fundamentals of engineering supplied-reference handbook - Ventech!

If the ambient fluid temperature varies periodically
according to the equation
1
T∞ = T∞,mean+ ( T∞, max−T∞, min)
cos ω t
2
the temperature of the body, after initial transients have died
away, is
βc2 ⎡ −1
ω ⎤
T = cos ⎢ωt− tan ⎥+
c1,
where
2 2
ω +β ⎣ β ⎦
c = T
1
,
∞ mean
1
c2 = ( T∞, max−T∞, min)
2
hAs
β =
ρcV
p
Natural (Free) Convection
For free convection between a vertical flat plate (or a
vertical cylinder of sufficiently large diameter) and a large
body of stationary fluid,
h = C (k/L) RaL n , where
L = the length of the plate in the vertical direction,
RaL = Rayleigh Number =
β
( T − T )
g s ∞
2
Ts = surface temperature,
T∞ = fluid temperature,
β =
2
coefficient of thermal expansion (
Ts + T∞
for an
v =
ideal gas where T is absolute temperature), and
kinematic viscosity.
v
L
3
Pr,
Range of RaL C n
10 4 – 10 9
10 9 – 10 13
0.59
0.10
1/4
1/3
For free convection between a long horizontal cylinder and
a large body of stationary fluid
Ra
D
=
C(
k D)
n
D
( T − T
3 ) D
h = Ra , where
gβ s
v
2
∞
Pr
Range of RaD C n
10 –3 – 10 2
10 2 – 10 4
10 4 – 10 7
10 7 – 10 12
1.02
0.850
0.480
0.125
0.148
0.188
0.250
0.333
71
HEAT TRANSFER (continued)
Radiation
Two-Body Problem
Applicable to any two diffuse-gray surfaces that form an
enclosure.
Q�
12
Generalized Cases
Radiation Shields
1
1
4 4 ( T − T )
σ 1 =
1−
ε1
1
+
ε A A F
1
12
2
1−
ε
+
ε A
One-dimensional geometry with low-emissivity shield
inserted between two parallel plates.
Q�
12
=
1−
ε
ε A
1
1
1
1
+
A F
1
13
σ
1−
ε
+
ε A
3,
1
2
2
2
4 4 ( T − T )
3,
1
3
1
2
1−
ε
+
ε A
3,
2
3,
2
3
1
+
A F
3
32
1−
ε
+
ε A
2
2
2