Macrosegregation during solidification of semiinfinite slab of binary alloys
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Macrosegregation During Solidification of Semiinfinite Slab of Binary Alloys V. KOUMP, R. H. TIEN, and W. J. KIM T H E d e n s i t y d i f f e r e n c e b e t w e e n solid and liquid p h a s e s will b r i n g about liquid flow within the s o l i d liquid r e g i o n of a s o l i d i f y i n g ingot. T h i s flow of i n t e r d e n d r i t i c liquid, a f f e c t s the a v e r a g e solute content of the solid, and c a u s e s m a c r o s e g r e g a t i o n . In a r e c e n t c o n t r i b u t i o n on the s u b j e c t of m a c r o s e g r e g a t i o n by F l e m i n g s and N e r e o , 1 a " l o c a l solute r e d i s t r i b u t i o n e q u a t i o n " was d e r i v e d b a s e d on the c o n s e r v a t i o n of solute m a s s . The s o l u t i o n was obtained by u s i n g a set of a s s u m e d t h e r m a l d a t a that included the s o l i d f r a c tion d i s t r i b u t i o n within the l i q u i d - s o l i d r e g i o n , r a t e of m o v e m e n t of liquidus and s o l i d u s f r o n t s , and so forth. In r e a l i t y , the h e a t and m a s s t r a n s f e r e f f e c t s a r e coupled during m a c r o s e g r e g a t i o n . The h e a t t r a n s f e r a n a l y s i s cannot be s e p a r a t e d f r o m the c o n s i d e r a t i o n of m a s s t r a n s p o r t , and h e n c e is not known b e f o r e h a n d . In the p r e s e n t w o r k m a c r o s e g r e g a t i o n d u r i n g the s o l i d i f i c a t i o n of a s e m i i n f i n i t e slab of a b i n a r y a l l o y is a n a l y z e d using F l e m i n g s ' l o c a l solute r e d i s t r i b u t i o n equation 1 and the p r o p e r heat t r a n s f e r a n a l y s i s f r o m a p r e v i o u s w o r k 2 by the p r e s e n t a u t h o r s . The a n a l y s i s i s d e m o n s t r a t e d with the use of two a r b i t r a r y b i n a r y a l l o y s y s t e m s having e i t h e r a l a r g e p o s i t i v e o r n e g a t i v e d e n s i t y change upon s o l i d i f i c a t i o n . F o r a given a l l o y s y s t e m and i n i t i a l m o l t e n alloy c o m p o s i t i o n and s u r V. KOUMP is w i t h C h a r i s m a I n t e r n a t i o n a l , Doder, Mass.; R. H. TIEN is with Edgar C. Bain L a b o r a t o r y for F u n d a m e n t a l Research, U. S. Steel Corp., Monroeville, Pc.; W. J. KIM is w i t h State University o f New Y o r k at S t o n y b r o o k , New York. Manuscript s u b m i t t e d J a n u a r y 9, 1970. 2 0 1 6 - V O L U M E 1 , J U L Y 1970
face t e m p e r a t u r e , the solution y i e l d s a) the solute c o n c e n t r a t i o n in t h e s o l i d i f i e d s o l i d , b) the t e m p e r a t u r e , solute c o n c e n t r a t i o n and the s o l i d f r a c t i o n within the l i q u i d - s o l i d r e g i o n , c) the v e l o c i t y d i s t r i b u t i o n of the i n t e r d e n d r i t i e liquid, and d) the p o s i t i o n s of liquidus and e u t e c t i c f r o n t s a s a function of t i m e . F l e m i n g s ' l o c a l solute r e d i s t r i b u t i o n equation can be w r i t t e n in the following f o
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