Modelling Thermal Diffusivity of Heterogeneous Materials Based on Thermal Diffusivities of Components with Implications for Thermal Diffusivity and Thermal Conductivity Measurement

Abstract

Effective thermal diffusivity models are useful for predicting thermal diffusivities of heterogeneous materials. The literature contains models that may be broadly categorised into four different types: (1) effective thermal diffusivity for highly specific applications (e.g. empirical curve fitting of measured data); (2) effective thermal diffusivity as a weighted averages of the components’ thermal diffusivities and volume fractions; (3) effective thermal diffusivity calculated from effective thermal conductivity, effective density and effective specific heat capacity known as the ‘lumped parameter’ approach (which is the most commonly employed method); (4) comparison of times for a fixed quantity of heat to be transferred to a composite material with the heat transfer time for a material with an effective thermal diffusivity. The latter three modelling methods were tested on theoretical composite materials, and none performed consistently better than the others, suggesting there is scope for further work in this area. Of the three methods, the least accurate on average was the lumped parameter method. Given that this relationship is often used to derive thermal conductivity data from thermal diffusivity data (or vice versa), it is possible that significant error is introduced to the derived property in addition to any measurement error, which is often not acknowledged.