Non-unique solutions of flow and temperature field are reported here for the first time for non-similar flows given by the laminar boundary layer equations for combined-convection flow past a vertical flat plate. The solution of the boundary layer equation for natural convection constitutes the self-similar solution whose perturbation with respect to the small parameter (ε), which is inversely proportional to the square root of the Richardson number (Gx), provides the nonsimilar solution. Solutions obtained by the shooting method indicate two sets for the self-similar solution (ε = 0) - one of them showing positive velocity every-where inside the shear layer (well-known oft-reported physical result). The other self-similar solution shows that recirculation in the outer part of the shear layer may not be physical - as it has not been experimentally demonstrated so far. In contrast, the perturbative part of the non-similar solution (ε ≠ 0) is seen to be either convergent or divergent depending upon the choice of integration domain of the shear layer equations - bringing forth the question of the validity of such perturbation procedures and possible stability of the basic solution itself.