The onset of thermal convection in a two-dimensional porous box is investigated analytically. One of the two lateral boundaries is in contact with a hydrostatic reservoir, where the saturating fluid can flow freely in and out. This open boundary is thermally insulating, but with the buoyancy of the fluid taken into account. For the second lateral wall, we study five different options for the boundary conditions. This leads to five different eigenvalue problems for the onset of convection. These five solutions are compared with the known solutions where the buoyancy along open sidewalls is neglected (Tyvand 2002).