Modelling of void shape effect on effective thermal conductivity of lotus-type porous materials

In this paper, a formula for estimating the effective thermal conductivity of lotus-type porous materials (LTPM) combining an analytical formula with a mean-field homogenisation technique is developed and validated. LTPMs are considered multi-phase materials in which each phase is defined by the pore shape. To estimate the effective thermal conductivities of multi-phase LTPMs, a two-step mean-field homogenisation method is implemented and validated. The validation is applied by comparing the results obtained with those of the representative volume element based finite element homogenisation method, which has been taken as a reference. The proposed formula is applied by replacing the first step of the two-step mean field homogenisation method using a formula for estimating the effective thermal conductivity of two-phase lotus-type materials. The good agreement between the results of the proposed formula and the reference results indicates that the proposed formula ensures an accurate estimation of the effective macroscopic thermal conductivities of multi-phase lotus-type porous materials.