Two-dimensional radiant conductivity model for heat-generating cylindrical porous media: Development and experimental validation

Accurate mathematical models describing high-temperature porous bed heat transfer can provide insights into the optimisation of industrial processes and improve their thermodynamic efficiency. Several heat transfer models have been proposed for various applications to achieve this objective. However, the thermal radiation characterisation of porous beds is difficult partly due to the physical complexity and the shortage of experimental validation of reported numerical models. Estimation of porous bed temperature profile through the radiant conductivity method is a subject of extensive study. However, the reported methods are bereft of multidimensional and generalized applications. Such specificity in their application renders these methods highly restricted. This paper presents a novel two-dimensional radiant conductivity model for a heat-generating porous bed of cylindrical rods. The radiant conductivity is assigned as a function of the radiation exchange factor $\left(F\right)$, and the average cylinder surface temperature $\left(\overline{T}\right)$. $F$ is estimated to be a function of the optical properties of the porous media. The presented model is verified and validated against a multi-dimensional experimental investigation of a heat-generating cylindrical bed with a deviation of less than 7 %. The proposed model is well adapted for estimating the thermal radiation field for various cylindrical bed configurations and can be easily implemented into the energy equation of the porous media. The radiant conductivity of the porous bed is revealed to be influenced by the arrangement of cylindrical rods and the number of interacting cylinders. The radiative field is estimated by the presented model with similar accuracy to the classical methods (for dilute systems; $\mathrm{porosity}\to 1$) with a significant reduction in the computational cost.