a3 F3-1 + a3 F3- 2 = a3 .
(119)
Substituting the reciprocity relations,
a2 F2-1 = a1F1- 2
(120)
a3 F3-1 = a1F1- 3
(121)
and solving the three equations for F12 yields
a1 + a2 - a3 .
F1- 2 =
(122)
2a1
Similarly for the triangle adb
a1 + a4 - a5 .
F1- 4 =
(123)
2a1
Noting that
F1- 2 + F1- 4 + F1-6 = 1
(124)
and solving eq 122124 for F16 yields
a2 + a5 - a3 - a4 .
F1-6 =
(125)
2a1
This procedure is implemented in the program FEVIEW (Richmond 1995); also
included is a routine to check for the shadowing of surfaces. A surface is consid-
ered shadowed if a line connecting the midpoints of two surfaces is intersected by
another radiation surface. No effort is made to distinguish partially shadowed
elements, and as long as the midpoints can be connected without interference, the
viewfactor is calculated using Hottel's method. The viewfactors are obtained prior
to running FECOME and appended to the FECOME grid data file. A FECOME sub-
routine uses eq 113, nodal temperatures and the viewfactors, to obtain the radia-
tion heat flux into or out of each of the radiation surfaces.
The radiation heat fluxes are recalculated at each iteration in FECOME using
the average nodal temperatures for each surface specified as a radiation bound-
ary. In the global formulation, the radiation flux is handled in the same manner as
a boundary heat flux (φ) in eq 73.
Model verification
Verification of the model consisted of comparing the model output to known
(analytical) or benchmark numerical solutions. Three types of verifications were
done to confirm that the model was producing accurate results; these are described
in the following paragraphs.
Several computer runs were made to verify the energy equation alone and the
implementation of the thermal boundary conditions. These runs also served to test
the matrix assembly and inversion routines. First, a square grid was constructed in
which all the elements were specified as a solid material and two opposite sides
were set at different temperatures, with the other two sides having unspecified
boundary conditions (this corresponds to a zero heat flux boundary). An exact
solution to this simple one-dimensional problem was obtained. A second test in this
phase was a two-dimensional conduction problem; here two adjacent sides were
21
Back to Contents
Previous Page
