A radiant heater, which is used for surface treatment processes, consists of a long cylindrical heating element of diameter D 1 = 0.005 m and emissivity ε 1 = 0.80 . The heater is partially enveloped by a long, thin parabolic reflector whose inner and outer surface emissivities are ε 2 i = 0.10 and ε 2 o = 0.80 , respectively. Inner and oilier surface areas per unit length of the reflector are each A ′ 2 i = A ′ 2 o = 0.20 m , and the average convection coefficient for the combined inner and outer surfaces is h ¯ 2 ( i , o ) = 2 W/m 2 ⋅ K . The system may be assumed to be in an infinite, quiescent medium of atmospheric air at T ∞ = 300 K and to be exposed to large surroundings at T sur = 300 K . (a) Sketch the appropriate radiation circuit, and write expressions for each of the network resistances. (b) If, under steady-state conditions, electrical power is dissipated in the heater at P ′ 1 = 1500 W/m and the heater surface temperature is T 1 = 1200 K , what is the net rate at which radiant energy is transferred from the heater? (c) What is the net rate at which radiant energy is transferred from the heater to the surroundings? (d) What is the temperature, T 2 , of the reflector?
A radiant heater, which is used for surface treatment processes, consists of a long cylindrical heating element of diameter D 1 = 0.005 m and emissivity ε 1 = 0.80 . The heater is partially enveloped by a long, thin parabolic reflector whose inner and outer surface emissivities are ε 2 i = 0.10 and ε 2 o = 0.80 , respectively. Inner and oilier surface areas per unit length of the reflector are each A ′ 2 i = A ′ 2 o = 0.20 m , and the average convection coefficient for the combined inner and outer surfaces is h ¯ 2 ( i , o ) = 2 W/m 2 ⋅ K . The system may be assumed to be in an infinite, quiescent medium of atmospheric air at T ∞ = 300 K and to be exposed to large surroundings at T sur = 300 K . (a) Sketch the appropriate radiation circuit, and write expressions for each of the network resistances. (b) If, under steady-state conditions, electrical power is dissipated in the heater at P ′ 1 = 1500 W/m and the heater surface temperature is T 1 = 1200 K , what is the net rate at which radiant energy is transferred from the heater? (c) What is the net rate at which radiant energy is transferred from the heater to the surroundings? (d) What is the temperature, T 2 , of the reflector?
Solution Summary: The author explains the radiation circuit with expressions for each of the network resistances. Energy transfer from the heater is by free convection and radiation
A radiant heater, which is used for surface treatment processes, consists of a long cylindrical heating element of diameter
D
1
=
0.005
m
and emissivity
ε
1
=
0.80
. The heater is partially enveloped by a long, thin parabolic reflector whose inner and outer surface emissivities are
ε
2
i
=
0.10
and
ε
2
o
=
0.80
, respectively. Inner and oilier surface areas per unit length of the reflector are each
A
′
2
i
=
A
′
2
o
=
0.20
m
, and the average convection coefficient for the combined inner and outer surfaces is
h
¯
2
(
i
,
o
)
=
2
W/m
2
⋅
K
. The system may be assumed to be in an infinite, quiescent medium of atmospheric air at
T
∞
=
300
K
and to be exposed to large surroundings at
T
sur
=
300
K
.
(a) Sketch the appropriate radiation circuit, and write expressions for each of the network resistances. (b) If, under steady-state conditions, electrical power is dissipated in the heater at
P
′
1
=
1500
W/m
and the heater surface temperature is
T
1
=
1200
K
, what is the net rate at which radiant energy is transferred from the heater? (c) What is the net rate at which radiant energy is transferred from the heater to the surroundings? (d) What is the temperature, T2, of the reflector?
Imagine you have two concentric, coaxial cylindrical tubes with an evacuated annular space, with equal lengths L. The outer radius of the inner cylinder is r, and the inner radius of the outer cylinder is R. If we want to minimize the self-viewing factor of the inner surface of the outer cylinder, which of the following geometric changes would you suggest?
r is fixed, decrease R with fixed R and L, decrease r
with fixed r and R, decrease L
R is fixed, increase L
r is fixed, increase R
A furnace is of cylindrical shape with a diameter of 1.2 m and a length of 1.2 m. The top surface has an emissivity of 0.70 and is maintained at 500 K. The bottom surface has an emissivity of 0.50 and is maintained at 650 K. The side surface has an emissivity of 0.40. Heat is supplied from the base surface at a net rate of 1400 W. Determine the temperature of the side surface and the net rates of heat transfer between the top and the bottom surfaces, and between the bottom and side surfaces.
A long electrical conductor of 10 mm diameter is concentric with a refrigerated cylindrical tube of 50 mm diameter whose surface has an emissivity of 0.9 and temperature of 27 °C. The electrical conductor has a surface emissivity of 0.6 and dissipates 6.0 W per meter length. Assuming that the space between the two surfaces is empty, calculate the surface temperature of the conductor.
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