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.