FDiff_6

Differential ring element on surface of a disk to a coaxial sphere

FDiff_6(r1, r2, h) provides the view factor from a differential ring (1) on a disk to a coaxial sphere (2).

Inputs:
r1 is the radius of the differential ring [m or ft]
r2 is the radius of the sphere [m or ft]
h   is the distance between the disk and center of the sphere [m or ft]

Example:
$TabStops 4 in
$UnitSystem SI K Pa J deg
"The following program uses integration to calculate the view factor of the entire disk to a sphere. This view factor could be found more directly using f3d_16, but use of the differential view factor allows the radiation heat transfer to be calculated even if the disk temperature varies with radius. "
$VarInfo r units=m
$VarInfo A_sphere units=m^2
$VarInfo A_disk units=m^2
r_o=1[m]   "radius of disk and sphere"
h=1[m]   "height of center of sphere above disk"
A_disk=pi*r_o^2   "area of disk"
F=fdiff_6(r,r_o,h)   "view factor from the differential ring to the sphere"
F_12=integral(F*2*pi*r,r,0,r_o)/A_disk   "view factor between the entire disk (1) and the sphere"
A_sphere=4*pi*r_o^2   "area of the sphere"
F_12`=f3d_16(r_o,h)*A_sphere/A_disk   "view factor between the disk and the sphere using f3d_16 - compare to F_12"

{Solution:
F_12 = F_12` =0.5858 }

Reference: Howell, www.me.utexas.edu/~howell/sectionb/B-91.html from Feingold and Gupta, 1970

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