Transcript Convection Experiment

Convection Experiment
Leader: Tom Salerno
Partners:
Greg Rothsching
Stephen Johnson
Jen DiRocco
What will you hear today?
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Introduction
Theory
Equipment and Procedure
Results and Discussion
Conclusions
Questions
Introduction
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What is convection?
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Heat transfer from fluid flowing over solid surface
Why study convection?
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Occurs in almost every process plant
Example: Heat Exchangers, Tray Dryers, etc.
Theory – Newton’s Law of Cooling
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Flat Plate:
q  hATs  Tb   hAT
h  Heat Transfer Coefficien t  Units of W
Finned Plate
(Resistances in
Parallel):
q  ho Ao  h f A f  f Ts  Tb 
tanh L  Tm
f 

L
Ts
dqconvection = hf *P dx * (Tfin @ x - T8 )
t
P
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Newton Rate Equation
z
dx
L

hf P
Ak
Theory – Forced Convection
A
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Physical Situation:
H
A
u8
T8
δT
δ
dx
dq w   kdx
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dT
dy
w
Solving Boundary Layer Equations
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 u   
 
  0
 x y  
Continuity Equation  u
u 
u
Momentum Balance u x   y    y


 T
T 
T
Thermal Balance –
u x   y    y


Rigorous analytical solution
2
2
2
2
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Theory – Forced Convection
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Forced Convection – analytically developed
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Dimensionless Parameters
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Reynolds:
Re x 
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Prandtl:
Pr 
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Nusselt:
Flat Plate:
 ux

 CP 


k
  x0 3/ 4 
hx x
1/ 3
1/ 2
Nu x 
 .332 Pr Re x 1    
k
  x  
Nu 
hL
 .664 Pr1/ 3 Re x1/ 2
k
1/ 3
for Re  5 1010
Theory - Natural Convection
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Physical Situation:
ρ = fucn(y)
T8
ρ8
U = func(y)
Ts
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New Momentum Equation:
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u
u
u
 2u

 g  (T  T )  2
x
y
y
Must now solve all three boundary layer equations
simultaneously
Theory - Natural Convection
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Experimental Correlation:
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Churchill and Chu
Dimensionless Parameters
g  (Ts  T ) L  uo L 
g  (Ts  T ) L3

  
u0 2
2


2
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Grashoff:
Rayleigh:
Correlation:
GrL 
RaL  GrL Pr 
Nu L  .68 
g  (Ts  T ) L3

.670 Ra1/L 4
  .492 9 /16 
1  
 
  Pr  
4/9
RaL  109
Equipment and Procedure
Chimney
Boundary Layer Profile Measurement
Heated Surface
Viewing Window
Inlet Air Measurement
Temperature Probe
Anemo meter
20 watts
Pump and Slide
Cover
Power Supply
Figure 9: Front view of convection duct.
Figure 10: Side view of convection duct.
Results and Discussions
Flat Plate: Laminar Flow
Heat transfer coefficients versus velocity for laminar flow over flat plate
90
80
h (Watts per meter squared degrees Celsius)
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70
60
50
Predicted
Experimental
Linear (Predicted)
40
30
20
10
0
0
0.5
1
1.5
2
(Velocity (meters per second))^.5
2.5
3
3.5
Results and Discussions
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Turbulent Mix
Turbulence begins because the
boundary layer formed over the
duct wall hits the edge of the
flat plate which is slightly
raised, thus disturbing the molecules in the boundary layer to
form a turbulent mix
u8
u8
T8
A8
u8
Duct Wall
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New Correlation -
Nu 
hL
 1.169 Pr1/ 3 Re x1/ 2
k
Results and Discussions
Flat Plate: Turbulent Mix
Heat transfer coefficients versus velocity for laminar flow over flat plate
90
80
70
h (Watts per meter squared degrees Celsius)
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60
50
Turbulent Mix Predicted
Experimental
Linear (Turbulent Mix Predicted)
40
30
20
10
0
0
0.5
1
1.5
2
-10
(Velocity (meters per second))^.5
2.5
3
3.5
Results and Discussions
Finned Plate: Laminar
Heat Transfer Coefficients for flow over Finned Plate
70
h (watts per meter squared degree celcius)
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60
50
40
Predicted
Experimental
30
Linear (Predicted)
20
10
0
0
0.5
1
1.5
2
2.5
(Velocity (m eters per second))^.5
3
3.5
Results and Discussions
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Turbulent Mix
Turbulence begins because the
incoming air will h it the blunt
side of the fin, causing the
mo lecules to be disturbed in
many different directions. This
causes the boundary layer to
have a slight turbulent mix.
u8
T8
A8
u8
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New Correlation -
Nu 
hL
 .90 Pr1/ 3 Re x1/ 2
k
Results and Discussions
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Finned Plate: Turbulent Mix
Results and Discussions
Effectiveness of Fin Addition
Overal Heat Transfet Com parison (a)
80
70
60
Delta T (degrees Celsius)
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34 deg
50
Flat Plate
40
Finned Plate
30
40 deg
20
29 deg
18 deg
10
0
0
2
4
6
8
Velocity (m eters per second)
10
12
Conclusions – What we learned
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The convective heat transfer coefficient increases
linearly with the square root of air velocity
Predictive Equations are useful for predicting trend in
data, but not the absolute numbers
Natural Convection is the limit to forced convection,
though it is difficult to predict
The addition of fins will increase the heat transfer
rate substantially at low air velocities, but not as
much at higher air velocities
Conclusions – Significance?
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Aid in design of heat exchangers
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How to increase heat transfer coefficient
How to increase heat transfer rate
Realize presence of natural convection for cheap
ways to cool electronic equipment
Confidence of Predictive Equations
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Use for other experiments, such as tray dryer
Only if can perfectly match geometry, or can run a
short scale experiment to obtain correction factor
Questions?