Heat flow in atomized metal droplets
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AND
R. MEHRABIAN
The s o l i d i f i c a t i o n of s p h e r i c a l d r o p l e t s with a d i s c r e t e m e l t i n g t e m p e r a t u r e is a n a l y z e d u s i n g a n enthalpy model. E q u a t i o n s d e s c r i b i n g the cooling of the i n i t i a l l y s u p e r h e a t e d liquid d r o p l e t and a n u m e r i c a l heat flow model for its s u b s e q u e n t s o l i d i f i c a t i o n a r e p r e s e n t e d . I m p o r t a n t p a r a m e t e r s like t i m e s for i n i t i a t i o n and c o m p l e t i o n of s o l i d i f i c a t i o n , cooling r a t e s and i n t e r f a c e v e l o c i t i e s in a l u m i n u m , iron, and n i c k e l a r e r e l a t e d to the p r o c e s s v a r i a b l e s g o v e r n i n g the r a t e of heat e x t r a c t i o n f r o m the d r o p l e t s . The a n a l y s i s is p e r f o r m e d for the r a n g e of Blot n u m b e r s of p r a c t i c a l i n t e r e s t where Newtonian cooling models a r e not c o n s i d e r e d applicable, 0.01 -< Bi -< 1.0, and the r e s u l t s a r e p r e s e n t e d in the f o r m of n o r m a l i z e d or d i m e n s i o n l e s s q u a n t i t i e s . It is shown that the a v e r a g e cooling r a t e in the liquid p r i o r to s o l i d i f i c a t i o n can be computed with the Newtonian cooling e x p r e s s i o n s . However, s i g n i f i c a n t t e m p e r a t u r e g r a d i e n t s a r e noted at the d r o p l e t s u r f a c e even for Blot n u m b e r s as low as 0.01. Reducing the d r o p l e t d i a m e t e r r e d u c e s the t i m e n e c e s s a r y for the i n i t i a t i o n and c o m p l e t i o n of solidification, i n c r e a s e s the i n t e r f a c e v e l o c i t i e s at e q u i v a l e n t f r a c t i o n s solidified and d e c r e a s e s the GL/R r a t i o . Although s m a l l e r d r o p l e t d i a m e t e r s p r o m o t e higher cooling r a t e s in the liquid at the b e g i n n i n g and in the solid at the end of solidification, the effect at the i n t e r m e d i a t e s t a g e s is m o r e complex and depends on the i n i t i a l s u p e r h e a t , the Biot n u m b e r and the t h e r m o p h y s i c a l p r o p e r t i e s of the m a t e r i a l .
I. INTRODUCTION I-)URING solidification of metal powders heat is extracted from the droplets by both convection and radiation at their surface. However, there are no accurately established values for the combined radiative and convective heat transfer coefficient, h, and direct measurement of the cooling rate or heat flux during solidification of an atomized droplet would be extremely difficult, if not impossible. In gas atomization the convective heat transfer coefficient is overriding and an upper limit of ~I0 ~ W/m2K can be estimated from existing expressions for h under the most favorable experimental conditions.1 Indirect estimates of heat transfer coefficients in various atomization processes have also been made by comparison of measured segregate (dendrite arm) spacings in crystalline alloy powders with predetermined relationship
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