TY - JOUR
T1 - A Mushy-Zone Rayleigh Number to Describe Interdendritic Convection During Directional Solidification of Hypoeutectic Pb-Sb and Pb-Sn Alloys
AU - Tiwari, R.
N1 - Tewari, S.N., & Tiwari, R. (2003). A Mushy-Zone Rayleigh Number to Describe Interdendritic Convection During Directional Solidification of Hypoeutectic Pb-Sb and Pb-Sn Alloys. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 34A, 2365-2376
PY - 2003/10/1
Y1 - 2003/10/1
N2 - Based on measurements of the specific dendrite surface area (S-nu), fraction of interdendritic liquid (phi), and primary dendrite spacing (lambda(1)) on transverse sections in a range of directionally solidified hypoeutectic Pb-Sb and Pb-Sn alloys that were grown at thermal gradients varying from 10 to 197 K cm(-1) and growth speeds ranging from 2 to 157 mum s(-1), it is observed that S-nu = lambda(1)(-1) S*(-0.33) (3.38 - 3.29 phi + 8.85 phi(2)), where S* = D-l G(eff)/V m(1) C-o (k - 1)/k, with D-l being the solutal diffusivity in the melt, G(eff) being the effective thermal gradient, V being the growth speed, m(l) being the liquidus slope, C-o being the solute content of the melt, and k being the solute partition coefficient. Use of this relationship in defining the mushy-zone permeability yields an analytical Rayleigh number that can be used to describe the extent of interdendritic convection during directional solidification. An increasing Rayleigh number shows a strong correlation with the experimentally observed reduction in the primary dendrite spacing as compared with those predicted theoretically in the absence of convection.
AB - Based on measurements of the specific dendrite surface area (S-nu), fraction of interdendritic liquid (phi), and primary dendrite spacing (lambda(1)) on transverse sections in a range of directionally solidified hypoeutectic Pb-Sb and Pb-Sn alloys that were grown at thermal gradients varying from 10 to 197 K cm(-1) and growth speeds ranging from 2 to 157 mum s(-1), it is observed that S-nu = lambda(1)(-1) S*(-0.33) (3.38 - 3.29 phi + 8.85 phi(2)), where S* = D-l G(eff)/V m(1) C-o (k - 1)/k, with D-l being the solutal diffusivity in the melt, G(eff) being the effective thermal gradient, V being the growth speed, m(l) being the liquidus slope, C-o being the solute content of the melt, and k being the solute partition coefficient. Use of this relationship in defining the mushy-zone permeability yields an analytical Rayleigh number that can be used to describe the extent of interdendritic convection during directional solidification. An increasing Rayleigh number shows a strong correlation with the experimentally observed reduction in the primary dendrite spacing as compared with those predicted theoretically in the absence of convection.
UR - https://engagedscholarship.csuohio.edu/encbe_facpub/1
U2 - 10.1007/s11661-003-0299-2
DO - 10.1007/s11661-003-0299-2
M3 - Article
VL - 34A
JO - Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science
JF - Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science
ER -