The influence of higher order effects on the linear wave instability of vertical free convective boundary layer flow

We examine the stability of free convective boundary layer flow over a vertical heated flat plate with respect to two-dimensional wave disturbances. In particular we determine the effect of the overall external geometry on the stability criterion. The fluid domain is taken to be bounded by two semi-infinite flat plates forming a wedge of angle α. The vertical plate is held at a uniform hot temperature while the other is either insulated or is held at the ambient temperature of the fluid. The basic flow used in the analysis is a two-term boundary-layer approximation using the method of matched asymptotic expansions. A modified version of the Keller-box method is used to solve the linearised wave-disturbance equations numerically. The neutral curves have been delineated for different values of wedge angle, α, where the working fluids are water and air. We find that the critical distance from the leading edge beyond which disturbances grow is strongly dependent on α, and this suggests that the external geometry of the fluid domain exerts a considerable influence on stability criteria.