Natural Convection in Enclosed Spaces Two vertical plates separated by a distance. Each plate at a...
Transcript of Natural Convection in Enclosed Spaces Two vertical plates separated by a distance. Each plate at a...
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Natural Convection in Enclosed Spaces
Two vertical plates separated by a distance. Each plate at a different temperature.
Ends are insulated.
Convective heat transfer occurs in the fluid within the space.
3 21 2
, 2
,
1 2
Gr
Nu
g T TN
hN
kq
h T TA
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Natural Convection in Enclosed Spaces
3, , Pr
1/ 4
, Pr 3 5, , Pr1/ 9
1/ 3
, Pr 5 7, , Pr1/ 9
For gases enclosed between vertical plates,
1.0 for 2 10
0.20 for 6 10 2 10/
0.0073 for 2 10 2 10/
For liqui
Nu Gr
Gr
Nu Gr
Gr
Nu Gr
hN N N
k
N NN N N
L
N NN N N
L
3, , Pr
1/ 4
, Pr 3 7, , Pr1/ 4
ds enclosed between vertical plates,
1.0 for 1 10
0.28 for 1 10 1 10/
Nu Gr
Gr
Nu Gr
hN N N
k
N NN N N
L
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Natural Convection in Enclosed Spaces
1/ 4 3 5, , Pr , Pr
1/ 3 5, , Pr , Pr
For gases enclosed between horizontal plates,
with lower plate hotter than upper
0.20 for 7 10 3 10
0.061 for 3 10
For liquids enclosed between ve
Nu Gr Gr
Nu Gr Gr
N N N N N
N N N N N
1/ 3 0.074 5 9, , Pr Pr , Pr
rtical plates,
with lower plate hotter
0.069 for 1.5 10 1 10Nu Gr GrN N N N N N
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Boiling
A: Free convection; B: Nucleate boiling; C: Transition Boiling;
D: Film boiling
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Boiling
Type Excess Temperature (deg. C)
Free Convection: < 5
Nucleate Boiling: 5 – 25
Transition Boiling: 25 – 120
Film Boiling: > 120
The excess temperature is the surface temperature above the boiling point of the liquid.
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Nucleate Boiling
Bubbles form at surface and separate, mixing the fluid. As temperature increases, the bubbles join to form bubble columns or jets. These eventually merge to form slugs. This type of boiling is the most desirable for a chemical process due to the high heat rates.
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Transition Boiling
Film begins to form at surface. Surface changes from nucleate to film boiling.
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Film Boiling
Surface completely covered with film blanket.
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Nucleate Boiling Correlations
o o
2 o 2
1/ 3 1/3
3 3
or
For horizontal surfaces:
English ( : BTU/hr-ft - F) Metric ( : kW/m )
151 / 5000 1043 / 16
0.168 / 5000 5.56 / 16
w satT T T K F
h h
h T q A h T q A
h T q A h T q A
2 o 2
1/ 7 1/7
/ 75,000 / 240
For vertical surfaces:
English ( : BTU/hr-ft - F) Metric ( : kW/m )
87 / 1000 537 / 3
q A q A
h h
h T q A h T q A
h
3 30.240 / 1000 7.95 / 3
/ 20,000 / 63
T q A h T q A
q A q A
0.4
Pressure Correction: multiply by
where is in atm.P P
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3 / 225 o 2 o
3 /1551 2
For forced convection inside tubes,
English: 0.077 : F; : BTU/hr-ft - F : psia
Metric: 2.55 : K; : W/m : kPa
P
P
h T e T h P
h T e T h K P
Nucleate Boiling Correlations
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Film Boiling Correlations
1/ 43( )
( )
where 0.62 for horizontal cylinders
0.67 for spheres
is the density
is the enthalpy change from liq. to vapor
l v fgNu
v v v s sat
fg
g h DhDN C
k v k T T
C
C
h
is the diameter of the pipe
is the specific volume
is the thermal conductivity
is the surface temperature
is the boiling point temperature s
sat
D
v
k
T
T of the liquid
Subscript refers to the vapor
Subscript refers to the liquid.
v
l
Film boiling not desirable! Better to have nucleate!
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Condensation
Film Condensation: Liquid film covers surface and flows continuously from the surface. Characteristic of clean, uncontaminated surfaces.
The presence of the liquid film reduces the heat transfer.
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Condensation
Droplet Condensation: drops form in cracks, pits and cavities on the surface and may grow and coalesce thru condensation. More than 90% of the surface is covered by drops, ranging from a few micrometers in diameter to agglomerations visable to the naked eye. The droplets flow from the surface due to gravity.
Heat transfer for droplet condensation is higher than film. To be conservative, most design calculations assume film.
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Condensation
Droplet Film
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Condensation
Homogeneous condensation or fog formation resulting from increased pressure due to expansion.
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Condensation
Direct contact condensation.
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Condensation
1/ 43
Re
For vertical surfaces in laminar flow:
( )1.13 1800
where the subscripts refers to the liquid and refers to the vapor.
is th
L L v fgNu
L L L
fg
gh LhLN N
k k T
L v
h
Re
e latent heat of vaporization for the liquid.
All properties, except , are evaluated at the film temperature.
The Reynolds number is defined by
4 for a vertical tube of
sat w
fg
L
T T T
h
mN
D
Re
v
diameter,
4 for a vertical plate of width,
Frequently, and can be neglected.L
L
D
mN W
W
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Condensation
Re
1/ 32 30.4
Re2
For turbulent flow, 1800,
0.0077
The solution is by trial and error since the
Reynolds number must be known.
LNu
L L
N
g LhLN N
k
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Condensation
For tubes, the liquid thickens as the condensate flows down the tube.
For banks of tubes, the liquid may flow as a film to the lower tube, or it may drip to the lower tubes.
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Condensation
1/ 43
For a vertical tier of horizontal tubes placed one below the other,
the average convective coefficient over the tubes is given by,
0.725
This equation works al
L L v fgNu
L L L
N
N
gh DhDN
k N k T
so for 1.N