Summing Up the Three Significant Models Related with the Bénard Convection Problem

This short chapter, with a summing up of Chapters 3, and 5 to 7, is, to a certain extent, a reponse to the above suggestion from Professor Moreau. Nevertheless, I hope that the preceding seven chapters have captured the interest of the majority of my readers and that, for them, this chapter will serve as only a concentrated review, at least concerning the sections devoted to RB, deep and BMconvections. In the preceding chapters, our main objective was a rational clarification of the various steps which lead to now well-known approximate leading-order, Rayleigh–Bénard (shallow-thermal), Zeytounian (deep-thermal) and Bénard–Marangoni (thermocapillarity-surface tension) convections. As a starting physical phenomemon we chose the simplest Bénard problem of a liquid layer heated from below, in the absence of rotation, magnetic field, porous-medium or two-component fluid (for definitions of such convections, see Chapter 10).