Incorporating convection into one-dimensional solute redistribution during crystal growth from the melt II. The initial transient solution

Abstract

Using the Laplace transform technique, a solution to the initial transient one-dimensional solute profile in a liquid under steady state convective flow and solidified at constant velocity has been developed. As the flow velocity approaches zero, the solution asymptotically approaches that for the no mixing case while, at the opposite extreme, the solution approaches the complete mixing limit. The length of the initial transient period scales inversely with the magnitude of the flow velocity. Possible uses of the present result are also discussed.