heat exchanger lecture.ppt
TRANSCRIPT
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Heat Transfer/Heat Exchanger How is the heat transfer?
Mechanism of Convection
Applications .
Mean fluid Velocity and Boundary and their effect on the rate of heattransfer.
Fundamental equation of heat transfer
Logarithmic-mean temperature difference.
Heat transfer Coefficients.
Heat flux and Nusselt correlation
Simulation program for Heat Exchanger
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How is the heat transfer?
Heat can transfer between the surface of a solid conductorand the surrounding medium whenever temperaturegradient exists.
ConductionConvection
Natural convection
Forced Convection
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Natural and forced Convection
Natural convection occurs whenever heat flows
between a solid and fluid, or between fluidlayers.
As a result of heat exchange
Change in density of effective fluid layers takenplace, which causes upward flow of heated
fluid.
If this motion is associated with heat transfer mechanism
only, then it is calledNatural Convection
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Forced Convection
If this motion is associated by mechanical means such as
pumps, gravity or fans, the movement of the fluid is
enforced.
And in this case, we then speak of Forced convection.
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Heat Exchangers A device whose primary purpose is the transfer of energy
between two fluids is named a Heat Exchanger.
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Applications of Heat Exchangers
Heat Exchangers
prevent car engine
overheating and
increase efficiency
Heat exchangers areused in Industry for
heat transfer
Heat
exchangers are
used in AC and
furnaces
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The closed-type exchanger is the most popular one.
One example of this type is the Double pipe exchanger.
In this type, the hot and cold fluid streams do not come
into direct contact with each other. They are separated by
a tube wall or flat plate.
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Principle of Heat Exchanger First Law of Thermodynamic: Energy is conserved.
generateds
in out
outin ewqhmhmdt
dE
..
outin
hmhm .. h
h
phh TCmAQ ...
c
c
pcc TCmAQ ...
0 0 0 0
Control Volume
Qh
Cross Section Area
HOT
COLD
Thermal Boundary Layer
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Q hot Q cold
T
h
Ti,wall
To,wall
Tc
Region I : Hot Liquid-
Solid Convection
NEWTONS LAW OF
CCOLING
dqxhh. ThTiw .dA Region II : ConductionAcross Copper Wall
FOURIERS LAW
dqx
k.dT
dr
Region III: Solid
Cold Liquid
Convection
NEWTONS LAW OF
CCOLING
dqxhc.TowTc .dA
THERMAL
BOUNDARY LAYER
Energy moves from hot fluid
to a surface by convection,
through the wall by
conduction, and then byconvection from the surface
to the cold fluid.
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Velocity distribution and boundary layer
When fluid flow through a circular tube of uniform cross-
suction and fully developed,
The velocity distribution depend on the type of the flow.
In laminar flow the volumetric flowrate is a function of the
radius.
V u2rdrr0
rD / 2
V = volumetric flowrate
u = average mean velocity
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In turbulent flow, there is no such distribution.
The molecule of the flowing fluid which adjacent to thesurface have zero velocity because of mass-attractive
forces. Other fluid particles in the vicinity of this layer,
when attempting to slid over it, are slow down by viscous
forces.
r
Boundary
layer
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Accordingly the temperature gradient is larger at the walland through the viscous sub-layer, and small in theturbulent core.
The reason for this is
1) Heat must transfer through the boundary layer byconduction.
2) Most of the fluid have a low thermal conductivity (k)3) While in the turbulent core there are a rapid movingeddies, which they are equalizing the temperature.
heating
cooling
Tube wall
Twh
Twc
Tc
Metalwall
Warm fluid
cold fluid
qxhATqxhA(Tw T)
qx
k
A(T
w
T)h
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Region I : Hot Liquid
Solid Convection
ThTiw qxhh.Ai
qxhhot. ThTiw .A
Region II : Conduction
Across Copper Wall
qxkcopper.2L
lnrori
To,wallTi,wall
qx.ln ro
ri
kcopper.2L
Region III : Solid
Cold Liquid Convection
To,wall Tc qx
hc.Ao
qxhcTo,wallTc Ao+
ThTc qx1
hh.Ai
ln rori
kcopper.2L
1
hc.Ao
qxU.A. T
hT
c
1
1
.
ln.
