Critical Rayleigh number of natural convection in high porosity anisotropic horizontal porous layers

The critical Rayleigh number RaC at the onset of natural convection was studied by linear stability analysis for high porosity anisotropic horizontal porous layers of uniformly arraying vertical thin circular wires stretched across a hot and a cold surface. Navier-Stokes equations including flow resistance by the wires were solved since Darcy's law cannot be applied due to high porosity. Ratio of permeability in the horizontal direction to the vertical direction is constant to be 0.5 but ratio of effective thermal diffusivity ξ is changed dependent on wire materials. The critical Rayleigh number RaC for the case of ξ = 1 obtained by the analysis agreed well with the experiment.