Planck’s Law of Radiation
Total heat transfer consists of radiation at different frequencies. The distribution of radiation energy in a spectrum and its dependency on temperature is determined from Planck’s law of radiation. Mmj, and MmA are the spectral radiation intensities for a blackbody:
|
2 irb V |
3 |
= f(v, T) |
(4.202) |
^■mv |
Nu, A. 103.3X0.60^ D 0.015 |
W m^ K |
= 4100 |
1.0*? x 0.015m x 1000 |
Re = id = = V rj |
-SI — = 1.32 x 10 |
3 kg ms 4200 |
1.14 • 10" |
Pj* = V^t> — 1.14 x 10 |
= 7.98 |
W m K |
0.6 |
The flow is turbulent, Re > 2300, and thus the part of Eq. (4.201) that considers the inlet flow region ~ 1 can be ignored. |
/ j2/3-i/ „ >0.14 L Vw V / -* V / |
Nud = 0.037(Re°’75 — 180)Pr0’42 |
1 + |
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( AT |
Exp |
He AT |
Exp |
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HEAT AND MASS TRANSFER
Where
H = Planck’s constant = 3.99028 x 10~7 J s/kmol = 6.62.52 x 10~34 j s
C = velocity of light = 2.9979 x 108 m/s
Cv = first radiation constant = Inhc1 = 3.7415 x 10~16 W m2
MJ Kmol |
Second radiation constant = be = 119.626 |xm
14387.9 jim K
When these are derived with respect to the wavelength, and the wavelength value, with the maximum value of radiation intensity, is solved for, the result is Wien’s law:
Amax • T = constant
= 2898 |xm K 24 093 |i, m kj/kmol
(4.204) |
Max
According to Wien’s law, the wavelength representing the maximum point decreases with increasing temperature (Fig. 4.29).
The visible region of the spectrum lies between the wavelengths of 0.4 and 0.7 ixm. When the temperature of a body is increased, its color changes toward smaller wavelengths—in other words, from the red region of the spectrum to the blue region.
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