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Radiation View Factors

View factors, also known as shape or configuration factors, play a direct role in heat transfer due to radiation. The view factor Fij between two small areas Ai and Aj is defined as the fraction of the radiation leaving area Ai that is intercepted by area Aj . In other words, Fij represents how well Ai sees Aj . The view factor Fij depends on the orientation of the small areas Ai and Aj and the distance between them.

For the two infinitesimal surfaces dA i and dA j , the view factor dF ij is given by:

where q i and q j are the angles between the unit normals to the areas and the line R ij connecting the two areas. If the two areas are finite, then the view factor is given by:

From the above equation, the following reciprocity relation always holds:

While many heat transfer books provide view factors for simple-shaped areas, calculating view factors for real life problems requires major effort even for fast computers. When requested to calculate view factors for the radiation between face A and face B, the software thinks of each face as composed of small areas (surfaces) defined by element faces. It then calculates a view factor for each element face relative to every other element face in the set. View factors between element faces on the same geometrical face are included in these calculations.

A concave face with a reasonably fine mesh can radiate to itself. Planar and convex faces do not radiate to themselves. Such effects are automatically considered.

Blocking

The radiation between two element faces can be blocked by a third element face. In that case, the view factor becomes 0. The software automatically considers blocking among all specified faces as illustrated in the figure. For proper blocking considerations, you must select faces participating in the radiation. In the example below, faces 3 and 4 partially block the radiation between faces 1 and 2. Incorrect results are obtained if you select faces 1, 2, and 3 only.

 



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