Intensity (heat transfer)

For other uses, see Intensity (disambiguation).

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.

References

Lienhard and Lienhard, A heat transfer textbook, 3rd Ed, 2008 (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.

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Intensity (heat transfer)

See also

References