If T s ≈ T s u r in Equation 1.9, the radiation heat transfer coefficient may be approximated as h r , a = 4 ∈ σ T ¯ 3 where T ¯ ≡ ( T s + T s u r ) / 2 . We wish to assess the validity of this approximation by comparing values of h r and h r , a for the following conditions. In each case, represent your results graphically and comment on the validity of the approximation. (a) Consider a surface of either polished aluminum ( ∈ = 0.05 ) or black paint ( ∈ = 0.9 ) , whose temperature may exceed that of the surroundings ( T s u r = 25 ° C ) by 10 to 100°C. Also compare your results with values of the coefficient associated with flee convection in air ( T ∞ = T s u r ) , where h ( W/m 2 ⋅ K ) = 0.98 Δ T 1 / 3 . (b) Consider initial conditions associated with placing a workpiece at T s = 25 ° C in a large furnace whose wall temperature may be varied over the range 100 ≤ T s u r ≤ 1000 ° C . According to the surface finish or coating, its emissivity may assume values of 0.05, 0.2, and 0.9. For each emissivity, plot the relative error, ( h r − h r , a ) / h r , as a function of the furnace temperature.
If T s ≈ T s u r in Equation 1.9, the radiation heat transfer coefficient may be approximated as h r , a = 4 ∈ σ T ¯ 3 where T ¯ ≡ ( T s + T s u r ) / 2 . We wish to assess the validity of this approximation by comparing values of h r and h r , a for the following conditions. In each case, represent your results graphically and comment on the validity of the approximation. (a) Consider a surface of either polished aluminum ( ∈ = 0.05 ) or black paint ( ∈ = 0.9 ) , whose temperature may exceed that of the surroundings ( T s u r = 25 ° C ) by 10 to 100°C. Also compare your results with values of the coefficient associated with flee convection in air ( T ∞ = T s u r ) , where h ( W/m 2 ⋅ K ) = 0.98 Δ T 1 / 3 . (b) Consider initial conditions associated with placing a workpiece at T s = 25 ° C in a large furnace whose wall temperature may be varied over the range 100 ≤ T s u r ≤ 1000 ° C . According to the surface finish or coating, its emissivity may assume values of 0.05, 0.2, and 0.9. For each emissivity, plot the relative error, ( h r − h r , a ) / h r , as a function of the furnace temperature.
Solution Summary: The author compares polished aluminum and black paint to exceed the surrounding temperature and the relation of free convection coefficient. The expression for the approximated values of linearized radiation coefficients is valid within 2% of these conditions.
If
T
s
≈
T
s
u
r
in Equation 1.9, the radiation heat transfer coefficient may be approximated as
h
r
,
a
=
4
∈
σ
T
¯
3
where
T
¯
≡
(
T
s
+
T
s
u
r
)
/
2
. We wish to assess the validity of this approximation by comparing values of
h
r
and
h
r
,
a
for the following conditions. In each case, represent your results graphically and comment on the validity of the approximation. (a) Consider a surface of either polished aluminum
(
∈
=
0.05
)
or black paint
(
∈
=
0.9
)
, whose temperature may exceed that of the surroundings
(
T
s
u
r
=
25
°
C
)
by 10 to 100°C. Also compare your results with values of the coefficient associated with flee convection in air
(
T
∞
=
T
s
u
r
)
, where
h
(
W/m
2
⋅
K
)
=
0.98
Δ
T
1
/
3
. (b) Consider initial conditions associated with placing a workpiece at
T
s
=
25
°
C
in a large furnace whose wall temperature may be varied over the range
100
≤
T
s
u
r
≤
1000
°
C
. According to the surface finish or coating, its emissivity may assume values of 0.05, 0.2, and 0.9. For each emissivity, plot the relative error,
(
h
r
−
h
r
,
a
)
/
h
r
,
as a function of the furnace temperature.
The rate of radiation heat transfer per unit area from a black surface is directly proportional to the fourth power of the absolute temperature of a surface.
A. Boltzmann’s Law
B. Kirchoff’s Law
C. Newton’s Law of Coding
D. Fourier’s Law
At the surface of the sun, the temperature is approximately 5800 K.
How much energy is contained in the electromagnetic radiation filling a cubic meter of space at the sun's surface?
Q#01:a) Define Radiation and give at least 3 examples.b) Define Stefan-Boltzmann Law and emissivity. Is there any surface whose emissivity valueis greater than 1? If no, explain the reason.
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