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Jul 4, 2012 09:22 AM
Discussion

### Diffusivity

I haven't seen thermal diffusivity mentioned in the discussions about pans. It's the conductivity divided by density and heat capacity. It in effect determines how uniformly the object heats up. The Wiki article mentions a flash method for measuring it - apply a pulse of heat at one end of the sample, and measure the temperature change along its length. Think of that as a refined version of putting a pan on the burner for a bit, and measuring the temperature away from the burner.

For copper, it is 111 mm2/s
pure aluminum lower at 84, with alloys in the 60s and 70s
carbon steel 12
stainless steels around 4
iron is 23 (on the Wiki table), but this is probably pure iron. My guess is that cast iron is more like carbon steel, or maybe even lower

Air is around 20, as is steam. But water is 0.14

Since diffusivity of water is so much lower than the metals, it's the property of the water that determines bulking heating time, much more so than the pan's. Convection, and eventually boiling bubbles speed up the heating of the water. And the pattern of bubbles reflects diffusivity in the pan bottom.

This property came to my attention in a food science article discussing thermal properties of foods, ending with an example of a baked Alaska, where the low diffusivity of meringue and cake keep most of the ice cream frozen while the meringue is browned.

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1. Hi, Paul:

It's been mentioned a few times, but not in the clear the way you just did. Thanks!

Aloha,
Kaleo

1. Paul,

It has been mentioned a few times here before. Of particular this article has been cited a few times for cookware:

Pulling it together: thermal diffusivity
If you've been paying attention, you'll realize that I've misled you when I discussed thermal conductivity. ....

http://www.cookingforengineers.com/ar...

The important takes home message is that thermal conductivity is only part of the thermal diffusivity. When we are talking about an empty copper pan and an aluminum pan, they do not conduct heat the same, but they create similar temperature profile.

1. re: Chemicalkinetics

I didn't recall any mention (though conductivity and heat capacity have been discussed), but I also did a search (default 1 yr) for 'diffusivity' and only got threads about 'diffusers'.

2. Another pot comparison

the cooling times for hot water in a cast iron pot v. stainless steel one.

The discussion points to higher convection+radiation heat losses from the cast iron pot.

7 Replies
1. re: paulj

Hi, Paul:

IMO, what it points to are: (a) the relatively huge thermal mass of water; (b) cast iron's terrible conductivity; and (c) SS's even worse conductivity.

I'm doubting this guy's temperature plots, too. 5L of water dropping 50-60C covered and bottom-insulated in 5 minutes? 2.5L dropping 40-50C in 2 minutes? This sounds too fast to me.

Aloha,
Kaleo

1. re: kaleokahu

The time scale is hours

1. re: paulj

Ooops, my bad. I guess I'm missing the practical point of waiting 5 or 2 hours for a liquid to cool.

Oh, there have been multiple links over the years to Sam Kinsey's eGullet article on understanding stovetop cookware. http://forums.egullet.org/index.php/t... The paragraph on diffusivity is abut 2/3 into the piece. NB: KInsey says thermal diffusivity is the material's conductivity divided by the product of its density and specific heat.

Aloha,
Kaleo

2. re: paulj

I am not sure how convection (air or water) comes into play here. Radiation sure. One of the discussion about blackbody radiation assumption is incorrect.

"The blackbody radiation terms, according to the reported emissivities, are 135W and 10W...."

If it is blackbody, then the emissivity is one. There won't be any difference. The fact is that they are NOT blackbody.

1. re: Chemicalkinetics

http://www.engineeringtoolbox.com/emi...

The table in original article gives the respective emissivity coefficents as .95 and .07, which is consistent with this link - a mat black cast iron surface versus a shiny stainless steel one. So that 135 v 10 w ratio is reasonable. And blackbody radiation about 100w for 1000 cm2 at around 50c is the right ball park.

1. re: paulj

Paul,

First, the response states that "The blackbody radiation terms, according to the reported emissivities, are 135W and 10W.". What I wrote was that these objects are not blackbodies, and if they are blackbodies, then there won't be coefficient difference, and definitely not 0.07 of a pot sitting on a stove with a temperature gradient.

Anyway, like I said, radiation can be a very good explanation here.

1. re: Chemicalkinetics

They aren't black bodies, but their thermal radiation can be estimated by multiplying the black body radiation (4th power of temperature in K) by the 'reported emissivities' of .95 and .07. That's what the 135 and 10w numbers represent.

I'd have to go back an look at the discussion, but weren't they talking about radiation while the pots were sitting on cork hot pads.

The working might not be quite right, but I think the concept and back-of-the-envelope numbers are valid.

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