Intensity (heat transfer) explained

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 todq = 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 ^{2 \pi} _{\phi =0} \int ^{\pi/ 2} _{\theta =0} 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 _{λ} 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.