Non-linear spectral analysis of Rayleigh-Benard convection in a high-porosity medium

A local non-linear stability analysis using the spectral method is made of the Rayleigh-Benard situation in a high-porosity porous medium. The series expansion solution so obtained is valid for a large range of imposed temperature differences and yields a quantitative estimate of the heat transport by convection. Streamline patterns and mean temperature distributions have been obtained. The temperature distributions show that at the middle of the fluid-filled porous layer a layer of isothermal mean temperature develops, thus limiting the major heat transport to thermal boundary layers. The damping nature of porous media on heat transport is also clearly brought out.