Developments on Convection Induced by Surface Tension and Buoyancy

In this book, we present a theoretical study of recent developments on thermal convection induced by surface tension and buoyancy. The existing literature on hydrodynamic and hydromagnetic stability reveals that there exists only a few analytical solutions of the problems especially pertaining to the area of thermal convection driven by surface tension or/and buoyancy, in the general framework of the boundary conditions which are physically more relevant and important. Further, in all these investigations, techniques used for solving such problems are analogous to that given by Lord Rayleigh, which do not distinguish whether the layer of the liquid under study is relatively hotter or cooler and predicts the same threshold conditions in both cases which is contrary to the physical intuition, and therefore, need to be re-examined in the light of modified analysis given by Banerjee et al. [4]. The intellectual challenge is involved to obtain explicit solutions of these eigenvalue problems and thereby characterizing the critical conditions at the threshold of instability because the eigenvalue equations contain parameters of the problem implicitly.