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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


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.

See also

A large number of 'standard' view factors can be calculated with the use of tables that are commonly provided in heat transfer textbooks.

  • list of view factors for specific geometry cases
  • Radiosity, a matrix calculation method for solving radiation transfer between a number of bodies.
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "View_factor". A list of authors is available in Wikipedia.
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