Journal of Applied Mathematics

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.
ProgramVariables calculatedParameters modifiedEquation numbers employedDimensionless 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