Characteristics and Stability of Compositional Convection in Binary Solidification with a Constant Solidification Velocity

Abstract − In binary solidification compositional convection in a porous mushy layer influences the quality of the final products. We consider the mushy layer solidifying from below with a constant solidification velocity. The distur-bance equations for the mushy layer are derived using linear stability theory. The basic-state temperature fields and the distribution of the porosity in the mushy layer are investigated numerically. When the superheat is large, the thickness of the mushy layer is relatively small compared to the thickness of the thermal boundary layer. With decreasing the super-heat the critical Rayleigh number based on the thickness of the mushy layer increases and the mushy layer becomes sta-ble to the compositional convection. The critical Rayleigh number obtained from the continuity conditions of temperature and heat flux at the mush-liquid interface is smaller than that from the isothermal condition at the upper boundary of th