Transport and hydrodynamic stability of an extensive fluid suddenly heated from below

The hydrodynamic stability of the growing conduction layer in an extensive fluid above a horizontal surface has been investigated both analytically and experimentally. The analysis involved a study of the stability of convective flows in the vicinity of a horizontal surface suddenly generating a spatially uniform and time independent heat flux in an extensive fluid. The transport phenomenon occurring next to such a horizontal flat surface is formalized herein in terms of new hydrodynamic stability equations, which constitute a two-point-boundary-value eigenvalue problem. These equations were derived using conservation laws and by assuming that periodic small disturbances are superimposed on a base flow. A simple new dimensionless parameter arose. These stability equations are stiff and were integrated using a computer code designed for especially precise solutions of two-point-value problems. Associated measurements using color Schlieren photography and a data acquisition system were conducted to verify this analysis.