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