Re: Constant area

[kenneth mark bryden <kmbryden@iastate.edu>]

Crispin et al

I usually work in the lab and stay out of the spot light but I would like 
to note that there are substantial downside issues for the solution that 
Crispin suggests.

At 11:50 PM 4/22/2002 +0200, Crsipin wrote:

>First, make the steel plate as thick as possible, especially as it is a
>comercial application.  The heat loss getting it hot in the morning is
>amortized over a long cooking day and the cost will be well worth it if it
>helps cook over a larger area.  The thinner the plate the worse your temp
>variations will be no matter what else you do.

While the heat loss may be negligible in some applications, it is not in 
all applications. In order to "smooth out" the temperature of the surface 
the steel plate will need to be substantially heavier. Additionally the 
heavier/thicker the plate the more heat capacity and the greater the 
potential for injury to the user and the children, this occurs both during 
use (the burn will go deeper - but I agree that they can get burnt on the 
thinner top) and following cooking during the much longer cooldown period. 
Remember that the top is much heavier.


>Second, one of the simple ways to greatly reduce the temperature right over
>the fire is to put another steel plate under that spot.  This is not a
>matter of thickening it, but of 'hanging' another plate with an air get
>between them.  The heat protection so provided varies with the distance it
>stands off.  Try a 200mm diameter 4mm plate 15mm down. The little plate will
>get very hot (I would use some sort of stainless like an old pot bottom or
>lid) but it will only pass a certain amount of heat through to the point on
>the top directly over the fire.

This will significantly reduce the efficiency and hence the effectiveness 
of the cooking surface and setup.


>This plate conserves heat in the flue gases so that as they get farther away
>they are hotter than they used to be.

Because the hot gases are kept away from the surface you allow slower 
motion in the boundary layer reducing the heat transfer to the surface 
relative to the scheme that Dean Still proposes. You also run the risk that 
the flow of hot gases will not reattach to the surface of the grill 
smoothly. The consequence of this is that more heat will end up in the 
exhaust gas and be wasted. Or that you will have to do substantial amounts 
of diddling to get everything to work right. This is in contrast to the 
relatively simple technique proposed by Dean which he has tested. I would 
note that keeping the area constant is not quite optimum, it is a good 
first cut that can be implemented in the field with little effort.


>Third, as the gases get farther away they cool down and conduct less heat to
>the plate.  This has to be factored into your calculation making if FAR more
>complicated.  For example, if you follow the method you described, the gases
>would drop from, say, 750C to 250C as it passes under the plate from center
>to chimney.  Clearly even though you are letting the gas touch the plate for
>the same amount of time at each point by tinkering with the gap, you should
>also have to slow it down so that it has more time to transfer remaining
>heat to the plate as the temperature is lower and the heat transfer rate is
>lower.  Nifty, huh?  So in fact the gap should be larger (to slow it down)
>than the simple calculation of 'equal areas' (as I call that type of
>solution).

No. if you slow it down the boundary layer thickens, the heat transfer 
coefficient is reduced, and the problem gets worse. At the slower 
velocities the flow may also become laminar. In fact a quick analysis 
(conservation of energy at the plate surface) shows that you want the gases 
to speed up toward the end, that is the optimum gap is smaller not larger.


>Fourth, as the transfer of heat is greatly enhanced by turbulence, you
>really should not have a smooth taper between two surfaces but rather have a
>series of 'annular rings' each of which is progressively higher than the
>previous (inner) one thus reducing the gap at that point only.  This would
>look like a stadium seating arrangement.  One might call it a Stadium Flue
>Control.

there are a couple of problems with this idea. Heat transfer is enhanced by 
turbulence but the annular rings with which I think you are trying to trip 
the flow into turbulence will only cause the flow to separate from the 
surface. Remember that the Reynolds number is the primary driver for 
turbulent flows and so trip wires only help flow that are already inclined 
to be turbulent. If the flow is too slow the viscosity of the fluid will 
return it to laminar. A micro pattern stamped on the surface may increase 
heat transfer but it would require some testing and would likely be 
difficult to implement in the field and would become gunked up shortly 
after use began. Also it is likely the pattern needed to ensure turbulence 
probably varies with the velocity of the hot gases. Since turn down is an 
important function of a stove this could be a problem.The rings could be 
used as fins to increase heat transfer but testing and computational 
modeling in my lab has shown that the losses caused by the separation 
region exceed the gain.


>Now combine that idea with the change in depth to speed up the flue gases,
>and you will have a series of donut-shaped chambers that get shallower
>either towards the outside (or the inside - it is not yet clear).  They will
>create chambers where the heat can 'rest a while' to mix and then rush
>through the gap to transfer heat to the plate.  If the first ones are small
>and shallow with a large clearance to the plate's underside, the hot gases
>will speed by, and then as they cool down, they will linger longer
>languishing around to dump their final heat upwards.

I don't quite understand this idea. Maybe you could draw it for me and I'll 
think about it for a bit.

Regards
Mark

----------
Professor Mark Bryden
Department of Mechanical Engineering
Iowa State University
Ames, Iowa USA



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