Non-unique solution for combined-convection assisting flow over vertical flat plate

Abstract. 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 equa-tions for combined-convection flow past a vertical flat plate. The solution of the boundary layer equation for natural convection constitutes the self-similar solu-tion whose perturbation with respect to the small parameter (ε), which is inversely proportional to the square root of the Richardson number (Gx), provides the non-similar 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 con-vergent 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