Intensity (heat transfer)

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

${\displaystyle dq=I\,d\omega \,\cos \theta \,dA}$

where

• ${\displaystyle dA}$ is the infinitesimal source area
• ${\displaystyle dq}$ is the outgoing heat transfer from the area ${\displaystyle dA}$
• ${\displaystyle d\omega }$ is the solid angle subtended by the infinitesimal 'target' (or 'aperture') area ${\displaystyle dA_{a}}$
• ${\displaystyle \theta }$ 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:

${\displaystyle q=\int _{\phi =0}^{2\pi }\int _{\theta =0}^{\pi /2}I\cos \theta \sin \theta d\theta d\phi }$

For diffuse emitters, the emitted radiation intensity is the same in all directions, with the result that

${\displaystyle E=\pi I}$

The factor ${\displaystyle \pi }$ (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 ${\displaystyle \theta }$; note that the solid angle corresponding to a hemisphere is equal to ${\displaystyle 2\pi }$ steradians.

Spectral intensity ${\displaystyle I_{\lambda }}$ 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.