Onset of Convection in a Permeable Medium Between Vertical Coaxial Cylinders

The onset of natural convection is examined for a fluid-saturated permeable medium contained between vertical coaxial cylinders of inner and outer radii ri and r0. 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*/ri and r0/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.