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Authors' Reply R . M E H R A B I A N , M. K E A N E , A N D M . C .
FLEMINGS
The essential point where the Discussor misinterp r e t s o u r w o r k is c o n t a i n e d in h i s s t a t e m e n t : " S i n c e the dendrite stalks and branches are thermal sinks, t h e n e c e s s a r y h e a t f o r d e n d r i t e r e m e l t i n g to o c c u r m u s t c o m e f r o m t h e e l e m e n t i t s e l f . " T h e " h e a t " to effect the remelting comes from local, and negligibly s m a l l , v a r i a t i o n s in t h e s e c o n d d e r i v a t i v e of t h e l o c a l t e m p e r a t u r e w i t h r e s p e c t to d i s t a n c e . M a c r o s c o p i c
1 7 4 6 - V O L U M E 2, JUNE 1971
t e m p e r a t u r e p r o f i l e is not s i g n i f i c a n t l y i n f l u e n c e d b y t h e s m a l l fluid f l o w s c o n s i d e r e d . T h i s c a n b e r e a d i l y s h o w n b y a s i m p l e h e a t b a l a n c e . R e c e n t w o r k of C o p l e y e t a l . ~9 a n d of o u r s e l v e s 2~ o n m e t a l s y s t e m s s e e m s to u s to b e c o n f i r m a t i o n of t h e e s s e n t i a l i d e a s e x p r e s s e d ha o u r p a p e r . A l t h o u g h w e e x p e c t s o m e d i f f e r e n c e s in b e h a v i o r b e t w e e n m e t a l a n d n o n m e t a l s y s t e m s , r e s u l t s of s t u d i e s o n t h e two d i f f e r e n t t y p e s of s y s t e m s s e e m to b e c l o s e l y c o m p a r a b l e , xg-z~ 14. C. J. SmitheUs: Metals Reference Book, 4th ed., p. 251, Butterworths, London, 1967. 15. A. Goldsmith, T. E. Waterman, and H. J. Hirschhorn: Handbook of Thermophysical Properties of Solid Material, Pergamon Press, New York, 1962. 16. A. Pokomy and J. Pokorny: Der FerriMetallographia, 1967, vol. 3, IRSID, Berger-Levrault, Paris. 17. K. W. Andrews and C. R. Gomer: The Solidification of Metals, Iron Steel Inst. Publ. No. 110, 1968, pp. 363-69. 18. M. Taniguchi, K. Narita, andA. Kujime: Tetsu ToHagane. 1969, vol. 55, p. 583. 19. S. M. Copley, A. F. Giamei, S. M. Johnson, and M. F. Hornbecker: Met. Trans., 1970, vol. 1, pp, 2193-2203_ 20. R. Mehrabian, M. Keane, and M. C. Flcramgs: Met. Tmn~, 1970, vol. 1, pp. 3o.38..41. 21. R. J. McDonald and J. D. Hunt: Trans. TMS-AIME, 1969, vol. 245, pp. 199397.
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