E81 Food Size - Diffusion and Heat

Topic

The size of the food item is a key determinant of its cooking time. When heating is primarily governed by internal conduction, the characteristic time required for heat to reach the center increases roughly with the square of the characteristic dimension and inversely with thermal diffusivity—consistent with the heat conduction principles established in another model within this set. Doubling the food's linear dimension can increase the characteristic heating time by approximately fourfold, provided geometric and thermal conditions remain comparable.

The Fourier number relates elapsed time, thermal diffusivity, and the square of the characteristic dimension, offering a dimensionless measure of thermal diffusion progress within the food. A low Fourier number indicates that heating is still largely confined to regions near the surface, whereas higher values ​​signify significant heat penetration toward the center. Analytical solutions for transient conduction—including those represented by Heisler charts or approximations—allow for the estimation of internal temperature changes when the relevant conditions are met. As time elapses, the Fourier number increases, and the center progressively approaches thermal equilibrium with the surroundings.

The characteristic depth of thermal penetration increases roughly with the square root of the product of thermal diffusivity and time. This value indicates how far the thermal disturbance has significantly advanced from the surface. If the item's size is small relative to this depth, heating will have reached virtually the entire interior; if it is much larger, the center may remain considerably cooler even after the surface is cooked. Increasing the cooking time causes this thermal penetration depth to advance progressively toward the interior.

The diffusion of a solute, such as salt, into the food is typically much slower than heat diffusion, because the molecular diffusion coefficient within a food matrix is ​​generally far lower than thermal diffusivity. Consequently, during standard cooking, heat can reach deep regions long before salt applied to the surface does. In contrast, marinating or dry-salting for several hours allows for significantly greater penetration, governed by the molecular diffusion described in another model within this set. Short cooking times make this disparity between heat transport and solute transport even more pronounced.

Finally, the Biot number compares the resistance to conduction within the food to the resistance to heat transfer between its surface and the surrounding medium. It increases with the food's characteristic dimension and the surrounding medium's convective heat transfer coefficient, while decreasing as the food's thermal conductivity rises. A low Biot number indicates that external resistance is relatively significant and the internal temperature tends to remain fairly uniform; a high Biot number indicates that internal resistance dominates, leading to substantial temperature gradients between the surface and the center. Heating the food in a medium with a higher convective heat transfer coefficient—such as moving water rather than air—increases the Biot number, making the food's internal conduction a more significant limiting factor in the cooking process.

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