Critical Rayleigh Number of Natural Convection in an Anisotropic Horizontal Porous Layer with High Porosity

Abstract

Linear stability analysis was applied to obtain the critical Rayleigh number Rac at the onset of natural convection for horizontal anisotropic porous fluid layers with vertical thin circular cylinders inserted by variational method with the consideration of non-Darcy viscous flow assumption. The permeability ratio of x-direction to z-direction is 0.5 and the effective thermal diffusivity ratio ξ of x-direction to z-direction for the anisotropic porous fluid layer is less than unity for any circular cylinders with high or low thermal conductivity. The analytical results show that Rac is the highest for the case of ξ=1 and decreases with the decrease in ξ. It decreases with the increase in Darcy number Da and asymptotically approaches to a constant value for Da→∞. The constant value of Rac for Da→∞ is the smallest to be 690.8 for ξ→0. The analytical results were compared with experimental results performed with silicon oil and plastic resin as a working fluid and circular cylinders respectively for ξ=1. The experiment agreed well with the analysis based on non-Darcy viscous flow assumption. The analysis showed that Darcy flow assumption is applied for small Da dependent on ξ.