View factor superposition rule

Sometimes the view factor associated with a given geometry is not available in standard tables and charts. In such cases, it is desirable to express the given geometry as the sum or difference of some geometries with known view factors, and then to apply the superposition rule, which can be expressed as the view factor fivm a surface i to a surface j is equal to the sum of the view factors from surface i to the parts of surface j. Note that the reverse of this is not true. That is, the view factor from a surface j to a surface i is not equal to the sum of the view factors from the parts of surface j to surface i. 

Suppose we need to find the view factor F, j. A quick check of the view factor exprcs.sions and charts in this section reveals that such a view fadior cannot be evaluated directly. However, the view factor F can be determined from Eq. 13-13 after determining both F,, 2 and F -,<2.3) from the chart in Table 13-2, Therefore, it may be possible to delenmine some difficult view factors with relative ease by expressing one or both of the areas as the sum or differences of areas and then applying the superposition rule. 

Let the base surface of radius ri = 10 cm be surface 1, the circular area of - 5 cm at the top be surface 2, and the circular area of r3 - 8 cm be surface 3. Using the superposition rule, the view factor from surface 1 to surface 3 can be expressed as... 

C What are the summation rule and Ihe superposition rule for view factors ... 

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