Heat transfer and the melting process in electroslag remelting: Part I. The behavior of small electrodes
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J. J. POVEROMO,
J. SZEKELY,
AND
A. MITCHELL
On the a s s u m p t i o n of one d i m e n s i o n a l axial heat flow a m a t h e m a t i c a l model i s developed for d e s c r i b i n g the t e m p e r a t u r e p r o f i l e in s m a l l ESR u n i t s . The m o d e l c o n s i d e r s the r e gions both above and below the slag level and a l l o w a n c e i s m a d e for the d e v e l o p m e n t of a s l a g c r u s t on the e l e c t r o d e n e a r the top slag levet. The g o v e r n i n g equations a r e solved n u m e r i c a l l y and the eomputed r e s u l t s a p p e a r to be in a g r e e m e n t with e x p e r i m e n t a l data r e p o r t e d on a l a b o r a t o r y s c a l e ESR unit, employing 1 in. e l e c t r o d e s .
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N
r e c e n t y e a r s t h e r e h a s been c o n s i d e r a b l e i n t e r e s t in E l e c t r o s l a g R e m e l t i n g a s t h i s p r o c e s s p r o v i d e s a novel, e c o n o m i c a l l y a t t r a c t i v e r o u t e for high p u r i t y ferrous alloys. Much of the i n t e r e s t to date has been c e n t e r e d on the slag c h e m i s t r y and on the p h y s i c a l and c h e m i c a l p r o p e r t i e s of the p r o d u c t . The t r a n s p o r t a s p e c t s of the p r o c e s s r e c e i v e d r a t h e r l e s s a t t e n t i o n , although s o m e v e r y i n t e r e s t i n g v i s u a l i z a t i o n s t u d i e s have been r e p o r t e d and work has b e e n done on the m o d e l i n g of the t e m p e r a t u r e p r o f i l e within the e l e c t r o d e . In t h i s l a t t e r group, i n t e r e s t i n g r e l a t e d work has been r e p o r t e d by E l l i o t t ~ and his c o w o r k e r s ; in a r e cent p a p e r , M i t c h e l l , e l a l . 2 d e s c r i b e d t h e i r e x p e r i m e n tal t e m p e r a t u r e m e a s u r e m e n t s in a l a b o r a t o r y s c a l e ESR unit and p r o p o s e d a m a t h e m a t i c a l model which p r o v i d e d a f a i r l y good d e s c r i p t i o n of the t e m p e r a t u r e p r o f i l e in the e l e c t r o d e , above the slag level. This m o d e l was quite complex, and contained a n u m b e r of fitted p a r a m e t e r s ; it was t h e r e f o r e thought worthwhile to develop a r a t h e r s i m p l e r r e p r e s e n t a t i o n for heat t r a n s f e r within an ESR unit and to t e s t the a p p r o p r i a t e n e s s of t h i s model by r e f e r e n c e to e x p e r i m e n t a l data. The p r i n c i p a l m o t i v a t i o n b e h i n d such work is the n e e d to obtain a r e l a t i o n s h i p c o n n e e t i n g the m a i n p a r a m e t e r s in the p r o c e s s and to allow the a s s e s s m e n t of the r e l a t i v e i m p o r t a n c e of the v a r i o u s t r a n s f e r mechanisms. In the following a f o r m u l a t i o n is given and computed r e s u l t s a r e p r e s e n t e d , whieh a r e then c o m p a r e d with experimental measurements. 1) FORMULATION
four d i s t i n c t z o n e s , a s shown in the sketch. Zone (i)
T h i s r e g i o n extends f
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