Effects of Coriolis force and surface tension on Bénard-Marangoni convective instability

Abstract

Abstract The effect of the Coriolis force on the onset of the Benard-Marangoni convective instability in a horizontal fluid layer, subject to a rotation, is investigated. The upper surface is deformably free and the lower surface is bounded with a solid plate, heated from below. The principle of exchange of stability is applied. The characteristic problem is solved numerically, using the Runge-Kutta-Gill's shooting method. The numerical results obtained compared very well with previously published ones. The thickness ratio d r , conductivity ratio k r , Biot number Bi , Crispation number C and Taylor number Ta are significant on determining the critical Rayleigh number R c or Marangoni number M c with the corresponding critical wavenumber a c . The results show that the system is more stabilizing at larger values of the thickness ratio d r , conductivity ratio k r , Biot number Bi and Taylor number Ta .