Cooking For Engineers

[Guest]

Heating an enameled cast iron dutch oven inside a stove (oven): rate of heat transfer by IR radition vs rate of heat transfer by conduction (air-to-metal)?

Given an enameled cast iron dutch oven color white vs an indentical vessel color black, how much faster will heat be transferred to black one relative to the white one when both are placed into a pre-heated 500deg oven? Big difference? Small difference?

Thanks,
JonnyP

[Dilbert]

technically one could do the math - it'd work for only one 'brand / model' as the IR coefficient of the oven internals will vary - along with the pots.

big / small? how about noticeable?

noticeable is a definite yes. here's a pix of the same dough, split into two loaves, into/out of same oven at same time (+/- seconds)

one in a silvery pan, one in a darker pan - see the crust.

[Jim Cooley]

I wonder of the color of an oven's interior also affects cooking times? I used to have an oven that was slow as hell, yet the temps were always spot on.

[JonnyP]

Dilbert, Great photo above; it shows a lot.

Still, can we figure out a ballpark ratio for how much energy is transferred to the cooking vessel per unit time by IR radiation (ideal, infinately large black oven, 500 deg F) vs conduction (air to vessel wall) for a black vessel, and compare that to an otherwise identical white one?

Expressing these as a ratios cancells out many variables. Assuming that convection keeps the air perfectly at 500 deg F around all parts of the vessel simplifies things further.

At 500 deg F, given a black vessel, is greater than 50% of heating done by IR radiation (vs conduction)?

Thanks,
JonnyP

[Dilbert]

if you want to do the exercise - be my guest (g)

throwing darts, I'd put the IR contribution on the order of 10%

I also have a clear glass loaf pan that bakes quite similar to the dark one.

oh, in an infinitely large oven the IR contribution is zero; radiant energy falling off at the distance squared and all that . . . .

[JonnyP]

JonnyP answers Dilbert:

"if you want to do the exercise - be my guest (g)"
To tackle this excersie, I'd need to start by pre-excercising my atrophied (now quite flabby) mathematical muscles...

"throwing darts, I'd put the IR contribution on the order of 10%"
10% IR contribution for white vessel, or for a black one?

"I also have a clear glass loaf pan that bakes quite similar to the dark one."
This is an important observation: Thick heavy clear glass loaf pan bakes quite similar to a thin dark metal pan. Assuming that you start both loaves in a "cold pan" placed into a preheated oven, you can see that the glass pan has more more mass, and much less thermal conductivity than your dark metal pan. Yet somehow, they bake quite similarly. This would seem to indicate that >50% of heating is done by IR through the glass.

"oh, in an infinitely large oven the IR contribution is zero; radiant energy falling off at the distance squared and all that . . . ."
As I understand it, an infinitely large oven, uniformly heated at 500deg, would have a uniform internal IR radiation spectra as described by blackbody radiation.

I continue to experiment with all sorts of vessels to bake my bread. In order to make sense of the results I see, I am coming to the #1 physics-guy-cooking site rather than seeking dopy answers elsewhere. I have photos of my bread, with 3 loafs baked in 3 very different vessles, but I see no way to upload them directly to this site.

Your "Common Materials of Cookware by Michael Chu" http://www.cookingforengineers.com/article/120/Common-Materials-of-Cookware is a powerhouse of prime content. Attempting a similar article regarding bakeware is the next logical step in defining what "Cooking for Engineers" is all about.

If you are game, can I help?

At 500 deg F (533 deg K), the backbody IR spectrum peaks at about 5.5 micrometers (um) wavelength (aka: "mid-infrared") with a sharp decline at lower wavelengths (see: http://www.spectralcalc.com/blackbody_calculator/blackbody.php).

So, what I'd like to know: is it possible to ballpark the emissivity (same as absorbtion; http://tes.asu.edu/MARS_SURVEYOR/MGSTES/TES_emissivity.html) of black vs white cookware at this temperature?

Thanks again,
JonnyP

[Michael Chu]

[JonnyP]

Michael Chu,

Thanks for your response; I will investigate this further. As I understand it, the emissivity for any given surface varies with respect to wavelength. Therefore, if the IR thermometer is designed to detect only one specific wavelength, then it may not represent the area over the emissitivity curve of that surface (which is always less than 1; as 1 is defined by the blackbody curve at that given temperature).

With further research, I am starting to think that differences DO exist in the emissivity of white vs black enameled bakeware, and that these differences are much more pronounced at 500F than 350F (or vice-versa). As oven temp increases, the black-body IR power curve grows taller and taller at shorter wavelengths.

As I investigate further, my daughter Sophia continues to enjoy my bread (see pics below).

Thanks,
JonnyP