A long cylindrical healer element of diameter D = 10 mm , temperature T 1 = 1500 K and emissivity ε 1 = 1 is used in a furnace. The bottom area A 2 is a diffuse, gray surface with ε 2 = 0.6 and is maintained at T 2 = 500 K . The side and top walls are fabricated from an insulating, refractory brick that is diffuse and gray with ε = 0.9 . The length of the furnace normal to the page is very large compared to the width w and height h . Neglecting convection and treating the furnace walls as isothermal, determine the power per unit length that must be provided to the healing element to maintain steady-state conditions. Calculate the temperature of the furnace wall.
A long cylindrical healer element of diameter D = 10 mm , temperature T 1 = 1500 K and emissivity ε 1 = 1 is used in a furnace. The bottom area A 2 is a diffuse, gray surface with ε 2 = 0.6 and is maintained at T 2 = 500 K . The side and top walls are fabricated from an insulating, refractory brick that is diffuse and gray with ε = 0.9 . The length of the furnace normal to the page is very large compared to the width w and height h . Neglecting convection and treating the furnace walls as isothermal, determine the power per unit length that must be provided to the healing element to maintain steady-state conditions. Calculate the temperature of the furnace wall.
Solution Summary: The author explains the power per unit length that must be provided to the heating element to maintain steady state condition, and the temperature of the furnace wall.
A long cylindrical healer element of diameter
D
=
10
mm
, temperature
T
1
=
1500
K
and emissivity
ε
1
=
1
is used in a furnace. The bottom area A2is a diffuse, gray surface with
ε
2
=
0.6
and is maintained at
T
2
=
500
K
. The side and top walls are fabricated from an insulating, refractory brick that is diffuse and gray with
ε
=
0.9
. The length of the furnace normal to the page is very large compared to the width w and height h.
Neglecting convection and treating the furnace walls as isothermal, determine the power per unit length that must be provided to the healing element to maintain steady-state conditions. Calculate the temperature of the furnace wall.
Two parallel gray planes that are very large have emissivities of ε1 = 0.8 and ε2 = 0.7; surface 1 is at 1100°F (866.5 K) and surface 2 is at 600°F (588.8 K). Use SI units for the following:
(a) What is the net radiation from 1 to 2?
(b) If the surfaces are both black, what is the net radiation?
Two concentric spheres of diameter D1= 0.9 m and D2= 1.2 m are separated by an air space and have surface temperatures of T1= 400 K and T2= 300 K. (a) If the surfaces are black, what is the net rate of radiation exchange between the spheres, in W? q12= Enter your answer for part (a) in accordance to the question statement W (b) What is the net rate of radiation exchange between the surfaces if they are diffuse and gray with ε1= 0.5 and ε2= 0.05, in W? q12= Enter your answer for part (b) in accordance to the question statement W (c) What is the net rate of radiation exchange if D2 is increased to 20 m, with ε2= 0.05, ε1= 0.5, and D1= 0.9 m, in W? q12= Enter your answer for part (c) in accordance to the question statement W (d) What is the net rate of radiation exchange if the larger sphere behaves as a black body (ε2= 1.0) and with ε1= 0.5, D2= 20 m, and D1= 0.9 m, in W? q12= Enter your answer for part(d) in accordance to the question statement W
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