Transition between natural laminar and turbulent natural convection along a vertical isotherm wall

This manuscript presents a theoretical study on the transition from laminar to turbulent natural convection flow of gas (Pr ≈ 1) along a vertical isothermal plate. The analysis of the transition to unstable flows is based on an approximate solution, deduced from the integral formulation of the boundary layer equations for Pr ≈ 1 (i.e. thickness of the momentum boundary layer is near to that of the thermal boundary layer), and on the Rayleigh equation. An approximate disturbance profile is then calculated. It allows the determination of the parameter kδ (product of the wave number by the boundary layer thickness) corresponding to retrograde, neutral and progressive wave modes. The Figures 7 to 13 and the Annexes A1 to A5 of the ref. [4], edited in 1998 by Elsevier Science Ltd, give to the reader all the necessary information.