Onset of convection in a permeable medium between vertical coaxial cylinders

Abstract

The onset of natural convection is examined for a fluid-saturated permeable medium contained between vertical coaxial cylinders of inner and outer radii r*i and r*0. The annular space is of height h*. The horizontal boundaries are isothermal, with heating from below and cooling from above. Both permeable and impermeable upper boundaries are considered. Critical Rayleigh numbers Rac and the preferred convective modes are determined as functons of the geometric ratios h*/r*i and r*0/r*i. The confining vertical walls of the annular space tend to increase Rac above the value for an infinite horizontal layer. The preferred modes are predominantly asymmetric.