I have been working on some calculations to determine the radiant heat pattern on the floor of the oven. This should shed some light on the effect of different dome shapes (e.g. high vs low, circular cross section or parabolic, tall soldier or no solider).

My calculations are ignoring any coals or fire, and are focused just on the pattern of heat radiated from the firebrick in the dome. I assume the entire dome is a uniform temperature. I assume the fire brick is radiating as a black body (Black body - Wikipedia, the free encyclopedia). The black body assumption simplifies the calculation and I believe is also correct. If anyone knows the absorption / reflection coefficients for fire brick at ~800degF please post. I believe the absorptance of fire brick is around 0.8. This means about 80% of the radiation that hits the firebrick is absorbed, and the other 20% is reflected. The absorbed radiation is re-radiated as black body radiation. So, I'm ignoring the ~20% of the energy that is reflecting off the surfaces inside the oven.

Briefly I'll discuss the calculation then show a few preliminary results. If anyone wants to discuss the math or review the calculation let me know and I'll start a separate thread.

Black body radiation is emitted from a surface uniformly in all directions. Therefore the energy of the radiation at a distance D from the surface is proportional to 1/D^2. So, to calculate the intensity of the radiation at a point on the floor of the oven you just have to add up 1/D^2 for every D formed between a point on the dome and the point on the floor. Then repeat this for every point on the floor. For those who suffered through multi-dimensional calculus you may recall this is a surface integral.

To get started I have not yet included the door opening in the oven. That is I assume the dome is complete and covers the space where the dome is. This is simplifies the math. Now that I have the calculations working, I will eventually go back and re-calculate with the door opening.

So, far I have just worked out the answer for two cases: 1) a hemispherical dome with 42" diameter and therefore a height 21", and 2) a spherical cap (Spherical cap - Wikipedia, the free encyclopedia) dome with a floor diameter of 42" and a height of 18" (this matches my oven)

The 2 images below show the intensity of radiation on the floor of the dome. The conclusion is that the difference between a 21" height and a 18" height is very negligible (I did all this math for that !?!?)

The final picture shows a cross section plot across the two images above. I think the most interesting thing I've learned is that the intensity is a bit more then double at the edges of the oven. Also in a 42" oven there's a good 20" middle section with nearly uniform radiation, but beyond that the intensity starts to increase quickly. Also here you clearly see that 18" vs 21" height didn't make much difference.

My calculations are ignoring any coals or fire, and are focused just on the pattern of heat radiated from the firebrick in the dome. I assume the entire dome is a uniform temperature. I assume the fire brick is radiating as a black body (Black body - Wikipedia, the free encyclopedia). The black body assumption simplifies the calculation and I believe is also correct. If anyone knows the absorption / reflection coefficients for fire brick at ~800degF please post. I believe the absorptance of fire brick is around 0.8. This means about 80% of the radiation that hits the firebrick is absorbed, and the other 20% is reflected. The absorbed radiation is re-radiated as black body radiation. So, I'm ignoring the ~20% of the energy that is reflecting off the surfaces inside the oven.

Briefly I'll discuss the calculation then show a few preliminary results. If anyone wants to discuss the math or review the calculation let me know and I'll start a separate thread.

Black body radiation is emitted from a surface uniformly in all directions. Therefore the energy of the radiation at a distance D from the surface is proportional to 1/D^2. So, to calculate the intensity of the radiation at a point on the floor of the oven you just have to add up 1/D^2 for every D formed between a point on the dome and the point on the floor. Then repeat this for every point on the floor. For those who suffered through multi-dimensional calculus you may recall this is a surface integral.

To get started I have not yet included the door opening in the oven. That is I assume the dome is complete and covers the space where the dome is. This is simplifies the math. Now that I have the calculations working, I will eventually go back and re-calculate with the door opening.

So, far I have just worked out the answer for two cases: 1) a hemispherical dome with 42" diameter and therefore a height 21", and 2) a spherical cap (Spherical cap - Wikipedia, the free encyclopedia) dome with a floor diameter of 42" and a height of 18" (this matches my oven)

The 2 images below show the intensity of radiation on the floor of the dome. The conclusion is that the difference between a 21" height and a 18" height is very negligible (I did all this math for that !?!?)

The final picture shows a cross section plot across the two images above. I think the most interesting thing I've learned is that the intensity is a bit more then double at the edges of the oven. Also in a 42" oven there's a good 20" middle section with nearly uniform radiation, but beyond that the intensity starts to increase quickly. Also here you clearly see that 18" vs 21" height didn't make much difference.

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