The purpose of this note is to present the results of numerical calculations of linear stability limits for free convection in layers of porous media or packed beds with throughflow. Effects of flow direction and of different boundary conditions are shown. Previous results were given by Homsy and Sherwood (1 976) for the special boundary conditions of constant velocity and temperature at upper and lower boundaries. These results were valid for any flow rate and direction. Wooding (1960) calculated linear stability limits for a semiinfinite layer with large upward flow when the upper surface was porous and submerged by a layer of liquid at constant temperature. Sutton (1970) presented results valid for small flow rates. For packed-bed applications, e.g., the reaction zone in a catalytic reactor or an ion exchange column, the porous or, as it is sometimes called, constant-pressure boundary condition is more appropriate. In this work, we show results for all combinations of boundary conditions and flow direction. The theory and results of calculations are presented within the framework of thermal convection. As is well known, complete analogy exists with concentration-driven convection and we only have to replace T with concentration, thermal diffusivity a' with the species diffusivity, and the thermal expansivity fl with the appropriate linear concentration coefficient of density.The linear theory has been given previously, for example by Homsy and Sherwood, and by Wooding. In summary, marginal states were calculated from Darcy's law and the conductionconvection energy equation. Property variations (density and viscosity) were assumed to be small-the Boussinesq approximation-and linear with temperature from some reference temperature To:where, for gases, both /3 and p' are positive. After elimination of the pressure and restatement in dimensionless form with the height H of the layer as the reference length, the resulting eigenvalue problem for the mass flux perturbation r and the temperature perturbation 0 is obtained by the usual normal mode analysis:In these equations, D = d/dz and z is the dimensionless vertical coordinate with origin at the lower extremity of the porous layer. The parameter Pe' = HG/a'p, is a modified thermal Peclet number in which a' = k,/pCp, is the modified thermal diffusivity and G is the steady mass flux, which is positive for upward flow. The parameter X is given by X = gfiHATK/u,a' -(p + (3')Pe'AT. The first term in this expression is the RayleighDarcy number and the second term is a contribution due to the throughflow. a = kH is the dimensionless wave number of the disturbance in the horizontal plane. F ( z ) is the dimensionless steady state temperature gradient.A single fourth-order ordinary differential equation is obtained by eliminating 8 in favor of r:with appropriate boundary conditions at z = 0 and 1. For constant mass flux (impermeable to perturbations) and temperature, r = 0,B = 0, or, in terms of I' only, For constant-temperature boundaries that are porous or permeable to f...