Computation of FREE CONVECTION P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi Quantification of Free …….
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Computation of FREE CONVECTION
P M V Subbarao
Associate Professor
Mechanical Engineering Department
IIT Delhi
Quantification of Free …….
Governing Equations
• Now, we can see buoyancy effects replace pressure gradient in the momentum equation.
2
2
)( y
uvTTg
y
uv
x
uu
0
y
v
x
u
2
2
2
y
u
cy
T
y
Tv
x
Tu
p
Strongly coupled and must be solved simultaneously
•The buoyancy effects are confined to the momentum equation, so the mass and energy equations are the same.
Dimensionless Similarity Parameter
• The x-momentum and energy equations are
velocityreferencearbitrary an is u
and length, sticcharacteri a is L where
T
TT
0
*
00
sTT
u
vvand
u
uu
L
yyand
L
xx
2*
*2*
20
*
**
*
**
Re
1 T
)(
y
u
u
LTTg
y
uv
x
uu
L
s
PrRe
1 2*
*2
*
**
*
**
y
T
y
Tv
x
Tu
L
Dimensionless Similarity Parameter
• Define new dimensionless parameter,
1Re2
L
LGr1
Re2
L
LGr
2
32
020
)()(
LTTgLu
u
LTTgGr ss
L
forced natural
•Grashof number in natural convection is analogous to the Reynolds number in forced convection.
•Grashof number indicates the ratio of the buoyancy force to the viscous force.
•Higher Gr number means increased natural convection flow
TTs
u(x,y)
y
g
sT
T
x
v
u
Laminar Free Convection on Vertical Surface
• As y : u = 0, T = T
• As y 0 : u = 0, T = Ts
• With little or no external driving flow, Re 0 and forced convection effects can be safely neglects
Pr),( LL GrfNu
1Re2
L
LGr
Analytical similarity solution for the local Nusselt number in laminar free convection
(Pr)4
4/1
fGr
k
hxNu L
x
4/1Pr238.1Pr 1.2210.609
Pr 75.0Pr
f
(Pr)43
4
4/1
fGr
k
LhNu L
L
Average Nusselt # =
Where
Effects of Turbulence
• Just like in forced convection flow, hydrodynamic instabilities may result in the flow.
• For example, illustrated for a heated vertical surface:
• Define the Rayleigh number for relativemagnitude of buoyancy and viscous forces
TTs
3
,,
)(
Pr
xTTg
GrRa
s
cxcx
Effects of Turbulence
• Transition to turbulent flow greatly effects heat transfer rate.
Empirical Correlations
Typical correlations for heat transfer coefficient developed from experimental data are expressed as:
3 Pr
LTTg GrRa s
LL
nLL CRa
k
LhNu
3/1
4/1
n
n For Turbulent
For Laminar
Vertical Plate at constant Ts
LNuLog10
LRaLog10
•Alternative applicable to entire Rayleigh number range (for constant Ts)
2
27/816/9
6/1
Pr)/492.0(1
387.0825.0
L
LRa
Nu
Vertical Cylinders
•Use same correlations for vertical flat plate if:
4/1
35 ~
LGrL
D
Free Convection from Inclined Plate
Cold plate or Hot fluid
Hot plate or Cold fluid
Horizontal Plate
Cold Plate (Ts < T)
Hot Plate (Ts > T)
Active Upper SurfaceActive Lower Surface
Empirical Correlations : Horizontal Plate
•Define the characteristic length, L asP
AL s
•Upper surface of heated plate, or Lower surface of cooled plate :
1173/1
744/1
1010 15.0
1010 54.0
LLL
LLL
RaRaNu
RaRaNu
•Lower surface of heated plate, or Upper surface of cooled plate :
1054/1 1010 27.0 LLL RaRaNu
Note: Use fluid properties at the film temperature2
TTT s
f
Empirical Correlations : Long Horizontal Cylinder
•Very common geometry (pipes, wires)
•For isothermal cylinder surface, use general form equation for computing Nusselt #
nDD CRa
k
DhNu
RaD C n
0.333 0.125 10 - 10
0.250 0.480 10 - 10
0.188 0.850 10 - 10
0.148 1.02 10 - 10
0.058 0.675 10 - 10
127
74
42
22
210
Constants for general Nusselt number Equation
free convection turbulent heat transfer in an enclosure
• Turbulent flow in an enclosed cavity or box is a model for many flows of practical interest:
• Heating of a room.• Flow in a double glazing Window.• Spreading of fire and fire generated gases in an
building.
