View factors (aka configuration factors) are utilized in some radiation heat transfer models to estimate heat transfer rates between surfaces. In particular, the thermal energy leaving a given surface is applied to other surfaces, as appropriate, based on how much the hot surface "sees" the other surfaces. As such, view factors are purely geometrical in nature. A range of view factor formulae are available here.
For this problem, calculate the view factor from surface 1 to surface 2 (F_1-2) for two directly opposed, infinitely long plates of different finite widths given the distance between the plates:
Each variable may be a vector of values. Also, note that B = b/a and C = c/a.
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Solution 551077
Same issue here as in your third problem. Please check the absolute value of the differences of the computed values with the correct ones. Otherwise, more silly answers (again, like this one :-) will slip through!
Thanks for the catch. I've updated the test suite to check against upper and lower bounds of each answer.