Stability Analysis of Natural Convection Evolving Along a Vertical Heated Plate

Abstract

Natural convection evolving along a vertical flat plate is considered under (i) isothermal and (ii) uniform-heat-flux plate boundary conditions. Basic flow is assumed to be governed by steady boundary-layer equations. Linear and weakly-nonlinear stability analyses of the basic flow are made with the aid of the Galerkin method in which the field variables are expanded in terms of Chebyshev polynomials. The Stewartson-Stuart equation for the two-dimensional propagating disturbance is derived and its stability is examined for the cases of the Prandtl number P r = 0.733 (air) and P r = 6.7 (water). The main results are such that (i) the motion is supercritical over almost all the linearly unstable region except for a narrow boundary region defined by small wavenumbers; (ii) Huerre's criterion shows that the motion is convectively unstable along the most highly amplified path over the whole computed range of the Reynolds number; (iii) Newell's criterion shows that the motion tends to be modulationally unstable...