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=Idωcos⁡θdA

where

* dA is the infinitesimal source area
* dq is the outgoing heat transfer from the area dA
* dω is the solid angle subtended by the infinitesimal 'target' (or 'aperture') area dAa
* θ 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=∫ϕ=02π∫θ=0π/2Icos⁡θsin⁡θdθdϕ

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

E=πI

The factor π (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 θ; note that the solid angle corresponding to a hemisphere is equal to 2π steradians.

Spectral intensity Iλ 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.

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