# Measurement and Model-Based Control of Solidification in Continuous Casting of Steel Billets
## 3 Results
### Dynamic Temperature and Solidification Model DynSolidCC
#### 3.1.2 FOTS Measurements in Mould Walls at ESF  
Figure 4 shows the layout of 64 optical temperature sensors arranged in four fibres within the mould wall, each with 16 sensors running around the mould perimeter at different distances of 0.1, 0.3, 0.5 and 0.65 m below the meniscus. The measurement technique uses the effect of temperature-dependent Bragg diffraction in the gratings imprinted on the fibres. In order to calculate the temperatures in the walls of the mould and compare them with the FOTS measurements, it would be necessary to model the heat transfer from the strand surface to the mould wall positions in detail as well as to model the further heat transfer from the mould wall to the cooling water box of the mould. This would involve further model parameters which cannot be tuned independently from the parameters a\({}_{\rm c}\), \(\alpha\) of Equation (1) describing the heat flow density across the strand surfaces in the mould. Thus, only qualitative validations regarding the assumptions and calculations of the Dyn-SolidCC model in the mould have been carried out. Thereby, the following conclusions could be drawn:  
* The symmetry assumption regarding heat flows across top/bottom and left/right strand surfaces and related measured FOTS temperatures fits better for the lower part of the mould (i.e., fibres 2 and 3) compared to the upper part (i.e., fibres 0 and 1). Moreover, the associated sensors near the middle of the walls show better congruence than those near corners. * After a significant decrease in measured mould wall temperatures from fibre 0 to fibre 1 to a level, which is more or less also measured at fibre 2, it increases again at fibre 3. At fibres 0 and 1, the top wall sensors have measured higher averaged temperatures than the left wall sensors. At fibre 2, all sensor measurements are quite close together, with mid-wall sensor results slightly higher than corner sensor results. At fibre 3, a symmetric temperature distribution can be observed with mid-wall values on an equal level significantly higher than the corner values, also on an equal level. This can be expected from the geometry with higher cooling effect from two faces near the edges and is related to the higher strand surface temperatures calculated at the middle of the strand compared to the temperatures at strand corners. * Thus, the heat transfer from the strand to the mould walls is homogenised in the range between fibre 1 and fibre 3, and for the lower part of the mould, the boundary conditions can be considered to be symmetric with respect to top/down and left/right strand surfaces. * Because the strand surface temperatures decrease with increasing distance from the meniscus, the observed increase in the mould wall temperatures at fibre 3 indicates an increase in the heat flow density by a better heat transfer at this mould length, e.g., due to better contact between strand surfaces and mould walls. This has been taken into account in the model parametrisation by choosing a more or less constant heat flow density at the strand surfaces along the mould length instead of a decreasing behaviour, which usually is suggested in the literature (see Equation (1)). However, simulations revealed no significant influence of the parameter \(\alpha\) in Equation (1) on the strand temperatures and shell thicknesses at the mould exit if the total heat extraction across the mould is kept constant. * The comparison of temporal evolutions of measured mould wall temperatures and associated calculated strand surface temperatures shows a correlation where a decrease/increase in wall temperatures is related to an increase/decrease in strand surface temperatures with a delay of about 45 s. The FOTS along the mould measure decreasing/increasing heat flows between strand and mould, which lead to increasing/decreasing surface temperatures. * All in all, it seems justified to use the assumption of symmetric boundary conditions in the mould with a more or less constant heat flow density across the different strand surfaces.