The fibrosis and nano-materialization of porous rod-shaped Co_0.5Ni_0.2Zn_0.3Fe₂O₄ (C5N2Z3-C) spinel ferrite structure allowed it to exceed the Snoek limit and its EAB_max reached 7.8 GHz (7.60 GHz–15.40 GHz) at only 2.8 mm.

The slag entrapment process under two different initial conditions during the end of casting in tundish is studied. A 3D multiphase mathematical model was developed to simulate the slag entrapment behaviour. The critical slag entrapment time (t_s) and the corresponding critical slag entrapment height (h_cs) were predicted. The results show the h_cs increases, the t_s decreases as the casting speed increases, but their relationships are not linear. The influence of casting speed on the h_cs in the range of 1.25–1.5 m min⁻¹ is higher than other ranges. The h_cs simulated from the steady flow field is higher than that from the static state. When the casting speed is 1.50 m min⁻¹, the difference between the h_cs calculated from two different initial conditions is the largest, reaching 9.83 mm (8.42%). The numerical simulation results are verified by a 1:2 scaled water model. GRAPHICAL ABSTRACT