Conference rusure::math

To radiate heat, you probably want some 'fins', as are used on some
electronic capacitors, or gizmos that attach to a stove-pipe.  The
heat is conducted to the fins, where the large surface area allows
for a high heat flux by radiation.

No, Peter.  To be quite frank, my desire is not just to get the most heat
into the house by the most effective total solution (jumping to woodstoves).

What I want to do is carry the fireplace evolution to a purist's conclusion;
Count Rumsford arrived at the correct ratio between firebox depth and throat/
smoke-shelf aperature to minimize the depth (hence maximize heat radiation into 
the room rather than up the chimney), without smoking up the room.  But his 
designs show angled, squared-off sidewalls.  I want to complete the effect by
flaring the sidewalls in the most mathematically correct way.

Then I can fill an entire winters' evening discussing abstract principles and
their physical realization.  Zen and the Art of Fireplaces, if you will.

--John

RE: .0 and .2

John, can you provide the correct specifications for a fireplace?  I have
heard of Count Rumsford's design before, but I have never seen the
specification.  Is his design the gospel for fireplace design, or have
there been further refinements?  I have had trouble with my fireplace
smoking up the house on occasion and I would like to compare its design
to what is the correct design.  I should mention that where I live there
is almost a constant wind blowing all winter.  Does this fact have an
effect on a properly designed fireplace?

	Mike

You seem to be thinking of what's usually called an exponential horn (though
I don't know exactly what function describes it).  Such horns are used in
things like speakers or microwave radiators.  I've always thought of them
as providing impedence matching between the radiator and free space.  I
think they also provide efficient transformers from a point source to a
plane wave.

It's not clear to me that the analogue for a heat source makes much sense.
Also, the geometry of such a horn is almost certainly frequency-dependent; 
for the very broad spectrum of radiation coming from a stove, no horn is
likely to be anything close to optimal.
							-- Jerry

    Re .0, .4: trumpets (and members of the trumpet family) have linearly
    increasing bores (apart from the first bit and the lead into the
    flare). The horn family (apart from the first few yards and through
    the valves, where they have them) have an exponential cross-section.
    
    (ex French Horn player)