1.0
set at a constant temperature
5
boundary and as a thermal
10
convection boundary, with
0.8
the remaining sides having a
zero heat flux. The results of
this test, compared with the
0.6
analytical solution given by
10
zisik (1980), are shown in
15
Figure 11; good agreement
0.4
was achieved. A third set of
15
tests was run to confirm the
0.2
correct implementation of the
heat flux boundary condition.
This was done by modeling a
0.0
square solid material with one
0.0
0.2
0.4
0.6
0.8
1.0
side at a constant tempera-
Distance (ft)
Boundary at 20F
ture, the opposite side with a
specified heat flux, and the Figure 11. Two-dimensional conduction problem.
remaining sides unspecified Dashed lines represent the analytical solution, solid lines
represent the numerical solution.
(zero heat flux). This configu-
ration was repeated so that all four directions were tested with both positive (out
of an element) and negative (into an element) heat flows.
In order to test the solution of the momentum equations and the continuity equa-
tion, and their interaction with the energy equation, a comparison with a well-
documented benchmark numerical solution was done. As mentioned earlier,
de Vahl Davis and Jones (1983) presented benchmark solutions for natural con-
vection in a vertical enclosure and compared their results with other investiga-
tors. A vertical enclosure is a closed cavity in which the horizontal surfaces are
insulated (zero heat flux boundaries) and the vertical sides are held at two differ-
ent temperatures. His solutions were for air at Rayleigh numbers of 103, 104, 105,
and 106. Table 2 compares the velocity maximums along the x = 0.5 and y = 0.5
locations. Good agreement is observed, with percent differences less than 1%. Also
Table 2. Comparison of published velocity predictions with
FECOME for a vertical enclosure.
Maximum velocity
Maximum velocity
@ y = 0.5
@ x = 0.5
Source
y coordinate
x velocity
x coordinate
y velocity
Benchmark* Ra=103
0.813
3.649
0.178
3.697
Gartling*
0.824
3.696
0.176
3.696
FECOME
0.825
3.640
0.175
3.697
Benchmark Ra = 104
0.823
16.178
0.119
19.617
Gartling
0.824
16.186
0.119
19.630
FECOME
0.825
16.185
0.125
19.601
Benchmark Ra = 105
0.855
34.73
0.066
68.59
Gartling
0.854
34.74
0.068
68.63
FECOME
0.850
34.71
0.067
68.63
Benchmark Ra = 106
0.850
64.63
0.038
219.36
Gartling
0.854
64.37
0.043
218.43
FECOME
0.850
64.76
0.033
218.58
* From de Vahl Davis and Jones 1983.
22
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