Discussion: “View Factor Algebra for Two Arbitrarily Sized Non-opposing Parallel Rectangles”
Larry W. Byrd · ASME Journal of Heat and Mass Transfer · 1993
give the fraction of radiation emitted from surface 1 that directly strikes surface 2. This discussion gives an equation to calculate the view factor between two arbitrarily sized nonopposing parallel rectangles in terms of view factors for opposing rectangles of the same size. This was originally presented by Hamilton and Morgan (1952) but their equation (referenced by Siegel and Howell, 1981, and Chapman, 1987) is missing one term. A closed-form solution derived by Hsu (1967) for the general case of two arbitrary parallel rectangles is also referenced as the recom mended method for calculating the view factor. Hsu's ap proach is later generalized by Yuen (1980) to incorporate general polygons that do not have to be parallel to each other. This discussion derives the expression for parallel rectangles that are not directly opposed. Using the notation of Fig. 1, this corresponds to i*i_ 9'. View factors for the geometries shown in Figs. 2 and 3 are used as building blocks for Ft-9'. The final result will be written entirely in terms of view factors for parallel opposing rectangular plates of the same size as shown in Fig. 4. This as well as basic view factor relations used in the derivation are given by Incropera and DeWitt (1990). The view factor Fa-b' for the geometry shown in Fig. 2 can be found using the notation of Hamilton and Morgan as follows: Let: Gi-j=AjFj-j G,_ ((/) ' =AjFj. Uj)'