Low Rayleigh Number Thermal Convection in a Vertical Cylinder Filled With Porous Materials and Heated From Below

Abstract

Low Rayleigh number (R<500) thermal convection is examined experimentally and analytically for a vertical circular cylinder filled with saturated porous materials. The cylinder is heated from below and cooled from above. The upper boundary is permeable to flow. Results are reported for the critical Rayleigh number at the onset of convection (Rc) and the Nusselt (Nu) versus Rayleigh (R) number correlation. The convective structure is deduced from temperature measurements. The lateral walls have a stabilizing effect and tend to increase Rc relative to the case of a laterally unbounded porous layer. The preferred convective patterns in the cylinder tend to be nonaxisymmetric. The experimental results are in good agreement with analytical predictions. A linear stability analysis is used to calculate Rc and the structure of the convective modes for a range of aspect ratios (radius/height). An integral technique is applied to obtain heat transfer rates for 1 < R/Rc < 5.5.