E82 Thickness - Cooking Control

Topic

The thickness of the food item is a critical dimension for determining both cooking uniformity and the time required for heat to reach the center. In a piece heated evenly from both sides, the characteristic distance heat must travel corresponds roughly to half the thickness, whereas heating primarily from one side means it must travel the full thickness. Consequently, cooking the piece from both sides reduces the maximum distance heat must travel and significantly accelerates the heating of the center.

When this characteristic dimension is large relative to the thermal penetration depth—a parameter established in another model within this set—the heating process can initially be approximated using conduction solutions for a semi-infinite solid, described by error functions. These solutions demonstrate that the characteristic distance reached by the heat increases roughly with the square root of time; conversely, the time required to heat to a specific depth increases roughly with the square of that distance. Thus, increasing the food's thickness means the center takes much longer to undergo a significant temperature rise.

This heating of the center also determines the thermal treatment received by microorganisms. The D-value represents the time required to achieve a decimal reduction in a microbial population under defined conditions and at a specific temperature, while the z-value represents the temperature change needed to alter the D-value by a factor of ten. Consequently, small temperature differences can lead to significant variations in the time required to achieve a specific level of microbial reduction. A thicker food item means the center takes longer to reach the necessary temperature, thereby requiring more time to achieve an equivalent thermal treatment at that location.

In thick pieces, a conflict also arises between sufficiently heating the center and browning the surface through reactions such as the Maillard reaction—a process addressed in another model in this set. The surface is directly exposed to the heat flux and can rapidly reach high temperatures, whereas the center responds much more slowly via conduction. Continuous exposure of a thick piece of food to very high external temperatures can cause the surface to brown excessively before the center reaches the desired level of cooking. Strategies that combine more moderate, prolonged heating with a brief high-temperature phase make it possible to partially decouple internal heating from surface browning.

The relationship between thickness and the depth of heat penetration allows for an assessment of cooking uniformity. When the distance from the surface to the center is small relative to the depth reached by the heat, internal temperature differences decrease, resulting in relatively uniform cooking. When that distance is large, a significant gradient persists between the hot surface and the still-cold center. Dividing the food into thinner pieces reduces the distance the heat must travel; given that the time required is roughly proportional to the square of that distance, this can drastically cut the time needed to achieve rapid, uniform cooking throughout the piece.

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