Micromechanical modeling of anisotropic effective thermal conductivity of gas-solid two-phase mixtures with ellipsoidal inhomogeneities and imperfect interfaces

•Micromechanical modelling of the thermal conductivity of gas-solid mixture medium with imperfect interface.•Eshelby's ellipsoidal inhomogeneity problem.•Green's function technique and integral equation,•Ellipsoidal harmonics method for the thermal conduction inside gas-solid mixture medium.•Analytical expressions of local mean intensity and effective thermal conductivity. The present paper deals with the micromechanical modeling of the thermal conductivity of two-phase gas-solid mixtures with ellipsoidal inhomogeneities. In some structural morphologies, when the characteristic size of the gas-filled inhomogeneity is comparable to the mean path of the gas molecule, the classical heat conduction theory is no longer applicable to the regions very close to the solid interfaces. The present work assumes a sliding flow regime and a Knudsen number such that: 0