Theoretical estimation of solidification length of continuously cast metals

• Guidelines are presented for designing a new continuous casting process.
• Model is developed with a constant surface temperature assumption.
• 2-D conduction equation is solved including the solidification effect.
• Solidification length increases with mass flow and surface temperature.
• Solidification length decreases with increase in width to thickness ratio.

A semi-analytical model is presented to find the solidification length of continuously cast metals. An existing theoretical solution for solidification in an infinite slab, which is maintained at constant surface temperature is extended to a finite slab. For the case of a finite slab, the governing 2-D heat conduction equation is solved in the non dimensional form using a constant surface temperature as a boundary condition. The solution also delivers the guidelines for the kind of cooling profile which has to be applied in reality. It is found that the total solidification length (metallurgical length) in a continuous casting process is proportional to the mass flow rate and specific heat capacity and inversely proportional to the conductivity and width to thickness ratio of the slab. The novelty of this study is that it provides design guidelines for the process engineers to find the solidification length beforehand for a given cast alloy and ingot geometry.