Rapid melting and solidification of surface due to stationary heat flux
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a r e c e n t p a p e r r a p i d m e l t i n g and s o l i d i f i c a t i o n of a m e t a l l i c s u r f a c e l a y e r s u b j e c t e d to high i n t e n s i t y heat fluxes, such as those achieved via e l e c t r o n b e a m and continuous CO2 l a s e r r a d i a t i o n , was d i s c u s s e d . ~ The effect of a b s o r b e d heat flux on the i m p o r t a n t s u r face l a y e r m e l t i n g and s u b s e q u e n t s o l i d i f i c a t i o n v a r i ables of t h r e e s u b s t r a t e m a t e r i a l s a l u m i n u m , i r o n , and nickel w e r e d e t e r m i n e d u s i n g a s i m p l i f i e d oned i m e n s i o n a l c o m p u t e r heat flow model. A second l i m i tation i m p o s e d on the p r e v i o u s p r o b l e m s t a t e m e n t was that only u n i f o r m heat fluxes w e r e c o n s i d e r e d . In g e n e r a l , both of these r e s t r i c t i o n s a r e violated in p r a c t i c e . Exception is noted for c a s e s where the spot d i a m e t e r of the i n c i d e n t r a d i a t i o n is l a r g e r e l a t i v e to the heat affected zone in the work p i e c e and the o n e - d i m e n s i o n a l heat flow model for the case of u n i f o r m heat flux is applicable. T h i s p a p e r a d d r e s s e s the t w o - d i m e n s i o n a l (axis y m m e t r i c ) heat flow p r o b l e m of the m e l t i n g and subsequent s o l i d i f i c a t i o n of a s u r f a c e l a y e r s u b j e c t e d to a s t a t i o n a r y high i n t e n s i t y heat flux over a c i r c u l a r r e g i o n on its b o u n d a r y s u r f a c e . A g e n e r a l method for the solution of this type of a p r o b l e m is developed which p e r m i t s t r e a t m e n t of both u n i f o r m and n o n u n i f o r m heat flux d i s t r i b u t i o n s in the c i r c u l a r region. R e s u l t s of n u m e r i c a l c o m p u t a t i o n s c a r r i e d out on a C o n t r o l Data CYBER 175 c o m p u t e r a r e p r e s e n t e d for a pure a l u m i n u m s u b s t r a t e s u b j e c t e d to both u n i f o r m and G a u s s i a n heat flux d i s t r i b u t o r s . S. C. HSU, formerly Graduate Research Assistant, Department of Mechanical and Industrial Engineering, Universityof Illinois, is now with G.T.E. Laboratories in Waltham, MA. S. KOU, formerly Research Associate, Department of Metallurgyand MiningEngineering, University of Illinois is now at the General Motors Research Center, Warren, MI. R. MEHRABIAN,formerly Professor at the University of Illinois, Urbana, IL, is now Chief of the Metal Science and Standards Division,National Bureau of Standards, Washington,D.C. Manuscript submitted December 28, 1978. METALLURGICALTRANSACTIONS B
The two m a i n a s s u m p t i o n s of this p a p e r a r e : a) t h e r m a l p r o p e r t i e s of the liquid and the solid a r e i n d e p e n dent of t e m p e r a t u r e , but d i f f e r e n t f r o m one a n o t h e r and b) convection in the liquid r e g i o n is not taken into consideration.
H. PROBLEM STATEMENT AND SOLUTION APPROACH C o n s i d e r
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