Mathematical analysis of dome geometry

[texassourdough]

Thanks, mklingles!

Would be interesting to do a conical oven also - easy shape to specify. I think you will find all of the options are very similar for the no fire case.

I believe the biggest advantage of the lower oven for pizza lies in the flame being closer to the pie - and wrapping more over the top of the pie. If we assume the flames are say 16 inches "tall" they will reach an inch or two further across a "low" dome compared to a taller one and will be several inches closer. We are all familiar with the fact that the side of a pizza cooks faster than the "dark" side (which is receives less flame radiation and more black body refractory radiation from a cooler source than the flame). As a note, for small flames there would be little difference.

Thanks for bringing up the topic and for your calculations!
Jay

[Neil2]

To sum it up then, for pizza cooking:

For smaller ovens a hemispherical shape will do fine and provide the opportunity for a somewhat higher door (maintaining the 63% door/dome ratio).

For a larger oven, say 40 inches or more, an elliptical or low dome shape might be more efficient for cooking pizza.

[mklingles]

Mathmatically:

- A parabola will focus radiant heat at a single point somewhere above the floor.
- A hemisphere will focus at a single point on the floor (center)
- An ellipse will focus on two points on the floor (or in three dimensions, a ring).

What Neil2 is describing here is the behavior of photons that are reflected off of the surface. For that fraction of the inferred radiation that is not absorbed and re-admitted the reflective properties would apply. This article at wikipedia has a good description of specular reflection from curved mirrors. Wikipedia - Curved Mirrors

I have not been able to find a reliable source of data on the amount of energy absorbed by fire brick vs the amount reflected. I believe from the numbers I have found that ~80% of the energy is absorbed and only 20% reflected.

Also the roughness of the firebrick will greatly distort any reflected "image

[Lburou]

I thought we had a good beginning for this discussion....Are we done? Ready to read more

[mklingles]

I'm working on adding the door opening to the calculation. Maybe a week or so, I'll get the next round of math done.

[benguilford]

mkingles, as an engineer I salute you sir! I liked your quote from a while back 'The maths keeps me out of trouble'

Surely there must be an engineer on this Forum with access to some professional thermal modelling software, three dimensional modelling of radiated heat is fairly complicated, and it doesn't take the effect of convection into account - even in a sealed dome there will be a surface temperature differential between the floor and the walls, which would set up a circulating air flow within the oven. Would this be considered negligible in this situation?

[mklingles]

For sure the Convection is a dominant factor in heating the oven and distributing the heat within the oven. For cooking, I think the radiation factor dominates. However, I don't know that to be the case.

I did talk to one physics professor about handing this off to have a student do some more work on it, but haven't even followed up on that. (To busy cooking pizzas, building wood shed, etc).

[Neil2]

It is not too complicated.

An elliptical oven has a lower dome than a hemisphere of the same diameter. The heat from the ceiling bricks is closer to the top of the pizza.

[david s]

This also applies to small ovens. The dome and flame from the active fire are much closer to the pizza. My own oven has the interior height at only 10 and a half inches. It still cooks much the same 90 sec to 2min pizzas. The larger the oven, the larger the fire so I guess it all evens out.