In radiative heat transfer, a view factor, F A → B {\displaystyle F_{A\rightarrow B}} , is the proportion of the radiation which leaves surface A {\displaystyle A} that strikes surface B {\displaystyle B} . In a complex 'scene' there can be any number of different objects, which can be divided in turn into even more surfaces and surface segments. View factors are also sometimes known as configuration factors, form factors, angle factors or shape factors.
Relations
Summation Radiation leaving a surface within an enclosure is conserved. Because of this, the sum of all view factors from a given surface, S i {\displaystyle S_{i}} , within the enclosure is unity as defined by the summation rule
∑ j = 1 n F S i → S j = 1 {\displaystyle \sum _{j=1}^{n}{F_{S_{i}\rightarrow S_{j}}}=1}
where n {\displaystyle n} is the number of surfaces in the enclosure. Any enclosure with n {\displaystyle n} surfaces has a total n 2 {\displaystyle n^{2}} view factors. For example, consider a case where two blobs with surfaces A and B are floating around in a cavity with surface C. All of the radiation that leaves A must either hit B or C, or if A is concave, it could hit A. 100% of the radiation leaving A is divided up among A, B, and C. Confusion often arises when considering the radiation that arrives at a target surface. In that case, it generally does not make sense to sum view factors as view factor from A and view factor from B (above) are essentially different units. C may see 10% of A's radiation and 50% of B's radiation and 20% of C's radiation, but without knowing how much each radiates, it does not even make sense to say that C receives 80% of the total radiation.
Reciprocity The reciprocity relation for view factors allows one to calculate F i → j {\displaystyle F_{i\rightarrow j}} if one already knows F j → i {\displaystyle F_{j\rightarrow i}} and is given as
A i F i → j = A j F j → i {\displaystyle A_{i}F_{i\rightarrow j}=A_{j}F_{j\rightarrow i}}
where A i {\displaystyle A_{i}} and A j {\displaystyle A_{j}} are the areas of the two surfaces.
Self-viewing For a convex surface, no radiation can leave the surface and then hit it later, because radiation travels in straight lines. Hence, for convex surfaces, F i → i = 0. {\displaystyle F_{i\rightarrow i}=0.}
For concave surfaces, this doesn't apply, and so for concave surfaces F i → i > 0. {\displaystyle F_{i\rightarrow i}>0.}
Superposition The superposition rule (or summation rule) is useful when a certain geometry is not available with given charts or graphs. The superposition rule allows us to express the geometry that is being sought using the sum or difference of geometries that are known.
F 1 → ( 2 , 3 ) = F 1 → 2 + F 1 → 3 . {\displaystyle F_{1\rightarrow (2,3)}=F_{1\rightarrow 2}+F_{1\rightarrow 3}.}
View factors of differential areas
Taking the limit of a small flat surface gives differential areas, the view factor of two differential areas of areas d A 1 {\displaystyle {\hbox{d}}A_{1}} and d A 2 {\displaystyle {\hbox{d}}A_{2}} at a distance s is given by:
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