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 Al (Formula presented.) Ge (Formula presented.) and Ti (Formula presented.) Al (Formula presented.) undercooled melts. © 2022 by the authors.