Use of simple thermal conductivity models to assess the reliability of measured thermal conductivity data

Physical property data (including thermal conductivity) are required for designing thermal processes such as freezing and chilling of foods. These data are necessary for design optimization to enhance quality as well as efficiency. Numerous thermal conductivity data have been reported; however, some of these are obviously inaccurate.

The inaccuracy observed in thermal conductivity data for food items may be due to indirect measurement methods, typographical errors or variability of food properties. It therefore becomes a problem assessing whether or not thermal conductivity data presented in the literature are accurate, especially when the measurement approach is not discussed. Dr. James Carson, a senior lecturer at University of Waikato in New Zealand discussed in his paper how thermal conductivity models can be helpful in assessing the integrity of thermal conductivity data presented in any piece of literature. His work is now published in the International Journal of Refrigeration.

Provided no chemical changes occur as a result of the mixing process, it is clear from simple heat transfer analysis that the thermal conductivities of mixtures should be greater than that of the component with the lowest thermal conductivity and lower than that of the component with the highest thermal conductivity value. Applying this simple principle to foods measured or published data which are lower than thermal conductivity of air or higher than that of liquid water (in the case of unfrozen foods) or ice (in the case of frozen foods) should be discarded. Specifically, unfrozen food should have thermal conductivities ranging between 0.02 and 0.63 W m m^-1 K^-1 (representing thermal conductivity values of air and water respectively) and for frozen food, between 0.02-2.6 W m^-1 K^-1 (representing the thermal conductivity of ice).

In addition, the thermal conductivity of a heterogeneous material is bounded by thermal conductivities calculated by the Series model (lower bound) and Parallel model (upper bound), together referred to as the Wiener Bounds. These two models are straightforward to apply to food products, requiring no knowledge of the actual structure of the food. If it is reasonable to assume that food structure is isotropic (at least when considered on a macroscopic scale) then the two forms of the Maxwell-Eucken model, provide the upper and lower bounds (known as the Hashin-Shtrikman bounds). Since the Hashin-Shtrikman bounds lie within the Wiener bounds, they place even tighter constraints on the range of realistic thermal conductivity values.

The author recommends using these bounds as a means to check the accuracy of measured thermal conductivity data before publishing or using published data in any computation; those that lie outside the applicable bounds (allowing for measurement uncertainty) are unreliable. Also, he recommends that thermal conductivity data must be published together with composition details.

Dr. Carson presented in his paper several examples to illustrate the use of the bounds to evaluate published data.