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:

:$q = \int_^ \int_^{\pi/2} I \cos \theta \sin \theta d\theta d\phi$

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.

See also

* Non-ionising radiation
* Emissivity
* Radiant intensity

References

* Lienhard and Lienhard,
A heat transfer textbook
', 5th Ed, 2019 (available for free online)
* J P Holman, '' Heat Transfer'' 9th Ed, McGraw Hill, 2002.
* F. P. Incropera and D. P. DeWitt, ''Fundamentals of Heat and Mass Transfer'', 4th Ed, Wiley, 1996.

Heat transfer
Radiation