2.4 Thermal radiation

2.4.1 Basics

This in depth chapter abouth thermal radiation is an extension of the basics. Please make sure you've read and understand the basics section.

First, the basic equations for radiative heat exchange are introduced and then the following two methods are presented:


Thermal radiation is an important factor in the heat transfer between objects. The interplay of energy exchange is described in the following sections.


These fractions are related by:

According to Kirchhoff’s law this emitted radiation at a given wavelength (ελ) is equal to the absorptivity

The rate at which energy is radiated from a black body is proportional to the fourth power of its absolute temperature, according to the Stefan-Boltzmann law: 

The distribution of emissive power of a black body of a certain temperature is given by Planck’s distribution rule:

The wavelength of the maximum flux of this curve can be expressed with Wien’s displacement law:

The emissivity ελ is the radiated heat flux of a certain body and wavelength in comparison with a black body.

It is common to use the weighted average of the emissivity and absorptivity over the entire Planck curve of the ‘gray’ body at a certain temperature. For the infrared radiation of a body near room temperature this fraction is called emissivity ε. The absorbtivity of this body at room-temperature is the same and therefore also the same symbol is commonly used.

The emissive power of a grey body can therefore be written as:

The fraction α is commonly used for the fraction of the absorbed (or emitted) radiation near the solar temperature (5671 K).