BOUNDARY EFFECTS ON THE BENARD-MARANGONI INSTABILITY UNDER AN ELECTRIC-FIELD

This article theoretically studies the Benard-Marangoni instability pr oblem for a liquid layer with a free upper surface, which is heated fr om below by a heating coil through a solid plate in an a.c. electric f ield. The boundary effects of the solid plate, which include its therm al conductivity, electric conductivity and thickness, have great influ ences on the onset of convective instability in the liquid layer. The stability analysis in this study is based on the linear stability theo ry. The eigenvalue equations obtained from the analysis are solved by using the fourth order Runge-Kutta-Gill's method with the shooting tec hnique. The results indicate that the solid plate with a higher therma l or electric conductivity and a bigger thickness tends to stabilize t he system. It is also found that the critical Rayleigh number R(c), th e critical Marangoni number M(c), and the critical a.c. Rayleigh numbe r E(ac) become smaller as the intensity of the ac. electric field incr eases.