank heat transfer surface. The
ethylene glycol flows through the tubes and the air flow around them
(i.e. figure 11.2B in Incropera and Dewitt). The tubes are made of 1"
diameter thin walled copper and are mounted in an aligned pattern (3
inches apart center to center – Review tube bank heat transfer data in
Chapter 7 of Incropera and Dewitt). Use the data for internal tube heat
transfer coefficient given in the Project 4 technical specifications.
Part 4:
Calculate the pressure drop for the ethylene glycol and the air. Use the
data for ethylene glycol friction factor given in the Project 4 technical
specifications.
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