Linear Stability of Bénard-Marangoni Convection in Two-Layer System with an Undeformable Interface

Abstract

Linear stability of Bénard-Marangoni convection in two-layer system is analyzed theoretically. Special attention is paid to the effect of the Biot number in both rigid boundaries and the thickness of the upper gas layer on the critical Marangoni number and the critical wavenumber. The deformation of interface is assumed to be neglected for linearizing the basic equation to the quiescent state. On the assumption of the exchange of stabilities, the eigenvalue problem for the neutral Marangoni number is derived, the analytical expression of the neutral curve and the linear modes are presented and the condition for the long-wave instability is discussed based on the structure of the mode.