Three-Dimensional Natural Convection in a Vertical Porous Layer With a Hexagonal Honeycomb Core

Numerical solutions are obtained for a three-dimensional natural convection heat transfer problem in a vertical porous layer with a hexagonal honeycomb core. The porous layer is assumed to be long and wide such that the velocity and temperature fields repeat themselves in successive enclosures. The natural convection problem is solved for only one honeycomb enclosure with periodic thermal boundary conditions. The porous layer is assumed to be homogeneous and isotropic and the flow is obtained by using the Darcian model. The numerical methodology is based on an algebraic coordinate transformation technique, which maps the hexagonal cross section onto a rectangle. The transformed governing equations are solved with the SIMPLE algorithm. The calculations are performed for the Darcy–Rayleigh number in the range of 10 to 10³ and for eight values of the aspect ratio (H/L = 0.25, 0.333, 0.5, 0.7, 1, 1.4, 2, and 5). Two types of thermal boundary condition for the honeycomb core wall are considered: conduction and adiabatic honeycomb core wall thermal boundary conditions. The results are presented in the form of average and local heat transfer coefficients and are compared with the corresponding values for two and three-dimensional rectangular enclosures.