In the central receiver concept of solar energy collection, a large number of heliostats (reflectors) provide a concentrated solar flux of q s " = 80 , 000 W/m 2 to the receiver, which is positioned at the top of a tower. The receiver wall is exposed to the solar flux at its outer surface and to atmospheric air for which T ∞ , o = 300 K and h o = 25 W/m 2 ⋅ K . The outer sur- face is opaque and diffuse, with a spectral absorptivity of α λ = 0.9 for λ <3 μ m α λ = 0.2 for λ > 3 μ m . The inner surface is exposed to a working fluid (a pressurized liquid) for which T ∞ , i = 700 K and h i = 1000 W/m 2 ⋅ K . The outer surface is also exposed to surroundings for which T s u r = 300 K . If the wall is fabricated from a high-temperature material for which K=15W/m ⋅ K ,what is the minimum thickness L needed to ensure that the outer surface temperature does not exceed T s , o = 1000 K ? What is the collection efficiency associated with this thickness?
In the central receiver concept of solar energy collection, a large number of heliostats (reflectors) provide a concentrated solar flux of q s " = 80 , 000 W/m 2 to the receiver, which is positioned at the top of a tower. The receiver wall is exposed to the solar flux at its outer surface and to atmospheric air for which T ∞ , o = 300 K and h o = 25 W/m 2 ⋅ K . The outer sur- face is opaque and diffuse, with a spectral absorptivity of α λ = 0.9 for λ <3 μ m α λ = 0.2 for λ > 3 μ m . The inner surface is exposed to a working fluid (a pressurized liquid) for which T ∞ , i = 700 K and h i = 1000 W/m 2 ⋅ K . The outer surface is also exposed to surroundings for which T s u r = 300 K . If the wall is fabricated from a high-temperature material for which K=15W/m ⋅ K ,what is the minimum thickness L needed to ensure that the outer surface temperature does not exceed T s , o = 1000 K ? What is the collection efficiency associated with this thickness?
Solution Summary: The author explains the minimum thickness L and the collection efficiency associated with this thickness.
In the central receiver concept of solar energy collection, a large number of heliostats (reflectors) provide a concentrated solar flux of
q
s
"
=
80
,
000
W/m
2
to the receiver, which is positioned at the top of a tower.
The receiver wall is exposed to the solar flux at its outer surface and to atmospheric air for which
T
∞
,
o
=
300
K
and h
o
=
25
W/m
2
⋅
K
. The outer sur- face is opaque and diffuse, with a spectral absorptivity of
α
λ
=
0.9
for
λ
<3
μ
m
α
λ
=
0.2
for
λ
>
3
μ
m
. The inner surface is exposed to a working fluid (a pressurized liquid) for which
T
∞
,
i
=
700
K
and h
i
=
1000
W/m
2
⋅
K
. The outer surface is also exposed to surroundings for which
T
s
u
r
=
300
K
. If the wall is fabricated from a high-temperature material for which
K=15W/m
⋅
K
,what is the minimum thickness L needed to ensure that the outer surface temperature does not exceed
T
s
,
o
=
1000
K
? What is the collection efficiency associated with this thickness?
PROBLEM 3.23
3.23 Under normal operating condi-
tions a motor exerts a torque of
magnitude TF at F. The shafts
are made of a steel for which
the allowable shearing stress is
82 MPa and have diameters of
dCDE=24 mm and dFGH = 20
mm. Knowing that rp = 165
mm and rg114 mm, deter-
mine the largest torque TF
which may be exerted at F.
TF
F
rG-
rp
B
CH
TE
E
1. (16%) (a) If a ductile material fails under pure torsion, please explain the failure
mode and describe the observed plane of failure.
(b) Suppose a prismatic beam is subjected to equal and opposite couples as shown
in Fig. 1. Please sketch the deformation and the stress distribution of the cross
section.
M
M
Fig. 1
(c) Describe the definition of the neutral axis.
(d) Describe the definition of the modular ratio.
using the theorem of three moments, find all the moments, I only need concise calculations with minimal explanations. The correct answers are provided at the bottom
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