Consider a cylindrical cavity of diameter D = 100 mm turn and depth L = 50 mm whose sidewall and bottom are diffuse and gray with an emissivity of 0.6 and are at a uniform temperature of 1500 K. The top of the cavity is open and exposed to surroundings that are large and at 300 K. (a) Calculate the net radiation heat transfer from the cavity, treating the bottom and sidewall of the cavity as one surface ( q A ). (b) Calculate the net radiation heat transfer from the cavity, treating the bottom and sidewall of the cavity as two separate surfaces ( q B ). (c) Plot the percentage difference between q A and q B as a function of L over the range 5 mm ≤ L ≤ 100 mm .
Consider a cylindrical cavity of diameter D = 100 mm turn and depth L = 50 mm whose sidewall and bottom are diffuse and gray with an emissivity of 0.6 and are at a uniform temperature of 1500 K. The top of the cavity is open and exposed to surroundings that are large and at 300 K. (a) Calculate the net radiation heat transfer from the cavity, treating the bottom and sidewall of the cavity as one surface ( q A ). (b) Calculate the net radiation heat transfer from the cavity, treating the bottom and sidewall of the cavity as two separate surfaces ( q B ). (c) Plot the percentage difference between q A and q B as a function of L over the range 5 mm ≤ L ≤ 100 mm .
Solution Summary: The diagram for the cylindrical cavity with sidewall and bottom is shown in Figure 1.
Consider a cylindrical cavity of diameter
D
=
100
mm
turn and depth
L
=
50
mm
whose sidewall and bottom are diffuse and gray with an emissivity of 0.6 and are at a uniform temperature of 1500 K. The top of the cavity is open and exposed to surroundings that are large and at 300 K. (a) Calculate the net radiation heat transfer from the cavity, treating the bottom and sidewall of the cavity as one surface (qA). (b) Calculate the net radiation heat transfer from the cavity, treating the bottom and sidewall of the cavity as two separate surfaces (qB). (c) Plot the percentage difference between qAand qBas a function of L over the range
5
mm
≤
L
≤
100
mm
.
Radiation heat transfer Example:
Q1: A large slab of steel 0.1 m thick has in it a 0.1 m-diam hole, with axis normal to
the surface. Considering the sides of the hole to be black, specify the rate of radiative
heat loss from the hole in W. The plate is at 811 K, the surroundings are at 300 K.
A₁
T₁ = 811 k
-D=0.1 m-
A₂
A3
Hole
T
S=0.1 m
Two concentric spheres of diameter Dj = 0.8 mand D2
T1 = 400 K and T2 = 300 K.
= 1.2 m are separated by an air space and have surface temperatures of
(a) If the surfaces are black, what is the net rate of radiation exchange between the spheres, in W?
912
i
(b) What is the net rate of radiation exchange between the surfaces if they are diffuse and gray with e = 0.5 and e2 = 0.05, in W?
912
i
w
(c) What is the net rate of radiation exchange if D2 is increased to 20 m, with &2 = 0.05, ɛ 1
= 0.5, and Di = 0.8 m, in W?
912
w
= 1.0) and with ej = 0.5, D2
= 20 m,
(d) What is the net rate of radiation exchange if the larger sphere behaves as a black body (82
and Di = 0.8 m, in W?
912 =
i
W
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