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Sector of circular disk to sector of parallel circular disk

Function F3D_77 returns the view factor between a sector of a disk and a sector of a parallel disk.  The angle and radii of the sectors can be different.

The calling protocol is:

F=F3D_77(N_rays, r1, r2, h, beta, alpha)

Inputs:

N_rays: number of rays for Monte Carlo simulation (<0 leads to use of default value, 1e6)

r1: radius of disk 1 (ft or m)

r2: radius of disk 2 (ft or m)

h: distance between disks (ft or m)

beta: angle (deg or rad)

alpha: angle (deg or rad)

Example: 

$UnitSystem Radian SI

r1=1.5 [m]

r2=2 [m]

h=1 [m]

beta=pi/2

alpha=pi

N_rays=10000

F=F3D_77(N_rays, r1, r2, h, beta, alpha)

{Solution

F=0.5186}

Reference: 

Monte-Carlo procedure programmed by Greg Nellis, Mechanical Engineering Department, University of Wisconsin, Madison, May, 2015