The Mixed Convection Number for Porous Media Flow

Abstract

Convection is a phenomenon, which can be attributed to density gradients, and which may cause altered flow patterns in systems with higher density fluid above lower density fluid. Where a density gradient is present, buoyancy may initiate an additional velocity component upward or downward, i.e. in direction of gravity. It depends on three system properties if the buoyancy impetus changes the flow field in the system. When there is a strong diffusivity, the density gradient may vanish without any effect on the motion. High viscosity of the fluid and/or low permeability of the porous medium are obstacles preventing any changes of flow. The quantitative measure for the relative strength of favouring/hindering processes is the porous medium Rayleigh number, Ra, defined by

$$ Ra = \frac{{k\Delta \rho gH}} {{\mu D}}, $$

(10.1)

with permeability k, maximum density difference Δρ, acceleration due to gravity g, system height H, dynamic viscosity μ and diffusivity D. The dimensionless parameter combination, given in equation (10.1), is basically identical to the dimensionless number introduced by Lapwood [14] and is sometimes referred to as the Lapwood number.