Boundary layer correlation for dendrite tip growth with fluid flow

A correlation is presented for the calculation of the size of a stagnant film located in the liquid ahead of a paraboloidal dendrite, which grows steadily into an undercooled melt in the presence of fluid flow. The coefficients of the correlation are deduced from a fitting exercise of the supersaturation versus dimensionless numbers to the analytical solution developed for the Stokes flow approximation. It is shown that the correlation presented in this contribution offers several advantages compared with the Wang and Beckermann correlation previously published in the literature (Metall. Mater. Trans. 27A (1996) 2754). Not only the fit is improved, but it can also be extended to account for the angle between the dendrite growth direction and the fluid flow direction. Applications are given for an Al–7 wt.% Si alloy.