The black body radiation in heat transfer has1. four laws, Stefan-Boltzmann law, Planck's law, Wine Displacement law, and Kirchhoff's Law.
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1. Stefan-Boltzmann Law
It states that the total energy emitted per unit area per unit of time by a black body is directly proportional to the fourth power of its absolute temperature.
Eb = T⁴ -----1.9
Eb = σ• T⁴
Where
T = Temperature in K
σ = Steafan-Boltzmann constant
= 5.67x10̄ ⁶ W/ m²•K⁴
For a non-black body
E/Eb = e ------2.0
E = e•Eb --------3.0
Combining equations 1.0 and 3.0, we get
E = e • σ• T⁴
Where e is the emissivity of this non-black body.
The Stefan-Boltzmann equation is a fundamental relation for all the radiant energy transfer calculations.
2. Planck's law of thermal radiation
This law gives a relationship between the monochromatic emissive power of a black body's absolute temperature and the corresponding wavelength. Planck radiation law derivation.
Eb, λ = 2πhc²λᐨ⁵/(ehc/kλT - 1) ------4.0
Where
Eb,λ is the monochromatic emissive power of the black body/black surface, W/m²•μm, h is the Plancks constant, K is the Boltzmann constant, c is the speed of light, T is the absolute temperature and λ is the wavelength of radiation.
Equation 4.0 can be written as
Eb λ = C₁λ ̄⁵ / (e C₂/λT - 1)
Where C₁ and C₂ are constants
C₁ = 3.472x10 ᐨ¹⁶ W.m² and C₂ = 0.01439 m.K
3. Wiens Displacement law
It states that the wavelength at which the maximum monochromatic emissive power is obtained (i.e. λmax) is inversely proportional to the absolute temperature, or Wien's radiation law formula.
T λmax = C
When λmax is in micrometers and T is in Kelvins, the value of Wiens constant C is equal to 2890.
Take these Notes is, Orginal Sources: Unit Operations-II, KA Gavhane