A Unit Cube-Based Model for Heat Transfer and Fluid Flow in Porous Carbon Foam

A unit-cube geometry model is proposed to characterize the internal structure of porous carbon foam. The unit-cube model is based on interconnected sphere-centered cubes, where the interconnected spheres represent the fluid or void phase. The unit-cube model is used to derive all of the geometric parameters required to calculate the heat transfer and flow through the porous foam. An expression for the effective thermal conductivity is derived based on the unit-cube geometry. Validations show that the conductivity model gives excellent predictions of the effective conductivity as a function of porosity. When combined with existing expressions for the pore-level Nusselt number, the proposed model also yields reasonable predictions of the internal convective heat transfer, but estimates could be improved if a Nusselt number expression for a spherical void phase material were available. Estimates of the fluid pressure drop are shown to be well-described using the Darcy-Forchhiemer law, however, further exploration is required to understand how the permeability and Forchhiemer coefficients vary as a function of porosity and pore diameter.