Summation rule, radiation

For a given geometry, view factors are related to each other, one example being the reciprocity relationship given in equation 9.126. Another important relationship is the summation rule which may be applied to the surfaces of a complete enclosure. In this case, all the radiation leaving one surface, say i, must arrive at all other surfaces in the enclosure so that, for n surfaces ... 

This means that the sum of the exchange areas associated with a surface in an enclosure must be same as the area of that surface. The principle of the summation rule may be extended to other geometries such as, for example, radiation from a vertical rectangle (area 1) to an adjacent horizontal rectangle (area 2), as shown in Figure 9.40iii, where they are joined to a second horizontal rectangle of the same width (area 3). In effect area 3 is an extension of area 2 but has a different view factor. 

The conservation of energy principle requires that the entire radiation leaving any surface i of an enclosure be intercepted by the surfaces of the enclosure. Therefore, t/ie svru of the view factors from surface i of an enclosure to all surfaces of the enclositne, including to itself, must equal unity. This is known as the summation rule for an enclosure and is expressed as (Fig. 13-9)... 

A simple example for the application of the relationships (5.132) and (5.133) is provided by radiation in an enclosure formed by two spherical surfaces 1 and 2, Fig. 5.52. There are four view factors in this case, l) i. fqo, Toi and F22 The summation rule is applied to the inner sphere in order to calculate them ... 

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