Thermal radiation is one of the three principal mechanisms of
heat transfer. It entails the emission of a spectrum of electromagnetic radiation due to an object's temperature. Other mechanisms are
convection and
conduction.
Electromagnetic waves Thermal radiation is characteristically different from conduction and convection in that it does not require a medium and, in fact it reaches maximum
efficiency in a
vacuum. Thermal radiation is a type of
electromagnetic radiation which is often modeled by the propagation of waves. These waves have the standard wave properties of frequency, \nu and
wavelength, \lambda which are related by the equation \lambda=\frac{c}{\nu} where c is the speed of light in the medium.
Irradiation Thermal irradiation is the rate at which radiation is incident upon a surface per unit area. (meaning the term "black body" does not always correspond to the visually perceived color of an object). These materials that do not follow the "black color = high emissivity/absorptivity" caveat will most likely have functional spectral emissivity/absorptivity dependence. Only truly
gray systems (relative equivalent emissivity/absorptivity and no directional transmissivity dependence in
all control volume bodies considered) can achieve reasonable steady-state heat flux estimates through the Stefan-Boltzmann law. Encountering this "ideally calculable" situation is almost impossible (although common engineering procedures surrender the dependency of these unknown variables and "assume" this to be the case). Optimistically, these "gray" approximations will get close to real solutions, as most divergence from Stefan-Boltzmann solutions is very small (especially in most
standard temperature and pressure lab controlled environments).
Reflectivity Reflectivity deviates from the other properties in that it is bidirectional in nature. In other words, this property depends on the direction of the incident of radiation as well as the direction of the reflection. Therefore, the reflected rays of a radiation spectrum incident on a real surface in a specified direction forms an irregular shape that is not easily predictable. In practice, surfaces are often assumed to reflect either in a perfectly specular or a diffuse manner. In a
specular reflection, the angles of reflection and incidence are equal. In
diffuse reflection, radiation is reflected equally in all directions. Reflection from smooth and polished surfaces can be assumed to be specular reflection, whereas reflection from rough surfaces approximates diffuse reflection. Blackbodies are idealized surfaces that act as the perfect absorber and emitter. It is given by
Planck's law per unit wavelength as: I_{\lambda,b}(\lambda,T)=\frac{2 h c^2}{\lambda^5}\cdot\frac1{e^{hc/k_{\rm B}T\lambda}-1} This formula mathematically follows from calculation of spectral distribution of energy in
quantized electromagnetic field which is in complete
thermal equilibrium with the radiating object. Planck's law shows that radiative energy increases with temperature, and explains why the peak of an emission spectrum shifts to shorter wavelengths at higher temperatures. It can also be found that energy emitted at shorter wavelengths increases more rapidly with temperature relative to longer wavelengths. The equation is derived as an infinite sum over all possible frequencies in a semi-sphere region. The energy, E=h \nu, of each photon is multiplied by the number of states available at that frequency, and the probability that each of those states will be occupied.
Stefan-Boltzmann law The Planck distribution can be used to find the spectral emissive power of a blackbody, E_{\lambda,b} as follows, E_{\lambda, b}=\pi I_{\lambda,b}. The total emissive power of a blackbody is then calculated as, E_b=\int_0^\infty \pi I_{\lambda, b}d\lambda. The solution of the above integral yields a remarkably elegant equation for the total emissive power of a blackbody, the
Stefan-Boltzmann law, which is given as, E_b=\sigma T^4 where \sigma is the
Steffan-Boltzmann constant.
Wien's displacement law . Although this shows relatively high temperatures, the same relationships hold true for any temperature down to absolute zero. The wavelength \lambda \, for which the emission intensity is highest is given by Wien's displacement law as: \lambda_\text{max} = \frac{b}{T}
Constants Definitions of constants used in the above equations:
Variables Definitions of variables, with example values:
Emission from non-black surfaces For surfaces which are not black bodies, one has to consider the (generally frequency dependent) emissivity factor \epsilon(\nu). This factor has to be multiplied with the radiation spectrum formula before integration. If it is taken as a constant, the resulting formula for the power output can be written in a way that contains \epsilon as a factor: P = \epsilon \sigma A T^4 This type of theoretical model, with frequency-independent emissivity lower than that of a perfect black body, is often known as a
grey body. For frequency-dependent emissivity, the solution for the integrated power depends on the functional form of the dependence, though in general there is no simple expression for it. Practically speaking, if the emissivity of the body is roughly constant around the peak emission wavelength, the gray body model tends to work fairly well since the weight of the curve around the peak emission tends to dominate the integral. ==Heat transfer between surfaces==