Estimating Non-Linear Heat Flux in Continuous Billet Casting Process With Limited Sensors

In a continuous billet caster, the heat transfer from the pool of molten steel to the cooling water via the copper mold depends non-linearly upon several casting parameters. A reliable and accurate methodology based on the principle of inverse heat transfer technique has been proposed in this work to obtain the nonlinear heat flux of a continuous billet casting mold. Differential evolution optimization technique has been used, in conjunction with the 2-D and 3-D steady state conduction heat transfer equations to develop the complete algorithm. It has been observed that both the 2-D and 3-D models are able to accurately predict the heat flux for different numbers and locations of temperature sensors. While the 2-D model estimates the 1-D heat flux profile varying along casting direction within a very short time period, the 3-D model offers the advantage of estimating a more accurate 2-D heat flux profile varying along both the mold length and width. The 2-D model has also been used to estimate the heat flux for an industrial continuous casting mold using measured plant data. It is observed that the present methodology accurately estimates the boundary heat flux in the continuous billet caster mold.