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Journal of Applied Mathematics
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Journal of Applied Mathematics
/
2012
/
Article
/
Tab 1
/
Research Article
Mathematical Analysis of Inclusion Removal from Liquid Steel by Gas Bubbling in a Casting Tundish
Table 1
Variables, parameters, and equations for each program developed.
Program
Variables calculated
Parameters modified
Equation numbers employed
Dimensionless constants
I
𝑑
𝑏
,
𝑢
𝑏
,
𝑃
𝑎
,
𝑃
𝑐
,
𝐸
r
i
,
𝑡
𝑖
,
𝑡
𝑐
,
𝑡
f
r
,
ℎ
c
r
i
t
𝑑
𝑝
,
𝑛
0
,
𝜏
,
𝑑
0
,
𝑄
𝑔
1, 2, 3, 5, 6, 7, 9, 10, 11
𝐴
,
𝐵
,
𝐶
,
𝐷
,
𝑋
,
𝑌
II
𝑢
𝑝
,
𝑃
𝑐
,
𝑃
𝑎
,
𝐸
r
i
,
𝑡
𝑐
,
𝑡
f
r
,
𝑡
𝑖
,
ℎ
c
r
i
𝑑
𝑝
,
𝑛
0
,
𝜏
,
𝑑
0
,
𝑄
𝑔
,
𝑑
𝑏
1, 2, 3, 5, 7, 9, 10, 11
𝐴
,
𝐵
,
𝐶
,
𝐷
,
𝑋
,
𝑌
III
𝑃
𝑐
,
𝑃
𝑎
,
𝑡
𝑐
,
𝑡
f
r
,
ℎ
c
r
i
t
𝑑
𝑝
,
𝑑
𝑏
1, 2, 3, 10, 11
𝐶
,
𝐷
,
𝑋
,
𝑌
IV
𝑑
𝑏
,
𝑢
𝑏
,
𝑃
𝑎
,
𝑃
𝑐
,
𝐸
r
i
,
𝑡
𝑐
,
𝑡
f
r
,
ℎ
c
r
i
t
𝑑
𝑝
,
𝑛
0
,
𝑑
0
,
𝑄
𝑔
1, 2, 3, 6, 7, 9, 10, 11
𝐴
,
𝐵
,
𝐶
,
𝐷
,
𝑋
,
𝑌
V
𝑃
,
𝑃
𝑎
,
𝑃
𝑐
,
𝑡
𝑠
,
𝑡
𝑐
,
𝑡
f
r
,
𝑡
𝑖
,
ℎ
c
r
i
t
𝑑
𝑝
,
𝑑
𝑏
1, 2, 3, 4, 5, 6, 7, 9, 10, 11
𝐴
,
𝐵
,
𝐶
,
𝐷
,
𝑋
,
𝑌