## Cooking Thermodynamics

This year for Christmas, knowing my love of comparative cooking methods, my wife Deborah got me an Air Fryer; the results have been delicious.(1) This got me thinking about the thermodynamics of cooking(2) and what it would take to model both an air fryer and a past present (the instant pot).(3)

## Physical (modeling)

Cooking is a heat transfer problem; move the energy from the cooking device into the food.

• Pan cooking: conduction
• Oven cooking: conduction and radiation
• Air frier: conduction, radiation and convection
• Instant pot: conduction

However there are limitations. The maximum temperature of an oven is limited to the energy of the heating method (gas or electric), boiling liquids are “capped” at the boiling point of water; this then is the “trick” to both the air fryer and the instant pot. The air fryer combines 3 methods for transferring heat, while the instant pot increases the pressure in the “pot” which raises the boiling point of water.(4)

## Three simple rules

Cooking with an air fryer has three simple rules:

1. Pre-heat: Heats the basket, giving conduction cooking
2. Space out: Aids in convection
3. Shake: Gives all sides a shot of conduction

From this we can determine that when you cook there is browning in the contact in the pan, that the air blows around the food from all sides (and the bottom) and that to get brown all sides of your food need to touch the bottom. So what would the physical model look like and how do we optimize the results?(5)

## Equation time!(6,7)

For now let’s assume a Platonic solid French Fry, e.g. cube 1 cm x 1cm x 1cm.(8) In this case the equations for the heat transfer could be written as…

• Conduction: Q/Δt = -k * A * ΔT/Δx (9)
• Convection: Q/Δt = A h(Tp – Tpf)(10,11)
• Radiation: By evaluation O(10-3): dropped

By further inspection we can see that Q is the energy from the heating unit. If we assume that the thermal mass can be treated as an infinite sink (and if we have Platonic Fries we can allow this) then we can reorder the equations as so…

Tpf = Q/(Δt) * ((1/k*A1) + (1/h*A2)) + Tp

Extensive field work is now ongoing to determine by experiment the values of k,h, A1 and A2 for Platonic fries (and other foods). The formula for “browning” is also under development, but as I hope this article has shown you, it is possible to determine through analysis and simulation.

## Footnotes

1. The biggest surprise is how good the “air fried” carrots are; they are a reliable “go-to” afternoon snack.
2. The control algorithm for this device is very simple, a boolean for the fan on or off, and a predictive element for the temperature.
3. I find it most interesting to alternate between new kitchen gadgets and experimenting with just a pan, bowl and knife.
4. I just had a thought; when you flambe food or cook with alcohol in general it boils off due to the lower boiling point than water; what would happen in the instant pot?
5. In this case optimizing the results means crispy exteriors and internal temperature cooked to “done.”
6. “Equation time” sounds like a kid show that I would like to see produced.
7. Despite the image we will not be covering solar roasters today.
8. When I picture this it sounds more like Platonic Hash Browns
9. The thermal conductivity of a potato should be similar to that of water due to the high water content of the potato.
10. Tp is the pan’s temperature and Tpf is Platonic fry’s temperature.
11. The “A” term in this equation is affected by the crowding of the pan; the more crowded the food the lower the A.

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