Convective–conductive heat transfer in dual-scale porous media: Theoretical model development and numerical validation

The volume-averaging method is applied to theoretically develop a continuum model to predict the energy transport phenomena in dual-scale porous structures. Closure problems are formulated to establish a two-equation model. The closure problems are numerically solved on three representative elementary volumes (REVs) of dual-porosity media consisting of three different arrangements of closely packed spheres of porous spherical particles to allow the determination of effective transport coefficients for the medium. Finally, a numerical experiment is performed to compare the heat transfer results obtained from the volume-averaged equations with effective coefficients to those of a pore-level simulation. The results of the numerical experiment show that the up-scaled continuum model with calculated effective properties can provides quite similar trends of energy transport in the three selected dual-porosity media with acceptable fidelity and, most importantly, at a considerably reduced computational cost.