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# View factor

In Radiative heat transfer, a view factor $F_{A \rarr B}$ is the proportion of all that radiation which leaves surface A and strikes surface B.

In a complex 'scene' there can be any number of different objects, which can be divided in turn in to even more surfaces and surface segments.

View factors are also sometimes known as configuration factors, form factors or shape factors.

## Summation of view factors

Because all of the radiation leaving a surface is a fixed amount, one can add up all of the view factors from a given surface Si, and they will always add up to one:

$\sum_{j=1 ... n} {F_{S_i \rarr S_j}} = 1$

For example, consider a case where two blobs, 'A' and 'B' are floating around in a cavity 'C'. All the radiation that leaves surface A must either hit surface B or the cavity surface C, or if the surface A is concave, might again hit A. In terms of fractions, 100% of the radiation leaving surface A is divided up between surfaces A, B, and C, which is equivalent to the expression above.

Confusion often arises when considering the radiation that arrives at a target surface. In that case there, summation of view factors does not apply, because each 'incoming' view factor is a fraction of the radiation leaving some other surface: there is no reason for those fractions to add up to anything at all; in fact they can add up to less than one, or many times one, but this value has no significance.

## Self-viewing surfaces

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, $F_{A \rarr A} = 0$

For concave surfaces, this doesn't apply, and so for concave surfaces $F_{A \rarr A} > 0$

## Reciprocity

The reciprocity theorem for view factors allows one to calculate $F_{B \rarr A}$ if one already knows $F_{A \rarr B}$. Using the areas of the two surfaces AA and AB,

$A_A F_{A \rarr B} = A_B F_{B \rarr A}$

## View factors in a triangle

For a triangle with sides of length a, b and c, the view factor $F_{a \rarr b}$ is given by

$F_{a \rarr b} = \frac {a+b-c} {2a}$

## Hottel's Crossed String Rule

The crossed string rule allows calculation of radiation transfer between opposite sides of a quadrilateral, and furthermore applies in some cases where there is partial obstruction between the objects. For a derivation and further details, see this article by G H Derrick.