FDiff_3

Plane element dA_1 to plane perdendicular rectangle

FDiff_3(a, b, c) calculates the view factor from a plane element dA_1 to a rectangle in plane 90 degrees to plane of element. The element is located above one corner of the rectangle.

Inputs:
a = height of rectangle [m or ft]
b = length of rectangle [m or ft]
c = distance from element dA_1 to rectangle [m or ft]

Notes:
If a and b are set to very large numbers relative to c, fDiff_3 will be 0.25. This behavior results from definition that the normal to the elements passes through the corner of the rectange.

Example:
$UnitSystem SI K Pa J deg
"This example determines the view factor between a rectangle of dimensions a x b and a differentially wide strip perpendicular to the rectangle. The calculation is done in two ways: 1) by integrating the FDiff_3 between 0 and x and between x and b for 0<x<b and 2) direct calculation using FDiff_4. The results are identical but the option of integrating allows temperature of other properties to vary with position."

a=1 [m]
b=2 [m]
c=0.5 [m]
F_strip=integral(fdiff_3(a, x, c)+fdiff_3(a, b-x, c),x,0,b)/b "integrate for 0<x<b"
F=fdiff_4(a, b, c)

{Solution: F_strip = F = 0.2153 [m]}

Reference: Siegel and Howell, Thermal radiation heat transfer, 4th edition, p.842.

View Factor Index