A novel numerical cubic filament model and method for the two-energy equation in porous media

A consistent rule, which requires the flow and heat transfer of both a numerical model and real porous media should simultaneously satisfy the same governing equations as well as the same or consistent transport properties, is proposed for establishing a numerical model by which the flow and heat transfer of real porous media can be simulated. A cubic filament model (CFM) with regular geometry solid matrix is modeled. In the procedure of modeling, transport properties of both the cubic filament model (CFM) and real porous media, including porosity, permeability, tortuosity, specific surface, inertial coefficient, surface heat transfer coefficient and thermal conductivity of both fluid and solid, are analyzed and developed. According to analysis of transport properties and the consistent rule, structure parameters of the cubic filament model (CFM) are determined. To avoid complexity of determining the effective conductivity, it is proposed that solid matrix and fluid are divided into two independent control volumes for the cubic filament model (CFM). Meanwhile, equivalent conductivity of solid matrix and average temperature differences of the source terms are derived for the cubic filament model (CFM).