Intensity (heat transfer)

In the field of heat transfer, intensity of radiation I {\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

d q = I d ω cos ⁡ θ d A {\displaystyle dq=I\,d\omega \,\cos \theta \,dA}

where

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

q = ∫ ϕ = 0 2 π ∫ θ = 0 π / 2 I cos ⁡ θ sin ⁡ θ d θ d ϕ {\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

E = π I {\displaystyle E=\pi I}

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

Spectral intensity I λ {\displaystyle I_{\lambda }} is the corresponding spectral measurement of intensity; in other words, the intensity as a function of wavelength.

Intensity (heat transfer)

See also