Estimation of effective thermal conductivity for porous material

In this study, an algebraic expression for the effective thermal conductivity (ETC) of two-phase porous materials is derived using a two-layer model, which is analogous to the electrical resistance in an electrical circuit. This analytical approach enables the evaluation of the ETC through the proposed algebraic expression for two-dimensional porous media. The geometries under consideration include arrays of non-touching in-line and staggered square and circular cylinders, as well as touching hexagonal arrangements, rectangular grilles, criss-cross grilles, hexagons, and touching square cylinders. Comparison of the results obtained from the proposed algebraic expression with existing numerical solutions demonstrates excellent agreement.