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MECE 4364 Heat Transfer
Prof. Dong Liu
Department of Mechanical Engineering
University of Houston
1
Lecture 23 – Nov 09, 2010
Lecture 23
Free (Natural) Convection
2
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View Full Document Lecture 23
Free Convection: Overview
±
Free Convection (or Natural Convection)
±
fluid motion
induced by
buoyancy forces
±
buoyancy forces
arise when there are
density gradients
in a fluid and a body
force proportional to density
±
Density Gradient
±
due to temperature gradient
±
Body Force
±
gravity (function of mass)
thermally driven flow
Basic Principle
: heavy fluid
falls and light fluid rises
creating
vortices
3
Lecture 23
Overview
±
Internal vs. External
±
free convection can be generated in a duct or enclosure (internal)
±
along a free surface (external)
±
in both internal & external cases, free convection can
interact
with
forced
convection (mixed convection)
±
Free Boundary Flow
±
occur in an extensive quiescent fluid (
i.e.
, infinite, motionless fluid)
²
no forced convection
±
induces a boundary layer on a
heated or cooled surface (T
s
≠
T
∞
)
±
can generate plumes and buoyant jets
4
Lecture 23
Dimensionless Parameters
±
Pertinent Dimensionless Parameters
±
Grashoff Number
±
Recall Reynolds number for forced convection:
±
Rayleigh Number
As Grashoff # increases
: buoyancy
overcomes
friction and
induces
flow
Gr
L
=
g
β
T
s
−
T
∞
()
L
3
ν
2
~
buoyancy force
viscous force
g
≡
gravitational constant
≡
thermal expansion coefficient (fluid property)
L
≡
characteristic length
≈
1
T
[K
1
]
ideal gas
Ra
L
=
Gr
L
Pr
=
g
T
s
−
T
∞
(
)
L
3
να
=
μ
ρ
≡
kinematic viscosity of fluid
Re
L
=
VL
~
inertial force
viscous force
comparable to Peclet number (Pe) for
forced convection
5
Lecture 23
Mixed Convection
±
Mixed Convection
±
a condition where both free and forced convection effects are comparable
±
free convection can
assist
,
oppose
, or act
orthogonally
to forced convection
±
When is mixed convection significant?
±
an assessment of scales is conducted through a comparison of free and forced
nondimensional parameters
±
Affect on heat transfer
±
forced and free convection DO NOT combine linearly
buoyancy force
inertial force
~
Gr
L
Re
L
2
>>
1
O
(1)
<<
1
⎧
⎨
⎪
⎩
⎪
free convection dominates
mixed convection condition
forced convection dominates
Nu
L
=
f
Re
L
,
Gr
L
,Pr
(
)
Nu
L
=
f
Re
L
Nu
L
=
fG
r
L
Nu
L
n
=
Nu
L
,
forced
n
±
Nu
L
,
free
n
→
n
=
3 assisting/opposing
n
=
7
2
or 4 transverse
⎧
⎨
⎩
+
Î
assisting/transverse

Î
opposing
6
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View Full DocumentLecture 23
Boundary Layers
±
Boundary Layer development on a vertical plate
±
heated plate: ascending flow with maximum velocity
occurring
in the boundary layer
and zero velocity at the
plate and
in the free stream
±
cooled plate: descending flow
±
Boundary Layer Equations
∂
u
x
+
v
y
=
0
ˆ
x direction :
u
u
x
+
v
u
y
=
ν
2
u
y
2
+
g
β
T
−
T
∞
()
ρ
c
p
u
T
x
+
v
T
y
⎛
⎝
⎜
⎞
⎠
⎟
=
k
2
T
y
2
+
μ
u
y
⎛
⎝
⎜
⎞
⎠
⎟
2
buoyancy body force due to gravity
Notes:
1. this formulation applied the
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This note was uploaded on 01/27/2011 for the course MECE 4364 taught by Professor Lipinglui during the Winter '10 term at University of Houston.
 Winter '10
 LipingLui

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