A Stable Mode of Dendritic Growth in Cases of Conductive and Convective Heat and Mass Transfer

Abstract

In this paper, we develop a theory of stable dendritic growth in undercooled melts in the presence of conductive and convective heat and mass transfer boundary conditions at the solid/liquid interface of a dendrite. To simplify the matter and construct the analytical theory, conductive and convective mechanisms are considered separately. Namely, the laws for total undercooling and selection criterion defining the stable growth mode (dendrite tip velocity and diameter) are derived for conductive and convective boundary conditions. To describe the case of simultaneous occurrence of these heat and mass transfer mechanisms, we sew together conductive and convective laws using power stitching functions. The generalised selection theory is compared with experimental data for Al24Ge76 and Ti45Al55 undercooled melts.

The Tip of Dendritic Crystal in an Inclined Viscous Flow

“…The more intense flow in the anterior region (left in Figure 5) compared to the much less intense flow in the posterior region (right in Figure 5) may indicate different heat and mass transfer mechanisms in these regions. It is well known that at strong currents, the heat (J h ) and impurity (J i ) fluxes at the boundary are determined by the difference between the temperatures (impurity concentrations) at the boundary and away from it (instead of classic Fick's laws) [31][32][33][34][35], i.e.,…”

“…Thus, convective flow affects phase selection [26,27], grain structure refinement [28,29], and generally the formation of solid structure of crystallizing materials [30]. In addition, intense convective melt flows near interfaces may change the mechanism of heat and mass transfer, i.e., instead of conductive boundary conditions of heat and mass transfer, the corresponding convective boundary conditions take place [31][32][33][34][35].…”