MORPHOLOGICAL INSTABILITY ON BENARD-MARANGONI CONVECTION DURING SOLIDIFICATION - SINGLE-COMPONENT SYSTEM

The critical conditions for the Benard-Marangoni convective and morpho logical instabilities of a horizontal liquid layer of a single compone nt, subject to a solidification process from below, are studied. The m orphological effects, including the thickness and thermal conductivity of the solid layer and the capillary effect of the solid-liquid inter face, have significant influences on the onset of instabilities at the marginal state. The analysis is based on the linear stability theory and the resulting eigenvalue equations are solved, using the shooting technique of Runge-Kutta-Gill's method of order four. The eigenvalue R ayleigh number, R, or Marangoni number, M, is evaluated. The numerical results indicate that the critical conditions decrease sensitively wi th the thickness ratio A for 0 < A < 1 and approach fixed values for A becoming large. The effects of the capillarity at the solid-liquid in terface and thermal conductivity in the solid layer tend to stabilize the system, The conducting ways of the latent heat act as dominant rol es on determining the possible instability of the system.