900F isn’t 3x300F or 1819F because the free convection heat transfer coefficient of air increases with temperature so the surface temperature of the chicken (and the temperature of the air touching the chicken) will be lower than 3x its value at 300F. If you want the chicken meat to experience a surface temperature that is 3x higher than 300F you need to up the heat a bit more.
Assuming the affects from Prandtl numbers are insignificant, and that a chicken is basically a sphere, the heat transfer coefficient should be roughly proportional to the fourth root of the Grashof number which is (roughly) linear with temperature difference (we’re neglecting viscosity changes because I’m tired, though those are probably significant)
Math I probably didn’t do right says that’s about 1.69x higher of a heat transfer coefficient
1.69x higher convection means 1.69x lower thermal resistance means we need roughly 1.69x as much temperature difference, so say the chicken is initially at 40F (refrigerator temp) that gives us 1.69x(1819-40)+40= 3,046.51°F
That’s pretty close to the temperature at which lead boils.
Unfortunately one shouldn’t cook around vaporized or superheated lead due to the likelyhood of it getting into the food, what a shame.
Just proving the example works. A PM wouldn’t expect 3x performance from 3x the people, maybe about 1.7x. But 3x temperature will come out poorly anyway.
I would say trying to cook 3x faster isnt a surface temp 3x higher, but the rate of heat transfer is 3x faster. Because then your laat step is backwards.
Q = h a dT
If you just calculated H goes up 1.69x, then dT doesnt need to go up MORE, it needs to go up LESS. A higher HTC increases the rate of heat transfer. Which… now you need to recalc your free conv HTC because temp changed. But if it didnt…
3Q = 1.69h a 1.78DT
Old DT was 260, now its 463, which is an ovev temp of 503F
Edit: this is a transient problem we’re trying to reduce to a steady state calculation with pretty poorly defined requirements. Sounds like a typical day at work for me lol
True, temperature was just the main part of the meme and a higher temp is funnier anyway so I went with it lol
Also for a transient solution, idk the avg thermal conductivity of a whole chicken, which we’d need for a one-term approximation if we assumed the chicken was a sphere of homogeneous material.
If we really wanted to be accurate, an FDM model probably wouldn’t be too hard to setup, and would let us more accurately account for changes in both the transient convection and the change in conductivity of the meat with temp. But I’m not motivated enough just to do all that for a nonsense problem lol
Then again I doubt we’d be able to create the exact same transient response just scaled by 3x without having to modify the setup since the insulation by the skin goes up as the fat melts (or is vaporized) and replaced by air which would happen sooner as we increase the temperature.
When I read ‘isnt a surface temp’ I instantly think of heat pipes you can run through the chicken to increase heat transfer from outside to inside. Not sure if that’s how anyone does it, but I wouldn’t be surprised if something like that is used somewhere
One can argue that 3 developers is also not the same as one developer multiplied by three, I’m not sure if incorrect use of temperature improves the joke or spoils it
900F isn’t 3×300F because 0F isn’t absolute zero.
3 × 300F =3 × (422K) =(1266K) =1819F
This is roughly the temperature of lava. So just mere seconds should be enough to get the chicken tasty as hell.
900F isn’t 3x300F or 1819F because the free convection heat transfer coefficient of air increases with temperature so the surface temperature of the chicken (and the temperature of the air touching the chicken) will be lower than 3x its value at 300F. If you want the chicken meat to experience a surface temperature that is 3x higher than 300F you need to up the heat a bit more.
Assuming the affects from Prandtl numbers are insignificant, and that a chicken is basically a sphere, the heat transfer coefficient should be roughly proportional to the fourth root of the Grashof number which is (roughly) linear with temperature difference (we’re neglecting viscosity changes because I’m tired, though those are probably significant)
Math I probably didn’t do right says that’s about 1.69x higher of a heat transfer coefficient
1.69x higher convection means 1.69x lower thermal resistance means we need roughly 1.69x as much temperature difference, so say the chicken is initially at 40F (refrigerator temp) that gives us 1.69x(1819-40)+40= 3,046.51°F
That’s pretty close to the temperature at which lead boils.
Unfortunately one shouldn’t cook around vaporized or superheated lead due to the likelyhood of it getting into the food, what a shame.
This person maths
Just proving the example works. A PM wouldn’t expect 3x performance from 3x the people, maybe about 1.7x. But 3x temperature will come out poorly anyway.
I would say trying to cook 3x faster isnt a surface temp 3x higher, but the rate of heat transfer is 3x faster. Because then your laat step is backwards.
Q = h a dT
If you just calculated H goes up 1.69x, then dT doesnt need to go up MORE, it needs to go up LESS. A higher HTC increases the rate of heat transfer. Which… now you need to recalc your free conv HTC because temp changed. But if it didnt…
3Q = 1.69h a 1.78DT
Old DT was 260, now its 463, which is an ovev temp of 503F
Edit: this is a transient problem we’re trying to reduce to a steady state calculation with pretty poorly defined requirements. Sounds like a typical day at work for me lol
True, temperature was just the main part of the meme and a higher temp is funnier anyway so I went with it lol
Also for a transient solution, idk the avg thermal conductivity of a whole chicken, which we’d need for a one-term approximation if we assumed the chicken was a sphere of homogeneous material.
If we really wanted to be accurate, an FDM model probably wouldn’t be too hard to setup, and would let us more accurately account for changes in both the transient convection and the change in conductivity of the meat with temp. But I’m not motivated enough just to do all that for a nonsense problem lol
Then again I doubt we’d be able to create the exact same transient response just scaled by 3x without having to modify the setup since the insulation by the skin goes up as the fat melts (or is vaporized) and replaced by air which would happen sooner as we increase the temperature.
When I read ‘isnt a surface temp’ I instantly think of heat pipes you can run through the chicken to increase heat transfer from outside to inside. Not sure if that’s how anyone does it, but I wouldn’t be surprised if something like that is used somewhere
Wouldn’t this be easier done in vacuum with thermal radiation?
A non-rotating spherical chicken in vacuum might simplify the calculations, but I prefer to get the rotisserie effect.
If you start getting into radiation heat transfer, then you have to consider the difference of temperatures, but both raised to the 4th power first.
One can argue that 3 developers is also not the same as one developer multiplied by three, I’m not sure if incorrect use of temperature improves the joke or spoils it
now you’ve got three ovens
Now this is ringing some bells