A circular metal disk having a diameter of 0.4 m is placed firmly against the ground in a barren horizontal region where the earth is at a temperature of 280 K. The effective sky temperature is also 280 K. The disk is exposed to quiescent ambient air at 300 K and direct solar irradiation of 745 W/m 2 . The surface of the disk is diffuse with ε λ = 0.9 for 0< λ <1 μ m and ε λ = 0.2 for 0>1 μ m . After some time has elapsed, the disk achieves a uniform, steady-state temperature. The thermal conductivity of the soil is 0 .52 W/m ⋅ K . (a) Determine the fraction of the incident solar irradiation that is absorbed. (b) What is the emissivity of the disk surface? (c) For a steady-state disk temperature of 340K, employ a suitable correlation to determine the average free convection heat transfer coefficient at the upper surface of the disk. (d) Show that a disk temperature of 340K does indeed yield a steady-state condition for the disk
A circular metal disk having a diameter of 0.4 m is placed firmly against the ground in a barren horizontal region where the earth is at a temperature of 280 K. The effective sky temperature is also 280 K. The disk is exposed to quiescent ambient air at 300 K and direct solar irradiation of 745 W/m 2 . The surface of the disk is diffuse with ε λ = 0.9 for 0< λ <1 μ m and ε λ = 0.2 for 0>1 μ m . After some time has elapsed, the disk achieves a uniform, steady-state temperature. The thermal conductivity of the soil is 0 .52 W/m ⋅ K . (a) Determine the fraction of the incident solar irradiation that is absorbed. (b) What is the emissivity of the disk surface? (c) For a steady-state disk temperature of 340K, employ a suitable correlation to determine the average free convection heat transfer coefficient at the upper surface of the disk. (d) Show that a disk temperature of 340K does indeed yield a steady-state condition for the disk
Solution Summary: The author calculates the tion of the incident solar irradiation that is absorbed, and the emissivity for the disk surface.
A circular metal disk having a diameter of 0.4 m is placed firmly against the ground in a barren horizontal region where the earth is at a temperature of 280 K. The effective sky temperature is also 280 K. The disk is exposed to quiescent ambient air at 300 K and direct solar irradiation of
745
W/m
2
. The surface of the disk is diffuse with
ε
λ
=
0.9
for 0<
λ
<1
μ
m and
ε
λ
=
0.2
for 0>1
μ
m
. After some time has elapsed, the disk achieves a uniform, steady-state temperature. The thermal conductivity of the soil is
0
.52 W/m
⋅
K
.
(a) Determine the fraction of the incident solar irradiation that is absorbed.
(b) What is the emissivity of the disk surface?
(c) For a steady-state disk temperature of 340K, employ a suitable correlation to determine the average free convection heat transfer coefficient at the upper surface of the disk.
(d) Show that a disk temperature of 340K does indeed yield a steady-state condition for the disk
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