The lower side of a 400-mm-diameter disk is heated by an electric furnace, while the upper side is exposed to quiescent, ambient air and surroundings at 300 K. The radiant furnace (negligible convection) is of circular construction with the bottom surface ( ε 1 = 0.6 ) and cylindrical side surface ( ε 2 = 1.0 ) maintained at T 1 = T 2 = 500 K . The surface of the disk facing the radiant furnace is black ( ε d , 1 = 1.0 ) while the upper surface has an emissivity of ε d , 2 = 0.8 . Assume the plate and furnace surfaces to be diffuse and gray. (a) Determine the net heat transfer rate to the disk, q net , d when T d = 400 K . (b) Plot q net , d as a function of the disk temperature for 300 ≤ T d ≤ 500 K , with all other conditions remaining the same. What is the steady−state temperature of the disk?
The lower side of a 400-mm-diameter disk is heated by an electric furnace, while the upper side is exposed to quiescent, ambient air and surroundings at 300 K. The radiant furnace (negligible convection) is of circular construction with the bottom surface ( ε 1 = 0.6 ) and cylindrical side surface ( ε 2 = 1.0 ) maintained at T 1 = T 2 = 500 K . The surface of the disk facing the radiant furnace is black ( ε d , 1 = 1.0 ) while the upper surface has an emissivity of ε d , 2 = 0.8 . Assume the plate and furnace surfaces to be diffuse and gray. (a) Determine the net heat transfer rate to the disk, q net , d when T d = 400 K . (b) Plot q net , d as a function of the disk temperature for 300 ≤ T d ≤ 500 K , with all other conditions remaining the same. What is the steady−state temperature of the disk?
Solution Summary: The author explains the energy balance on the disc that identifies: q_rad, net radiation exchange between the surroundings and the disk.
The lower side of a 400-mm-diameter disk is heated by an electric furnace, while the upper side is exposed to quiescent, ambient air and surroundings at 300 K. The radiant furnace (negligible convection) is of circular construction with the bottom surface
(
ε
1
=
0.6
)
and cylindrical side surface
(
ε
2
=
1.0
)
maintained at
T
1
=
T
2
=
500
K
. The surface of the disk facing the radiant furnace is black
(
ε
d
,
1
=
1.0
)
while the upper surface has an emissivity of
ε
d
,
2
=
0.8
. Assume the plate and furnace surfaces to be diffuse and gray.
(a) Determine the net heat transfer rate to the disk,
q
net
,
d
when
T
d
=
400
K
. (b) Plot
q
net
,
d
as a function of the disk temperature for
300
≤
T
d
≤
500
K
, with all other conditions remaining the same. What is the steady−state temperature of the disk?
Problem 2: A black body of total area 0.045 m² is completely enclosed in a space bounded by 5 cm
thick walls. The walls have a surface area 0.5 m² and thermal conductivity 1.07 W/m-deg. If the inner
surface of the enveloping wall is to be maintained at 215°C and the outer wall surface is at 30°C,
calculate the temperature of the black body. Neglect the difference between inner and outer surfaces
areas of enveloping material. Note: Under steady condition, the heat conducted through the wall must
eaqual to the net radiation loss from the black body.
Ans. 955.9 K
Radiation. A black body of total area 0.054m? is completely enclosed in a space bounded by 57 mm
thick walls. The walls have a surface area 0.5 m² and thermal conductivity 1.05W/m.K. If the inner
surface of the enveloping wall is to be maintained at 185°C and the outer wall surface is at 25°C,
calculate the temperature of the black body. Neglect the difference between inner and outer surfaces
areas of enveloping material. Stefan-Boltzmann constant o = 5.67x10* W/m²K'.Note: Under steady
condition, the heat conducted through the wall must equal to the net radiation loss from the black body.
Question #9
A circular ceramic plate that can be modelled as a blackbody is being heated by an electrical
heater. The plate is 30cm in diameter and is situated in a surrounding ambient temperature
of 15°C where the natural convection heat transfer coefficient is 12W/m² K. The efficiency
of the electrical heater to transfer heat to the plate is 80%, the electric power is required
such that the heater needs to keep the surface temperature of the plate at 200°C.
Ambient 15°C Tsurr = 15°C
h = 12 W/m².K
Ceramic plate
-T₂ = 200°C
Welec
(A) Determine the heat emitted from the plate, as a blackbody.
(B) Determine the radiation incident on the plate from the surroundings.
(C) Determine the heat transfer from the plate to the surroundings.
(D) Determine the required electric power.
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