Electrical conductors, in the form of parallel plates of length L = 40 mm , have one edge mounted to a ceramic insulated base and are spaced a distance w = 10 mm apart. The plates are exposed to large isothermal surroundings at T sur = 300 K . The conductor (1) and ceramic (2) surfaces are diffuse and gray with emissivities of ε 1 = 0.8 and ε 2 = 0.6 , respectively. For a prescribed operating current in the conductors, their temperature is T 1 = 500 K . (a) Determine the electrical power dissipated in a conductor plate per unit length, q ′ 1 , considering only radiation exchange. What is the temperature of the insulated base, T 2 ? (b) Determine q ′ 1 and T 2 when the surfaces experience convection with an airstream at 300 K and a convection coefficient of h = 25 W/m 2 ⋅ K .
Electrical conductors, in the form of parallel plates of length L = 40 mm , have one edge mounted to a ceramic insulated base and are spaced a distance w = 10 mm apart. The plates are exposed to large isothermal surroundings at T sur = 300 K . The conductor (1) and ceramic (2) surfaces are diffuse and gray with emissivities of ε 1 = 0.8 and ε 2 = 0.6 , respectively. For a prescribed operating current in the conductors, their temperature is T 1 = 500 K . (a) Determine the electrical power dissipated in a conductor plate per unit length, q ′ 1 , considering only radiation exchange. What is the temperature of the insulated base, T 2 ? (b) Determine q ′ 1 and T 2 when the surfaces experience convection with an airstream at 300 K and a convection coefficient of h = 25 W/m 2 ⋅ K .
Solution Summary: The diagram shows the electrical power dissipated in a conductor per unit length, and the temperature of the isothermal surrounding.
Electrical conductors, in the form of parallel plates of length
L
=
40
mm
, have one edge mounted to a ceramic insulated base and are spaced a distance
w
=
10
mm
apart. The plates are exposed to large isothermal surroundings at
T
sur
=
300
K
. The conductor (1) and ceramic (2) surfaces are diffuse and gray with emissivities of
ε
1
=
0.8
and
ε
2
=
0.6
, respectively. For a prescribed operating current in the conductors, their temperature is
T
1
=
500
K
.
(a) Determine the electrical power dissipated in a conductor plate per unit length,
q
′
1
, considering only radiation exchange. What is the temperature of the insulated base, T2? (b) Determine
q
′
1
and T2when the surfaces experience convection with an airstream at 300 K and a convection coefficient of
h
=
25
W/m
2
⋅
K
.
A long conduit is constructed with diffuse, gray walls 0.5 m wide. The top and bottom of the conduit are insulated. The emissivities of
the walls are ₁ = 0.45,₂ = 0.65, and 3 = 0.15, respectively, while the temperatures of walls 1 and 2 are 500 K and 725 K.
respectively.
A₁ T₁ -
-A₂, T₂, 2
(a) Determine the temperature of the insulated walls, in K.
(b) Determine the net radiation heat rate from surface 2 per unit conduit length, in W/m.
Determine the net heat transfer by radiation between two gray surfaces, A (εA= 0.90) andB (εB= 0.25) at temperatures 500°C and 200°C, respectively if a. surfaces are infinite parallel planes b. surface A is a spherical shell 3 m in diameter and surface B is a similar shell concentric with A and 0.3 m in diameter c. surfaces A and B concentric cylindrical tubes with diameters of 300 mm and 275 mm, respectively d. both surfaces are squares 2 m × 2
Define the absorption of radiation incident on an opaque surface of absorptivity α.
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