.
coldicopper
i
oo
ihot
o
hrk
r
rr
rh
rU
U = The Overall Heat Transfer Coefficient [W/m.K]
ThTc qx
R1R2R3
U 1
A.R
r
o
r
i
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Calculating U using Log Mean Temperature
coldhot dqdqdq
ch TTT
ch dTdTTd )(h
h
phh dTCmdq ..
ccpcc dTCmdq ..
Hot Stream :
Cold Stream:
c
pc
c
h
ph
h
Cm
dq
Cm
dqTd
..
)(
dATUdq ..
c
pc
h
ph CmCmdATUTd
.
1
.
1...)(
2
1
2
1
..
1
.
1.
)( A
Ac
pc
h
ph
T
TdA
CmCmU
T
Td
outc
inc
outh
inhch TTTTq
AUTTq
AU
T
T
...
ln1
2
2
1
2
1 ..
)( A
Ac
c
h
hT
T dAq
T
q
T
UT
Td
1
2
12
ln
.
T
T
TTAUq
Log Mean Temperature
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CON CURRENT FLOW
1
2
12
lnT
T
TTTLn
731 TTTTT in
c
in
h
1062 TTTTT out
c
out
h
COUNTER CURRENT FLOW
1062 TTTTT in
c
out
h
731 TTTTT out
c
in
h
Umh.
Cph. T3T6
A.TLn
mc.Cpc. T7T10
A.TLn
T1 T2T4 T5
T3
T7 T8 T9
T10
T6
Counter - Current Flow
T1 T2T4 T5
T6T3
T7
T8 T9
T10
Parallel Flow
Log Mean Temperature evaluation
T1
A
1 2
T
2
T
3 T
6
T
4
T
6
T7
T
8 T
9 T10
WallT1
T2
A
A
1 2
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T1
A
1 2
T
2
T
3 T
6
T
4T6
T
7
T
8 T
9 T10
Wall
qhhAiTlm
Tlm(T3 T1) (T6 T2)
ln(T3 T1)
(T6 T2)
qhcAoTlm
Tlm(T1T7) (T2T10)
ln(T1T7)(T2T10)
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Nu f(Re,Pr,L /D,b /
o)
DIMENSIONLESS ANALYSIS TO CHARACTERIZE A HEAT EXCHANGER
..Dvk
Cp .
k
Dh.
Nua.Reb.PrcFurther Simplification:
Can Be Obtained from 2 set of experiments
One set, run for constant Pr
And second set, run for constant Re
q k
A(TwT)
h
NuD
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For laminar flow
Nu = 1.62 (Re*Pr*L/D)
Empirical Correlation
14.0
3/18.0 .Pr.Re.026.0
o
bLnNu
Good To Predict within 20%
Conditions: L/D > 10
0.6 < Pr < 16,700Re > 20,000
For turbulent flow
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Experimental
Apparatus
Two copper concentric pipes
Inner pipe (ID = 7.9 mm, OD = 9.5 mm, L = 1.05 m)
Outer pipe (ID = 11.1 mm, OD = 12.7 mm)
Thermocouples placed at 10 locations along exchanger, T1 through T10
Hot Flow
Rotameters
Temperature
Indicator
Cold Flow
rotameter
Heat
Controller
Switch for concurrent
and countercurrent
flow
Temperature
Controller
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0
50
100
150
200
250
150 2150 4150 6150 8150 10150 12150
Pr^X Re^Y
Nus
Examples of Exp. Results
4
4.2
4.4
4.6
4.8
0.6 0.8 1 1.2 1.4
ln (Pr)
ln(Nu
)
2
2.5
3
3.5
4
4.5
5
5.5
6
9.8 10 10.2 10.4 10.6 10.8 11
ln (Re)
ln(Nu)
Theoretical trend
y = 0.8002x 3.0841
Experimental trend
y = 0.7966x 3.5415
Theoretical trend
y = 0.3317x + 4.2533
Experimental trend
y = 0.4622x 3.8097
Theoretical trend
y = 0.026x
Experimental trendy = 0.0175x 4.049
Experimental Nu = 0.0175Re0.7966Pr0.
4622
Theoretical Nu = 0.026Re0.8Pr0.33
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0
5000
10000
15000
20000
25000
30000
35000
0 1 2 3 4
Velocity in the core tube (ms-1
)
hi (W/m2K)
ho (W/m2K)
U (W/m2K)
Effect of core tube velocity on the local and
over all Heat Transfer coefficients