FDiff_7

Ring element on interior of right circular cylinder to circular disk at end of cylinder

FDiff_7(r, x) provides the view factor from a differential element on the inside surface of a right circular cylinder (1) to a disk at one end of the cylinder (2).

Inputs:
r is the radius of the cylinder [m or ft]
x is the distance along the axis of the cylinder from the base that serves as surface 2 [m or ft]

Example:
$UnitSystem SI K Pa J deg
"The following program uses integration to calculate the view factor of the inside surface of a cylinder to its base at one end. This view factor could be found more directly using f3d_17, but use of the differential view factor allows the radiation heat transfer to be calculated even if temperature varies with axial position along the cylinder."
$TabStops 4 in
$VarInfo A_cyl units=m^2
$VarInfo A_base units=m^2
$VarInfo x units=m
r=1 [m]      "radius of the cylinder"
h=2 [m]      "length of the cylinder"
F=fdiff_7(r,x) "view factor from a differential element"
F_21=integral(F*2*pi*r,x,0,h)/(A_cyl) "view factor from base to the inside surface"
A_cyl=2*pi*r*h      "insider surface area of the cylinder"
F_12=F_21*A_cyl/A_base      "reciprocity to determine view factor from inside surface to base"
A_base=pi*r^2      "area of the base"
F_12`=f3d_17(r,h)    "compare with f3d_17"

{Solution:
F_12=0.8285
F_12`=0.8284
}

Reference: Howell, www.me.utexas.edu/~howell/sectionb/B-93.html

View Factor Index