If you looked at that **NASTY quintuple
integral calculus equation**, you already realize that the situation
is not quite as simple as
it looks. Every single speck of flame tip and every speck of
glowing wood emits radiation (dependent on its temperature alone)
in all directions (were you paying attention??). This means that
every speck of interior surface of the JUCA's firebox is going to
receive radiative energy from each of those specks of fire and flame.
(That's actually why there were 5 squiggly lines in that integral
equation. Whoops! Actually, that's not entirely true! There should
be SIX squiggly lines, but the lazy JUCA designers took the easy
road and assumed that the fire was flat, having only width and depth,
and not height. [It turns out that this has less than 0.05% effect
on performance and efficiency calculations])

The complicated, angled structure of the JUCA firebox made this difficult problem even harder. In some of our computer simulations, the computer ran for over half an hour while calculating the results of such equations.

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