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Chapter 9
Natural Convection
Combined Natural and Forced Convection
972C
In combined natural and forced convection, the natural convection is negligible when
Gr
/ Re
.
2
01
<
. Otherwise it is not.
973C
In assisting or transverse flows, natural convection enhances forced convection heat transfer
while in opposing flow it hurts forced convection.
974C
When neither natural nor forced convection is negligible, it is not correct to calculate each
separately and to add them to determine the total convection heat transfer. Instead, the correlation
(
29
n
n
n
/
1
natural
forced
combined
Nu
Nu
Nu
+
=
based on the experimental studies should be used.
975
A vertical plate in air is considered. The forced motion velocity above which natural convection
heat transfer from the plate is negligible is to be determined.
Assumptions
1
Steady operating conditions exist.
2
Air is an ideal gas with constant properties.
3
The
atmospheric pressure at that location is 1 atm.
Properties
The properties of air at 1 atm and 1 atm and the film
temperature of (
T
s
+
T
∞
)/2 = (85+30)/2 = 57.5
°
C are (Table A15)
1

2
5
K
003026
.
0
K
)
273
5
.
57
(
1
1
/s
m
10
871
.
1
=
+
=
=
×
=

f
T
β
υ
Analysis
The characteristic length is the height of the plate,
L
c
= L =
5 m. The Grashof and Reynolds numbers are
∞

∞
∞

∞
×
=
×
=
=
×
=
×

=

=
V
V
L
V
L
T
T
g
Gr
s
5
2
5
11
2
2
5
3
1
2
2
3
10
67
.
2
/s
m
10
871
.
1
)
m
5
(
Re
10
829
.
5
)
/s
m
10
871
.
1
(
)
m
5
)(
K
30
85
)(
K
003026
.
0
)(
m/s
81
.
9
(
)
(
and the forced motion velocity above which natural convection heat transfer from this plate is negligible
is
m/s
9.04
=
→
=
×
×
=
∞
∞
V
V
Gr
1
.
0
)
10
67
.
2
(
10
829
.
5
1
.
0
Re
2
5
11
2
971
Air
T
∞
= 30
°
C
V
Plate,
T
s
= 85
°
C
L
= 5 m
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View Full Document Chapter 9
Natural Convection
976
"!PROBLEM 976"
"GIVEN"
L=5
"[m]"
"T_s=85 [C], parameter to be varied"
T_infinity=30
"[C]"
"PROPERTIES"
Fluid$='air'
rho=Density(Fluid$, T=T_film, P=101.3)
mu=Viscosity(Fluid$, T=T_film)
nu=mu/rho
beta=1/(T_film+273)
T_film=1/2*(T_s+T_infinity)
g=9.807
"[m/s^2], gravitational acceleration"
"ANALYSIS"
Gr=(g*beta*(T_sT_infinity)*L^3)/nu^2
Re=(Vel*L)/nu
Gr/Re^2=0.1
T
s
[C]
Vel [m/s]
50
5.598
55
6.233
60
6.801
65
7.318
70
7.793
75
8.233
80
8.646
85
9.033
90
9.4
95
9.747
100
10.08
105
10.39
110
10.69
115
10.98
120
11.26
125
11.53
130
11.79
135
12.03
140
12.27
145
12.51
150
12.73
972
Chapter 9
Natural Convection
50
70
90
110
130
150
5
6
7
8
9
10
11
12
13
T
s
[C]
Vel [m/s]
973
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View Full DocumentChapter 9
Natural Convection
977
A vertical plate in water is considered. The forced motion velocity above which natural convection
heat transfer from the plate is negligible is to be determined.
Assumptions
1
Steady operating conditions exist.
Properties
The properties of water at the film temperature of
(
T
s
+
T
∞
)/2 = (60+25)/2 = 42.5
°
C are (Table A15)
υ
β
=
×
=

0 65
10
0 00040
6
.
.
m
/ s
K
2
1
Analysis
The characteristic length is the height of the plate
L
c
= L =
5
m. The Grashof and Reynolds numbers are
∞

∞
∞

∞
×
=
×
=
=
×
=
×

=

=
V
V
L
V
L
T
T
g
Gr
s
6
2
6
13
2
2
6
3
1
2
2
3
10
6
.
4
/s
m
10
65
.
0
)
m
5
(
Re
10
063
.
4
)
/s
m
10
65
.
0
(
)
m
5
)(
K
25
60
)(
K
0004
.
0
)(
m/s
81
.
9
(
)
(
and the forced motion velocity above which natural convection heat transfer from this plate is negligible
is
m/s
2.62
=
→
=
×
×
=
∞
∞
V
V
Gr
1
.
0
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This homework help was uploaded on 03/19/2008 for the course ME 410 taught by Professor Benard during the Spring '08 term at Michigan State University.
 Spring '08
 BENARD
 Heat Transfer

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