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10/25/2010
1
Free Convection:
General Considerations
and Results for
Vertical and Horizontal Plates
Chapter 9
Sections 9.1 through 9.6.2
• Pertinent Dimensionless Parameters
h
Grashof Number:
= Buoyancy force/viscous force
h
Rayleigh Number:
2
3
)
(
ν
β
L
T
T
g
Gr
s
L
∞
−
≡
να
3
)
(
Pr
L
T
T
g
Gr
Ra
s
L
L
∞
−
=
≡
Vertical Plates
• Free Convection Boundary Layer Development on a
Heated Plate
:
h
Ascending flow
with the maximum velocity occurring in the boundary layer
and zero velocity at both the surface and outer edge.
(
)
?
s
T
T
∞
<
The fluid close to the plate is _________ the fluid beyond it.
a) Less dense than
b) More dense than
c) As dense as
• Form of the
x
Momentum Equation
for Laminar Flow
Net Momentum Fluxes
(
Inertia Forces
)
Buoyancy Force
Viscous Force
h
Temperature dependence requires that solution for
u
(
x,y
)
be obtained concurrently with solution of the
boundary layer
energy equation
for
T
(
x,y
).
–
The solutions are said to be
coupled
.
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If we need to couple these two equations, what do we
need to use?
a) The error function
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This note was uploaded on 11/17/2010 for the course CHEN 3210 at Colorado.
 '10
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