3D ANALYTICAL STEADY SOLUTION OF NATURAL-CONVECTION PROBLEM

An analytical study of free convection in a cubic cavity of fluid-satu rated porous material is reported. The analytical algorithm integrates the Darcy-Boussinesq equations formulated in terms of pressure and te mperature. The dependent variables (P, T) are expressed using an asymp totic development in the parameter epsilon = (Ra - Ra-c)(1/2)/pi where Ra-c = 4 pi(2) denotes the value of the critical Rayleigh number; in a cubic cavity (Ra-c1 = 4 pi(2) for the 2D flow and Ra-c2 = 4.5 pi(2) for 3D flow). Terms tip to order 48 for the 2D flow and up to order 16 for the 3D flow are computed. The analytical value of the Nusselt num ber is in good agreement with a numerical one obtained using a Legendr e spectral collocation method. (C) Academie des Sciences/Elsevier; Par is.