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Background:

As some may know, pizza stones, used to accumulate heat before the pizza dough is put into the oven, are often made of cordierite. If it's well heated it should provide the underside of the pizza with a slightly-scorched crust by the time the 90 seconds or so for crusting the upperside are over.

I plan to special-order a round stainless steel (316) plate for my butane-burning gas oven, which reaches about 500 degrees Celsius. I want to estimate how well will the stainless steel heat up and then transfer heat in comparison to the cordierite stone, to adjust heat-up time and material thickness to prevent burning or under-cooking.

Question:

From one website I gathered the specific heat for stainless steel 316 is 490 J/kg.K while thermal conductivity is 13 W/m.K. For cordierite it's up to 850 and 1.7 respectively. So the heat capacity for the stainless steel is about 40% lower, but it's thermal conductivity is about 700% higher.

Should heat transfer from the gas burners within the oven be mostly conduction or radiation? How does that affect the ability of the stainless steel plate to heat up, and does its polishing level matter? And should the heat emitted back from the stainless steel have greater difficulty reaching the dough evenly considering the dough might not sit completely flat on the plate due to air pockets?

Thank you.

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  • $\begingroup$ Do you place the pizza on the plate (steel or cordierite), then enter plate with pizza in the oven for cooking of the pizza? $\endgroup$
    – Gert
    Commented Mar 6, 2022 at 15:51
  • $\begingroup$ @Gert The plan is to heat the steel plate in advance. Otherwise the underside of the pizza will probably remain a half-baked mess stuck to the plate by the time the cheese starts burning. $\endgroup$
    – TLSO
    Commented Mar 6, 2022 at 16:12
  • $\begingroup$ Ok, I see. I'll formulate an answer. $\endgroup$
    – Gert
    Commented Mar 6, 2022 at 16:28
  • $\begingroup$ @Gert Thanks. By the way, to add some more information, the pizza stone in this case would stay in the oven and the steel plate would sit on top of it. I saw in some place that people discussing this suggested a steel would cool down too quickly, and I planned to have the steel at just 2.5mm thickness so it won't weigh too much (the idea is to be able to rotate the plate itself relatively easily). Cordierite stones are usually over 1cm thick, which density-adjusted weigh like a 2.5mm stainless steel 316 or more. So perhaps that's a little under-massive, but with the reserved stone still below? $\endgroup$
    – TLSO
    Commented Mar 6, 2022 at 17:45

1 Answer 1

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We need to distinguish two processes here:

  1. preheating of the plates, prior to use for 'cooking' the pizza,
  2. use of the plates for 'cooking' pizza.

For the first process we assume the plate to be thin ($z$-direction) compared to its other dimensions and these other dimensions ($x$ and $y$-directions) to be small compared to the oven itself.

Pizza plates

If so then we can assume there are no temperature gradients in the plate:

$$\frac{\partial T}{\partial x}=\frac{\partial T}{\partial y}=\frac{\partial T}{\partial z}=0$$

In plain English this means that although the temperature $T(t)$ of the plate will rise during heating, the plate's temperature will be homogeneous.

At $500^{\circ}\mathrm{C}$ oven temperature we can't exclude radiative heating, in addition to convective heating. But with the above assumption conductive heat transfer will not be considered.

Radiative heat transfer (oven$\to$plate) is prescribed by Stefan Boltzmann Law and looks like this, where $T_{\infty}$ is the oven temperature (presumed homogeneous and constant):

$$P_R=\sigma \left(T_{\infty}^4-T(t)^4\right)$$

Convective heat transfer is prescribed by Newton's Law of Cooling/Heating $$P_C=hA\left(T_{\infty}-T(t)\right)$$ So: $$P=P_R+P_C=\frac{\mathrm{d}q}{\mathrm{d}t}$$ And: $$\mathrm{d}q=m c_p\mathrm{d}T$$ $$\frac{\mathrm{d}T(t)}{\sigma \left(T_{\infty}^4-T(t)^4\right)+hA\left(T_{\infty}-T(t)\right)}=\frac{\mathrm{d}t}{mc_p}\tag{1}$$ The ODE $(1)$ could be integrated between $[0,T_0]$ and $[t,T(t)]$ (the form of the undetermined integral can be found here) but we don't really need to do this for our purpose.

Rather we can evalutate the RHS of $(1)$ which shows us that the temperature evolution $T(t)$ (or heating rate $\frac{\mathrm{d}T(t)}{\mathrm{d}t}$) will be slower for higher $c_p$, as well as for higher $m$. This is hardly surprising and well in line with intuitive expectations.


The 'cooking' phase can itself be regarded as the result of two processes:

  1. radiative heating for the pizza top, as above,
  2. heating of the pizza base by heat transfer from the plate to the pizza.

This second mode does pose some problems to a modeler and requires some choices to be made.

I suggest the lumped capacitance method suggested in this excellent ebook at p.194 to 196 (note that $\bar{h}$ in the text is not equal to $h$ above).

In it, the temperature of the pizza's base, is assumed to jump sharply at $t=0$ (the point we put the pizza on the plate) to some value $T_i$.

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  • $\begingroup$ Thanks, although I perhaps I need it more dumbed-down in order to conclude anything for the oven situation, as I'm not sure how to apply your answer yet. Also worth noting is that A. there is a great thermal gradient in the oven as the burners are only at its innermost side, and B. regarding convective heating, I understand the gasses transfer heat throughout the air like that, but the metal itself is solid and thus isn't directly heated through convection but through conduction, and the question is how are radiative absorption and conductive absorption compare for stainless steel. $\endgroup$
    – TLSO
    Commented Mar 6, 2022 at 20:55
  • $\begingroup$ Ovens like the one you describe have remarkably homogeneous temperatures, due to hot gas turbulence. A steel plate in an oven like that receives heat from radiation, as well as convection. For a relatively thin plate heat conduction can be reasonably neglected (as I did). To evaluate the relative importance of radiative and convective heating, compare $P_R$ and $P_C$. $\endgroup$
    – Gert
    Commented Mar 6, 2022 at 22:25
  • $\begingroup$ Also, please don't underestimate the power of simple experimentation: a kitchen IR thermometer and a stopwatch can go a very long way in understanding what is going on. $\endgroup$
    – Gert
    Commented Mar 6, 2022 at 22:32
  • $\begingroup$ In regards to temperature homogeneousy, the inside is definitely hotter than the outside: I don't remember if I tested that myself after giving the cordierite a decent pre-heating time, but in reviews of a similarly-designed oven, which has the same open, no-door design (even if the opening is relatively narrow and designed to circulate turbulence inwards), it was shown the outermost part of the stone was maybe 300° Celsius vs 500° near the burners. I want to add a stainless steel plate so I could easily rotate the entire thing with the pizza, which is crucial for baking uniformity. $\endgroup$
    – TLSO
    Commented Mar 7, 2022 at 4:44
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    $\begingroup$ Read and noted. Good luck! $\endgroup$
    – Gert
    Commented Mar 8, 2022 at 21:00

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