A composite wall is comprised of two large plates separated by sheets of refractory insulation, as shown in the schematic. In the installation process, the sheets of thickness L = 50 mm and thermal conductivity k = 0.05 W/m ⋅ K are separated at 1-m intervals by gaps of width w = 10 mm . The hot and cold plates have temperatures and emissivities of T 1 = 400 ° C , ε 1 = 0.85 and T 2 = 35 ° C , ε 2 = 0.5 , respectively. Assume that the plates and insulation are diffuse-gray surfaces. (a) Determine the heat loss by radiation through the gap per unit length of the composite wall (normal to the page). (b) Recognizing that the gaps are located on a 1-m spacing, determine what fraction of the total heat loss through the composite wall is due to transfer by radiation through the insulation gap.
A composite wall is comprised of two large plates separated by sheets of refractory insulation, as shown in the schematic. In the installation process, the sheets of thickness L = 50 mm and thermal conductivity k = 0.05 W/m ⋅ K are separated at 1-m intervals by gaps of width w = 10 mm . The hot and cold plates have temperatures and emissivities of T 1 = 400 ° C , ε 1 = 0.85 and T 2 = 35 ° C , ε 2 = 0.5 , respectively. Assume that the plates and insulation are diffuse-gray surfaces. (a) Determine the heat loss by radiation through the gap per unit length of the composite wall (normal to the page). (b) Recognizing that the gaps are located on a 1-m spacing, determine what fraction of the total heat loss through the composite wall is due to transfer by radiation through the insulation gap.
Solution Summary: The author analyzes the heat loss by radiation through the gap per unit length of the composite wall. The temperature of hot plate is T_1=400°C.
A composite wall is comprised of two large plates separated by sheets of refractory insulation, as shown in the schematic. In the installation process, the sheets of thickness
L
=
50
mm
and thermal conductivity
k
=
0.05
W/m
⋅
K
are separated at 1-m intervals by gaps of width
w
=
10
mm
. The hot and cold plates have temperatures and emissivities of
T
1
=
400
°
C
,
ε
1
=
0.85
and
T
2
=
35
°
C
,
ε
2
=
0.5
, respectively. Assume that the plates and insulation are diffuse-gray surfaces.
(a) Determine the heat loss by radiation through the gap per unit length of the composite wall (normal to the page). (b) Recognizing that the gaps are located on a 1-m spacing, determine what fraction of the total heat loss through the composite wall is due to transfer by radiation through the insulation gap.
A composite wall is comprised of two large plates separated by sheets of refractory insulation. In the
installation process, the sheets of thickness L = 50 mm and thermal conductivity k = 0.05 W/mK are separated at
1-m intervals by gaps of width w = 10 mm. The hot and cold plates have temperatures and emissivities of T1 =
400 deg C, emissivity1 = 0.85 and T2 = 35 deg C, emissivity2 = 0.5, respectively. Assume that the plates and
insulation are diffuse-gray surfaces.
%3D
Determine the heat loss by radiation through the gap per unit length of the composite wall (normal
to the page).
Recognizing that the gaps are located on a 1-m spacing, determine what fraction of the total heat
loss through the composite wall is due to transfer by radiation through the insulation gap.
Hot side
Gap
w = 10 mm
A. 47 W/m, 9.2%
T1
= 400°C
B. 47 W/m, 10.2%
L = 50 mm
C. 37 W/m, 10.2%
D. 37 W/m, 9.2%
T2 = 35°C
Cold side
1 m
Insulation, k = 0.05 W/m-K
Consider a silicon wafer positioned in a furnace that is zone-heated on the top section and cooled on the
lower section. The wafer is placed such that the top and bottom surfaces of the wafer exchange radiation
with the hot and cold zones respectively of the furnace. The zone temperatures are Tsur,h = 1050 K and
Tsur.e = 330 K. The emissivity and thickness of the wafer are e = 0.65 and d = 0.78 mm, respectively.
With the ambient gas at T. = 700 K, convection heat transfer coefficients at the upper and lower
surfaces of the wafer are 8 and 4 W/m²-K. Find the steady-state temperature of the wafer, in K.
Tw
i
K
Consider a silicon wafer positioned in a furnace that is zone-heated on the top section and cooled on the lower section. The wafer is
placed such that the top and bottom surfaces of the wafer exchange radiation with the hot and cold zones respectively of the furnace.
The zone temperatures are Tsur.h = 900 K and Tsur.c = 330 K. The emissivity and thickness of the wafer are ɛ = 0.65 and d = 0.78
mm, respectively. With the ambient gas at T, = 700 K, convection heat transfer coefficients at the upper and lower surfaces of the
wafer are 8 and 4 W/m2-K. Find the steady-state temperature of the wafer, in K.
Tw
i
K
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