FDiff_1

Plane element dA_1 to plane parallel rectangle

Function FDiff_1(a, b, c) returns the view factor between a differential element dA_1 and a plane parallel rectangle. A normal to the element passes through the corner of the rectangle.

Inputs:
a and b are the dimensions of the rectangle [m or ft]
c is the distance between the plane of the rectangle and the plane of the element dA_1 [m or ft]

Notes:
If a and b are set to very large numbers relative to c, fDiff_1 will be 0.25. This behavior results from definition that the normal to the elements passes through the corner of the rectange.

Example:
"This example determines the view factor between a rectangle of dimensions a x b and a differentially wide strip parallel and below the rectangle. The calculation is done in two ways: 1) by integrating the FDiff_1 for the strips between 0 and x and between x and b for 0<x<b and 2) direct calculation using FDiff_2. Note that the results are identical but the option of integrating allows temperature of other properties to vary with position."
$UnitSystem SI
$VarInfo x units=m
a=3 [m]
b=2 [m]
c=0.5 [m]
F_strip=integral(fdiff_1(a, x, c)+fdiff_1(a, b-x, c),x,0,b)/b "integrate for 0<x<b"
F=fdiff_2(a, b, c)

{Solution:
F_strip=F=0.3886}

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

View Factor Index