Heat and mass transfer and fluid flow in porous media are usually characterized by, or
associated with, the effective thermal conductivity, the effective mass diffusivity and the
permeability, respectively. All these macroscopic quantities are conceptually established on a
phenomenological “equivalence” basis. They may contain the influence of porous micro-structures
upon the corresponding diffusive process; however, the detailed nature inside the porous medium is
lumped and neglected. Pore scale numerical modelling has the potential of providing adequate
meso-/micro- scale insight into the transport process in porous medium, as well as obtaining
macroscopic properties, which can encompass the complex pore-structure details. Modelling
heat/mass transfer and fluid flow in complicated porous micro-structures presents a major challenge
to numerical methods due to their multiscale and multiphysics nature. A relatively-novel numerical
technique - the meshless Lagrangian-based Smoothed Particle Hydrodynamics (SPH) method is
thought to be capable of making a significant contribution to this research field. This work deals
primarily with the SPH modelling of heat conduction and fluid flow in 2-D isotropic porous media.
The porous matrix is formed by randomly including a different component into a base component.
Various pore-structures are realized by changing the inclusion shape/size, or the relative
arrangement condition between inclusions. Pore-scale heat transfer and fluid flow streams are
visualized, and both heat transfer and fluid flow always follow, as expected, the paths of least
resistance through the porous structures. In what concerns the effective thermal conductivity, for
the porous media with the base component of larger bulk thermal conductivity, the “flexible” EMT
model, which can accommodate, to some extent, the influence from the porous micro-structures on
the effective thermal conductivity by adjusting the so-called flexible factor ff, gives effective
thermal conductivities agreeable to the SPH predictions across the whole composition range if ff is
taken to be ~ 4.5; the effective thermal conductivity shows a weak dependence on the inclusion
shape/size and the relative arrangement condition between inclusions; however, for porous media
with dispersed inclusions, which component has larger bulk thermal conductivity presents a strong
effect upon the effective thermal conductivity. The SPH fluid flow simulation results confirm the
macroscopic Darcy’s law to be valid only in the creeping flow regime; the dimensionless
permeability (normalized by the squared characteristic dimension of the inclusions) is found to have
an exponential dependence on the porosity within the intermediate porosity range, and the derived
dimensionless permeability /""porosity relation is found to have only a minor dependence on either
the relative arrangement condition between inclusions or the inclusion shape/area.
An analysis of effective thermal conductivity of heterogeneous materials