NON-UNIQUE SOLUTION OF COMBINED-CONVECTION ASSISTING FLOW OVER VERTICAL FLAT PLATE

By K. Venkatasubbaiah, Amrita Mittal & T.K. Sengupta

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 equations for combined-convection flow past a vertical flat plate. Solution of boundary layer equation for natural convection constitutes the self-similar solution whose perturbation with respect to the small parameter, Epsilon that is inversely proportional to the square root of the Richardson number provides the non-similar solution. Solutions obtained by shooting method indicate two sets for the self-similar solution (Epsilon = 0) - one of them showing positive velocity everywhere inside the shear layer (well known oft-reported physical result). The other self-similar solution shows 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 ( Epsilon # 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 on the validity of such perturbation procedure and possible stability of the basic solution itself.