Convection currents in liquids in a uniformly accelerating Einsteinian frame of reference

Angels? Pins? What have I been missing??! :-) Actually, due to troubles with
one of our gateways, I missed several issues of the list. Thanks to a friend,
I got issues 111 thru 113 (113 came) but missed 109 & 110. Perhaps they are
still out there floating on the ether. :-) If someone has archives, let me 
know and then you could forward them. (Please not EVERYONE!)

Ok, let me throw in a couple of angels worth of gedanken experiment. (BTW
I'm also a Canadian but currently in LA logged remotely to my Canadian
computer, so I'm not sure WHICH side of the fence I'm on ;-) Those of you
who don't care or get bored by long winded scientific jargon, kindly skip
to the last paragraph. :-) I'll talk to you later.

Convection currents happen because some region of the liquid has a temperature
gradient in it. This causes some part of the liquid to have a different
density and, due to hydrostatic pressure differentials, that liquid begins
to accelerate if it's hotter, in the upwards direction (in most liquids at
most temperatures). When the temperature gradient is only in the vertical
direction (ignoring the case when we're accelerating in outerspace :-)
these laminar convection currents continue because a) nothing is ever
perfectly uniform b) random brownian motion will introduce a perturbation.
Once a slight bubble forms, the convection heat engine begins transferring
kinetic heat energy into kinetic motion energy. With uniform heating along
a level, flat lower surface, we get formation of the hexagonal, laminar
bubbles. Even though we have a uniform heat source at the bottom, we have 
local horizontal temperature gradients which is what makes the convection
engine run!! These bubbles don't streak to the surface at the speed of light
because of two things a) their inertia (mass) b) viscosity. Now the equations
to solve to predict the steady state equilibrium are just to hard to solve
even for us computer types. (well, most of us ;-) There is very little 
difference in the volumetric flows introduced when many wires across the
bottom of a tank of liquid supply a given amount of heat energy or when
that heat is introduced more or less uniformly from the bottom surface for
a liquid such as water. So Kevin is right.

Sort of.

But if the heat were applied all on one side, well, the engine would be more 
efficient, because we could introduce a temperature grandient across a much 
larger distance!! (we don't have to solve any nasty differential equations
to deduce this fortunately :-) But let's get to the interesting bit. What if
we throw a layer of gravel into the equation and see what sort of non-linearities
we introduce? Well for one thing, we're going to introduce a LOT more viscosity
effects. The other thing is the gravel itself is going to act as a heat buffer
and tend to smooth out some of our temperature gradients. With wires in the
substrate, we're kind of forcing our own horizontal temperature gradients so
we know there will be convection, just less than with the free flow situation.
(thank goodness, because we wouldn't want that much!) Would the convection
bubbles still form? Yes of course but the two effects I mention mean that the
convection heat engine is much less efficient. So George is right.

Kind of.

Because maybe exactly how much flow there is is not important. There will be a
point in the permiability (and age) of a substrate when the wires would provide
enough flow and the uniform heating would not. We don't know because it's hard
for us to measure the effectiveness of our methods because we don't know some
1) how to predict substrate permeability.
2) for a given mix of nutrients, plants, pH, temperature how much flow is 
optimal or the range of acceptable flows.
3) how to solve those nasty, non-linear, differential equations -or-
how to measure very low fluid velocity inside the substrate.

However, you could put a kind of UG filter plate under the gravel (to equalize
the pressure on the top and bottom) and measure the flow rate through a tube
to fairly accurately measure substrate flows produced by heating coils in the
gravel. (assuming laminar flow through the tube, we CAN predict the volume flow
pretty accurately using fist year fluid mechanics). 

You could do a similar experiment using a tube and measuring the rate of water 
level drop in the tube vs. the height of water in the tube to measure the 
permeability of that particular substrate.

You could even take fluid and substrate samples for a range of substrates, pH,
temperature, nutrients and plant species and actually correlate things like
plant growth, H2S concentration and other wonderful things.

LAST paragraph: (welcome back everyone else! :-)

OR, you could sit at home in your comfortable chair content in the knowledge that
those are all things you COULD do (if you wanted to), take a sip of your
favourite beverage and just admire the beautiful fully planted tank, filled with
exotic specimens from around the world and wonderfully colored fish placidly
drifting amidst their green surroundings. THIS is why us aquarium folk are such
nice and pleasant people; because we know that the enjoyment of beauty is a
sufficient happy ending to our day! :-)