Development of correlations for effective thermal conductivity of a tetrakaidecahedra structure in presence of combined conduction and radiation heat transfer

The variations in the total effective thermal conductivity (keff,t) of a tetrakaidecahedra unit cell structure as functions of porosity (ϕ), thermal conductivity of the solid phase (ks) and the average temperature of the medium (Tavg), in the presence of combined conduction and radiation heat transfer, are presented in this article. For this purpose, the governing energy conservation equation is numerically solved using the blocked-off region approach based on the finite volume method. In addition, the variations in the radiative properties of the structure as functions of surface reflectivity (ρs), pore density (PPC) and ϕ are investigated, for which, a pure radiation heat transfer based numerical model is developed and used. From the detailed numerical simulations, three different correlations for keff,t are proposed. Correlation 1 is developed by fitting the raw simulated data, although its form does not respect some of the limiting conditions. Particularly for ks<5W/mK and in the absence of thermal radiation, it under-predicts the effective thermal conductivity due to pure heat conduction (keff,PC). Correlation 2, on the other hand, satisfies all possible limiting conditions, although it requires one additional simulation or correlation for keff,PC. Finally, correlation 3 is obtained by superposing the effective thermal conductivities due to pure radiation (keff,R) and keff,PC, while introducing an adjustable coefficient in order to account for the coupling between them. From the investigation on radiative properties, it is observed that the extinction coefficient increases with the decrease in ϕ and with the increase in PPC as well as ρs and hence keff,t as well as keff,R is expected to decrease for these conditions.