E11 Heat conduction

Topic

When a food item—whether a solid or semi-solid, such as a steak, a potato, or a bread crust—comes into contact with a hot surface, heat conduction is initiated within the food itself: heat propagates toward the interior without any macroscopic movement of matter, occurring solely through direct contact between adjacent particles within the food. Fourier's Law establishes that the heat flux passing through the food is proportional to the internal temperature gradient and inversely proportional to the thermal resistance of the material—a resistance that characterizes the food's thermal conductivity. Consequently, a food with high thermal conductivity (such as lean, water-rich meat) conducts heat more rapidly than one with low thermal conductivity (such as a high-fat food). Thus, higher thermal conductivity results in a greater heat flux passing through the food, in accordance with Fourier's Law.

During the transient phase following initial contact with the hot surface, the temperature profile within the food evolves according to the diffusion equation. This evolution is governed by the food's thermal diffusivity—a property combining thermal conductivity with the capacity to store received thermal energy. A food with high thermal diffusivity heats its interior more quickly than one with low thermal diffusivity—even if both share the same thermal conductivity—because the former experiences a greater temperature rise for every unit of thermal energy received. Therefore, higher thermal diffusivity causes the interior of the food to heat up more rapidly, in accordance with the diffusion equation. Thus, this model—based on the heat conduction and thermal diffusivity parameters introduced at the outset—uses the Biot number to compare the food's internal thermal resistance with the thermal resistance at its surface relative to the surrounding environment: when the Biot number falls below a low threshold, the food's internal thermal resistance becomes negligible compared to the surface thermal resistance, allowing the entire piece of food to be treated as a single lumped mass at a uniform temperature; conversely, when the Biot number rises well above that threshold, internal thermal resistance dominates, making the temperature profile within the food—rather than the lumped-mass approximation—the decisive factor. Consequently, if the food is thinner (having a smaller characteristic dimension), the Biot number is lower and the food reaches its cooking temperature more quickly; conversely, if the food is high in fat—possessing lower thermal conductivity and thermal diffusivity than a high-water-content food—it takes longer to cook.

ID:2418