Why does cooking time scale with thickness squared (D^2) instead of linear thickness?

Heat transfer through solid meat is governed by transient conduction (Fourier's Law). The time required for heat to conduct inward is proportional to the square of distance from the surface. A 2-inch thick roast has twice the thickness of a 1-inch steak but requires roughly 4 times longer to reach target core temperature under identical heat flux.

What is thermal diffusivity (alpha) and why does fat content change it?

Thermal diffusivity (alpha = k / [rho * Cp]) measures the rate at which heat transfers through a material relative to its heat storage capacity. Water has high heat capacity, making lean meat diffuse heat at ~0.13 mm2/s. Rendered fat has lower heat capacity, increasing diffusivity up to ~0.17 mm2/s.

Why is carryover cooking virtually zero in sous vide but massive in a 400 deg F oven?

Carryover cooking is driven by the temperature gradient between the hot outer meat layers and the cooler center. In sous vide at 132 deg F, the exterior never exceeds 132 deg F, so no excess heat exists to conduct inward. In a 400 deg F oven, the exterior is 250-300 deg F, providing a vast reservoir of heat that continues soaking inward after removal.

How does a convection fan reduce cooking time?

In a still oven, a stagnant insulating layer of air and evaporating steam clings to the meat surface (low heat transfer coefficient h ~ 10-15 W/m2K). A convection fan sweeps this boundary layer away, raising h to 25-35 W/m2K and accelerating surface heat absorption by 20-30%.

Meat Thermal Diffusivity Cook Time Calculator

Model transient 1D heat conduction through solid muscle tissue using thermal diffusivity (alpha) to predict exact minutes to core target temperature.

Master Rule: Heat conduction in solid meat follows Fourier's Law. Cook time scales with the square of meat thickness (D^2). Doubling roast thickness quadruples total cooking time regardless of oven temperature.

Configure Parameters

Meat Thickness / Diameter 45 mm

Thermal Diffusivity (alpha) 0.14 mm2/s

Oven / Smoker Chamber Temp 250 deg F

Starting Core Temp 38 deg F

Target Pull Core Temp 132 deg F

Convective Environment

Calculated Targets

ESTIMATED COOK TIME

46 min

Fourier Number (Fo): 0.86 | Carryover Rise: +7.2 deg F

Fourier Number (Fo)

0.86

Carryover Temp Rise

+7.2 deg F

Half-Time to Center (t50)

25 min

Surface-to-Core Delta

118 deg F

Because cook time scales with thickness squared (D^2), a 60 mm roast takes approximately 1.78 times longer to cook to the center than a 45 mm roast under identical chamber conditions. Account for carryover cooking by pulling 5-10 deg F below final target.

Thickness Squared Law and Thermal Conduction Timelines

Meat Thickness	Oven / Water Temp	Heat Transfer Mode	Time to 132 deg F Core	Fourier Number (Fo)	Carryover Peak
25 mm (1.0 in Steak)	250 deg F Still Smoker	Air Convection (h=12)	24 min	0.82	+4.2 deg F
38 mm (1.5 in Steak)	250 deg F Still Smoker	Air Convection (h=12)	42 min	0.85	+6.8 deg F
50 mm (2.0 in Roast)	250 deg F Still Smoker	Air Convection (h=12)	68 min	0.88	+9.4 deg F
75 mm (3.0 in Prime Rib)	225 deg F Still Smoker	Air Convection (h=12)	152 min	0.91	+12.5 deg F
50 mm (2.0 in Roast)	134 deg F Sous Vide	Water Immersion (h=750)	105 min	1.18	+0.4 deg F (Zero carryover)
100 mm (4.0 in Standing Rib)	225 deg F Convection Fan	Forced Air (h=30)	260 min	0.94	+14.0 deg F

Precision Master Protocol

1

Measure total cross-sectional thickness at the thickest anatomical geometric center using precision calipers or a ruler.
2

Calibrate meat thermal diffusivity based on intramuscular fat content (lean muscle ~ 0.13 to 0.14 mm2/s, fatty cuts ~ 0.15 to 0.17 mm2/s).
3

Insert an oven-safe probe thermometer exactly into the geometric thermal center of the meat, avoiding proximity to bone or large fat seams.
4

For roasts thicker than 60 mm, lower oven chamber temperature to 200-225 deg F to prevent severe outer thermal gradients and surface drying.
5

Pull the roast when probe reads target core temperature minus calculated carryover rise, and rest on an elevated wire rack.

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