| Since Darcy's pioneering experimental study of porous medium flow, a great number of analytical, numerical, and experimental works have been carried out to provide qualitatively and quantitatively macroscopic descriptions of the overall viscous resistance or heat transfer across the porous media. Recent advances in experimental measuring techniques have uncovered the importance of structural heterogeneity within the porous media. Thus, in order to gain a better understanding of phenomena at the scale of pores, new numerical approaches must be taken.; A general numerical simulation capability at pore-scale level is developed and validated in this thesis study, predicting global phenomena in close agreement with classical results. This technique has been successfully applied to two and three dimensional porous systems. In particular, it is shown that three dimensional solutions that couples the fluid and solid systems simultaneously at the pore scale are feasible with today's computer resources and are extremely beneficial, shedding a new light into phenomena unavailable otherwise.; This study also emphasizes numerical simulations of mass, momentum, and heat transfer phenomena induced in complex porous media, providing details of local velocity profiles and heat transfer. It is shown that the porous structures---shape, size, and locations have significant effects on the macroscopic description. It is concluded that a microscopic description at the pore scale should be included in the study of porous medium flow. The flow pathlines are tortuous, determined by the local pore structure. Hence, the mixing caused by a porous insert can offer an efficient way to dissipate the heat from the heat source. The qualitative description of transport phenomena of flow through a three-dimensional duct demonstrates the capability of the numerical approach proposed in this thesis.; It is also found that the interplay among viscosity, heat conductivity and convection gives rise to a complex dynamical system. The effects of Reynolds number, Peclet number, local effective heat conductivity and properties of porous material on the local and global description of pressure, velocity field and heat transfer are studied in detail.; Finally, a summary of the thesis work and recommendation for future work are given. |
