# Intensity (heat transfer)

In the field of heat transfer, intensity of radiation $I$ is a measure of the distribution of radiant heat flux per unit area and solid angle, in a particular direction, defined according to

$dq=I\,d\omega \,\cos \theta \,dA$ where

• $dA$ is the infinitesimal source area
• $dq$ is the outgoing heat transfer from the area $dA$ • $d\omega$ is the solid angle subtended by the infinitesimal 'target' (or 'aperture') area $dA_{a}$ • $\theta$ is the angle between the source area normal vector and the line-of-sight between the source and the target areas.

Typical units of intensity are W·m−2·sr−1.

Intensity can sometimes be called radiance, especially in other fields of study.

The emissive power of a surface can be determined by integrating the intensity of emitted radiation over a hemisphere surrounding the surface:

$q=\int _{\phi =0}^{2\pi }\int _{\theta =0}^{\pi /2}I\cos \theta \sin \theta d\theta d\phi$ For diffuse emitters, the emitted radiation intensity is the same in all directions, with the result that

$E=\pi I$ The factor $\pi$ (which really should have the units of steradians) is a result of the fact that intensity is defined to exclude the effect of reduced view factor at large values $\theta$ ; note that the solid angle corresponding to a hemisphere is equal to $2\pi$ steradians.

Spectral intensity $I_{\lambda }$ is the corresponding spectral measurement of intensity; in other words, the intensity as a function of wavelength.