ANALYTICAL STUDY OF BUOYANCY-DRIVEN CONVECTION EFFECTS ON DENDRITIC GROWTH AND HEAT TRANSFER

This paper presents a matched asymptotic analysis of dendritic crystal growth in an undercooled melt affected by buoyancy-driven convection. Focusing on small Grashof numbers ( ), we derive asymptotic solutions for the flow and temperature fields by dividing the domain into near-field and far-field regions and matching solutions in between. The analysis explicitly incorporates buoyancy effects, revealing how gravity alters flow patterns, enhances heat transfer, and can cause interface instability. This extended model broadens classical dendritic growth theories by including gravitational influences, with implications for materials processing and geological phenomena.