By Doru Stefanescu
Stefanescu the following makes an attempt to explain solidification conception throughout the advanced mathematical gear required for a basic remedy of the matter. the math is in spite of the fact that constrained to the weather necessary to reach a operating wisdom within the box. this can be in accordance with the most target of the booklet, that is to coach the reader within the fast paced sector of computational modeling of solidification of castings. a distinct attempt has been made to introduce the reader to the newest advancements in solidification conception together with, during this moment variation, a brand new bankruptcy on semi-solid casting.
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Extra info for Science and Engineering of Casting Solidification, Second Edition
Other effects must be considered in order to obtain an accurate description of the process, as follows (Ohnaka, 1992): • • • • • gravity effect on density differences caused by phase, compositional or thermal variations (natural convection) solidification contraction capillary forces external centrifugal or electromagnetic forces deformation of solid phases due to thermal stress and static pressure Most of these effects are related to the fluid flow and will be discussed later. 7 47 Zone melting The understanding of segregation phenomena has led to the development of solidification techniques for metal purification.
9) This equation is called the equilibrium lever rule. It is valid assuming ρS = ρL. At the end of solidification, because of rapid solid diffusion, the composition of the solid is uniform across the volume element, and equal to the initial composition of the liquid. Note that in spite of the equilibrium nature of solidification, substantial solute redistribution occurs during solidification. The material is homogeneous only before and after solidification. For the more general case, when ρS ≠ ρL, a similar equation can be obtained by using volume fractions, gS and gL, rather than mass fractions.
The steady state, at TS III. the final transient, between TS and TE: buildup of solute occurs because the boundary layer reaches the end of the crucible The initial and final transient represent chemical segregation. 6 must be equal to conserve mass balance, so that the average composition remains Co. 6. Solute redistribution for non-equilibrium solidification for DS = 0 and 0 < DL < ∞. Calculation of solute redistribution during the initial transient can be done by using the time dependent form of the diffusion Eq.
Science and Engineering of Casting Solidification, Second Edition by Doru Stefanescu