Velocity Vectors on A Central Vertical Plane
Isotherms on A Central Vertical Plane
Nusselt Number Correlations
Small Window Large Window
)( satss TThq
Natural Convection in A Pool of Saturated Liquid
Tsat
Onset of Convection Tsurface
Further Behavior of Saturated Liquid
Increasin
g T
Natural Convection
Onset of Boiling
Isolated Bubble Regime
High Overshoots !!!
Wall Superheat (T=Ts – Tsat)
Heat Flux
Overshoot
A BA: Onset of Natural convection
B: Onset of Nucleate Boiling
BOILING HEAT TRANSFER
P M V Subbarao
Associate Professor
Mechanical Engineering Department
IIT Delhi
A Basic means of Power Generation……A science which made Einstein Very Happy!!!
Boiling
• In a steam power plant convective heat transfer is used to remove heat from a heat transfer surface.
• The liquid used for cooling is usually in a compressed state, (that is, a subcooled fluid) at pressures higher than the normal saturation pressure for the given temperature.
• Under certain conditions some type of boiling can take place.
• It is an important process in nuclear field when discussing convection heat transfer.
• More than one type of boiling can take place within a
nuclear facility.
Nuclear Power Plant
Steam Boiler
Classification of Boiling
• Microscopic classification or Boiling Science basis:
• Nucleated Boiling
• Bulk Boiling
• Film Boiling
• Macroscopic Classification or Boiling Technology basis:
• Flow Boiling
• Pool Boiling
Nucleate Boiling
• The most common type of local boiling encountered in nuclear facilities is nucleate boiling.
• In nucleate boiling, steam bubbles form at the heat transfer surface and then break away and are carried into the main stream of the fluid.
• Such movement enhances heat transfer because the heat generated at the surface is carried directly into the fluid stream.
• In the main fluid stream, the bubbles collapse because the bulk temperature of the fluid is not as high as the heat transfer surface temperature where the bubbles were created.
• This heat transfer process is sometimes desirable because the energy created at the heat transfer surface is quickly and efficiently "carried" away.
Bulk Boiling
• As system temperature increases or system pressure drops, the bulk fluid can reach saturation conditions.
• At this point, the bubbles entering the coolant channel will not collapse.
• The bubbles will tend to join together and form bigger steam bubbles.
• This phenomenon is referred to as bulk boiling.
• Bulk boiling can provide adequate heat transfer provided that the steam bubbles are carried away from the heat transfer surface and the
surface is continually wetted with liquid water.
• When this cannot occur film boiling results.
Film Boiling
• When the pressure of a system drops or the flow decreases, the bubbles cannot escape as quickly from the heat transfer surface.
• Likewise, if the temperature of the heat transfer surface is increased, more bubbles are created.
• As the temperature continues to increase, more bubbles are formed than can be efficiently carried away.
• The bubbles grow and group together, covering small areas of the heat transfer surface with a film of steam.
• This is known as partial film boiling. • Since steam has a lower convective heat transfer coefficient than
water, the steam patches on the heat transfer surface act to insulate the surface making heat transfer more difficult.
• As the area of the heat transfer surface covered with steam increases, the temperature of the surface increases dramatically, while the heat flux from the surface decreases.
• This unstable situation continues until the affected surface is covered by a stable blanket of steam, preventing contact between the heat transfer surface and the liquid in the center of the flow channel.
• The condition after the stable steam blanket has formed is referred to as film boiling.
• The process of going from nucleate boiling to film boiling is graphically represented in Figure.
• The figure illustrates the effect of boiling on the relationship between the heat flux and the temperature difference between the heat transfer surface and the fluid passing it.
Boiling Curve
Related Documents
