NATURAL CONVECTION IN ANISOTROPIC HETEROGENEOUS POROUS MEDIUM Analytical and numerical investigation

摘要

In this chapter we have analysed both numerically and analytically the thermal anisotropy and hydrodynamic heterogeneity effect on natural convection within a horizontal multilayer porous domain subject to cross fluxes of heat and mass. The influences of the buoyancy ratio N, thermal anisotropy λ~r, depth depending permeability K(y) and the relative size of the two superposed layers on the strength of convection Ψ_0, heat and mass transfer have been established and discussed. The problem is mainly characterised by the existence of diffusive and/or convective solution depending on the controlling parameters. Adding an anisotropic layer, λ~r, can improve or reduce the strength of the convection depending on the value of this parameter. Also it affects the value of the critical buoyancy ratio, N, allowing the transition from diffusive to convective solution. The agreement between the numerical and the analytical results can be considered very good to excellent for all the cases analysed. This suggests that the numerical method is useful in identifying complex flows and to check the possibility of multiple solutions and in identifying the slender cavity conditions to obtain a valid parallel flow assumption. Further, the use of analytical model is useful for practical applications, order of magnitude evaluation and identifying unstable solutions.