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.
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
A 3-in-diameter cylindrical wire is coated in 3 inches of polyethylene insulation. The wire can be modeled as a grey body with an emissivity of .85. Due to the electrical resistance, the wire is at a temperature of 300 degrees Celsius. The insulation is also a great body with an emissivity of .95, at a temperature of 40 degrees Celsius. (Assume F12=1). What is the heat flux (W/m^2) of the energy going from the wire to the insulation?
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