Transient stability and convection in impulsively heated porous layers

Experiments are reported on initial instability and convection in a porous medium impulsively heated from below. The porous medium comprises either water or a water-glycerin solution and randomly stacked glass spheres in an insulated cylinder of height-to-diameter ratio of 1.9. Heating is accomplished with a constant flux lower surface and a constant temperature upper surface. Results include measurement of the initial transition to convection, overall heat transfer coefficient over a range of Rayleigh-Darcy numbers, and temperature profiles. Time-averaged temperature profiles suggest the existence of a unicellular flow over the range of Rayleigh numbers of the present experiments. The critical Rayleigh number for the onset of convection is obtained in terms of a length scale normalized to the thermal penetration depth as Ra_c = 83/(1.08η-0.08η²) for 0.02 < η < 0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is represented by a new correlation form, Nu = 0.047 Ra^0.91Pr^0.11(μ/ μ₀)^0.72 where Ra is the Rayleigh-Darcy number, 400 < Ra < 5000, and the viscosity ratio is found sufficient to account for strongly temperature-dependent viscosity.