Thermal radiation emitted by one surface does not necessarily reach another surface completely. Geometry determines what fraction of the emitted radiation is intercepted.

A view factor $F_{i\to j}$ is the fraction of radiation leaving surface $i$ that reaches surface $j$ directly.

Geometric properties

For an enclosure, the view factors from one surface sum to one:

$$\sum_j F_{i\to j}=1.$$

Two surfaces also obey the reciprocity relation

$$A_iF_{i\to j}=A_jF_{j\to i}.$$

Two black surfaces

For ideal black surfaces exchanging radiation directly, the net transfer from surface 1 toward surface 2 can be written

$$\dot Q_{1\to2}=\sigma A_1F_{1\to2}(T_1^4-T_2^4).$$

Real gray surfaces also reflect radiation, so multiple exchanges between surfaces must be accounted for.

Radiation networks

Emission, reflection and geometric coupling can be organized using radiative-resistance or radiosity methods, analogous in spirit to other network models of transport.

View factors separate the geometry of radiative exchange from the temperature and surface properties that determine emission and absorption.