My latest work has been published in the IMA Journal of Applied Mathematics. The full text PDF can be downloaded for free here .

Abstract

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, \(\mu_f(T)\), 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.