Effective Thermal Conductivity Model for Tetragonal Pin Array Stack

Thermoacoustics is the science which describes the energy conversion between mechanical energy, in the form of acoustic waves, and heat. This energy conversion takes place in a particular porous material, named “stack” or “regenerator”, which represents the core of these devices. In literature, convex uniform cross-section geometries, such as longitudinal pin array, are found to be the most efficient stack for thermoacoustic applications, thanks to the low viscous losses. On the other hand, another fundamental characteristic required for thermoacoustic porous cores is the ability to sustain a static thermal gradient along their axial length. For this reason, stack configurations with low thermal conductivity, such as transversal pin, have been also considered. Therefore, a tetragonal pin array geometry comes out as thermoacoustic stack from a trade-off between the classical longitudinal pin array (low viscous losses and high thermal conductivity) and the transversal pin array (high viscous losses and low thermal conductivity). In this work, an analytical model to assess the effective thermal conductivity of the tetragonal pin array stack is provided in order to correctly estimate the heat flux along this typology of stack. Such an analytical model has been then verified both by FEM-based numerical simulations and other correlations found in the literature.