This paper investigates the different possible behaviours of a recent asymptotic model for oscillation-mark formation in the continuous casting of steel, with particular focus on how the results obtained vary when the heat transfer coefficient (⁠|$m$|⁠), the thermal resistance (⁠|$R_{mf}$|⁠) and the dependence of the viscosity of the flux powder as a function of temperature, |$\mu _{f}\left ( T\right ),$| are changed. It turns out that three different outcomes are possible: (I) the flux remains in molten state and no solid flux ever forms; (II) both molten and solid flux are present, and the profile of the oscillation mark is continuous with respect to the space variable in the casting direction; (III) both molten and solid flux are present, and the profile of the oscillation mark is discontinuous with respect to the space variable in the casting direction. Although (I) gave good agreement with experimental data, it suffered the drawback that solid flux is typically observed during actual continuous casting; this has been rectified in this work via alternative (II). On the other hand, alternative (III) can occur as a result of hysteresis-type phenomenon that is encountered in other flows that involve temperature-dependent viscosity; in the present case, this manifests itself via the possibility of multiple states for the oscillation-mark profile at the instants in time when solid flux begins to form and when it ceases to form.

中文翻译：

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钢连铸中折叠型振荡痕迹形成模型的分析

本文研究了最新的渐近模型在钢的连续铸造中形成振荡痕迹的不同可能行为，特别关注当传热系数（⁠| $ m $ |⁠），热电阻（⁠| $ R_ {mf} $ |⁠）和助焊剂粉末的粘度与温度的关系，| $ \ mu _ {f} \ left（T \ right），$ |被改变了。事实证明，可能出现三种不同的结果：（I）助焊剂保持熔融状态，并且从未形成固体助焊剂；（II）熔融和固体熔剂均存在，并且振动痕迹的轮廓相对于在铸造方向上的空间变量是连续的；（III）熔融熔剂和固体熔剂均存在，并且振动痕迹的轮廓相对于沿铸造方向的空间变量不连续。尽管（Ⅰ）与实验数据吻合得很好，但它的缺点是在实际的连续铸造过程中通常会观察到固熔剂。这已通过替代方法（II）在这项工作中得到纠正。另一方面，由于在其他与温度相关的粘度流中遇到的滞后现象，可能会出现替代方案（III）。