(119)

Substituting the reciprocity relations,

(120)

(121)

and solving the three equations for *F*12 yields

(122)

2*a*1

Similarly for the triangle *adb*

(123)

2*a*1

Noting that

(124)

and solving eq 122124 for *F*16 yields

(125)

2*a*1

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

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.

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