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Sun, 3 Jan 2010 13:49:42 EST |
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From:
_http://www.im.pwr.wroc.pl/~hugo/HSC/imprezy/ModellingWeek/reports/Report_pr
oject02.pdf_
(http://www.im.pwr.wroc.pl/~hugo/HSC/imprezy/ModellingWeek/reports/Report_project02.pdf)
From the heat plots, there are approximately two to three cells
horizontally around the heat source (pupae) before reaching ambient. The plot does
not show the heat source w.r.t to the comb width.
density (kg m exp-3) specific heat (J kg exp-1 K exp-1) thermal cond (W m
exp-1 K exp-1) heat src (W m exp-3)
honey 1400 2300 0.60
0
pollen 420 2720 0.15
0
pupae 996 4180 0.61
103
air 1.1774 1005.7 0.02624
0
bee 996 4180 0.61
2:9x10exp5
Table 1: Physical properties of di erent substances occupying a honeycomb
cell.
cp - speci c heat, k - thermal conductivity and T is
the temperature at (x,y,t). The function G represents a source of heat. It
could
be either pupae or cell-heating bee.
If we assume the thermal conductivity of a two cell bee comb width is
approximately what it is of two cells horizontally on the comb (there will be
some exposed surface differences) then the thermal conductivity of a two cell
comb width is approximately ( with honey) 1.2, (with pollen) 0.30, ( with
air) .05248, and (with bee/pupae) 1.22. If the R value or insulating
value is the reciprocal of the thermal conductivity, then ( with honey)
.8333, (with pollen) 3.333, ( with air) 19.055, and (with bee/pupae) 0.82.
This means that ( with honey) .8333 is 83.33% less insulating than water
, (with pollen) 333.3% more insulating than water, ( with air) 1905.5% more
than water, and (with bee/pupae) 082. % less insulating than water.
From this I would ascertain that empty cells around the bee nest is the way
to go. This is basicly what the bees have with a band of pollen ( more
difficult to move 333.3% insulating), then a band of honey ( easier to
move 83.33% insulating) and then empty cells ( 1905.5% insulating). From
what I remember, the bee nest does have 2-3 empty cells around it.
Figure 6: Surface integral of temperature function Ti over all pupae cells
with
respect to time. The kink in the plots appears at the 10-minute point where
the problem changes from heating to cooling.
I takes approximately 600 seconds for the temperature to reach peak from
Figure 6 of the
_http://www.im.pwr.wroc.pl/~hugo/HSC/imprezy/ModellingWeek/reports/Report_project02.pdf_
(http://www.im.pwr.wroc.pl/~hugo/HSC/imprezy/ModellingWeek/reports/Report_project02.pdf) article.
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