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.

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.