**3. Concluding Remarks**

Over the years, several aspects regarding the BF dead man have been studied by means of dissection investigations, physical experiments, and theoretical and numerical calculations. Today, the importance of the dead man state and its influence on the performance of the BF hearth have been commonly recognized, even though direct (long-term) measurements of the pertaining state variables are still impossible.

The structure and renewal mechanisms of the dead man have been clarified. It has been demonstrated that the dead man is heterogeneous in terms of its permeability distribution, and that the permeability can be improved in practice by charging high-quality coke into the BF center. The dead man bottom shape and position strongly depend on the balance between the buoyancy force exerted by the in-hearth liquid iron and slag, and the downward-acting force that is reduced towards the furnace wall due to the drag of the upward-flowing gas from the raceways and wall friction. In general, the dead man sits completely on the hearth bottom when the levels of the in-hearth liquids are low. If the liquid levels are high, however, the dead-man bottom assumes a profile where it floats higher at the hearth corner.

Observed hearth lining wear profiles, i.e., elephant-foot-shaped and bowl-shaped, are intimately related to the dead man floating state and its permeability distribution. The lining profile can be estimated utilizing hearth wear models, whereby an inverse problem of heat conduction is solved to predict the position of the 1150 ◦C isotherm. Such models are today used in several BFs as monitoring and diagnosis tools. The estimated profile can be used to assist the interpretation of the in-hearth liquid flow pattern and the floating state of the dead man. By analyzing the estimated hearth wear profile, indications may also be obtained pertaining to the need to change the operation towards conditions less prone to cause erosion, including lowering of the production rate, blanking of tuyeres in regions with strong local hearth wear, or modifying the tapping strategy.

The drainage of the BF hearth is complicated and a dry tap is impossible because some amount of slag always remains in the hearth at the end of a normal tap. It has been shown that the slag residual ratio at the tap end can be correlated with the flow-out coefficient. In practice, an increase in the slag residual ratio is often attributed to a decrease in dead man permeability, or an increase in draining rate or in slag viscosity. The complexity of the hearth drainage behavior is basically due to the multiphase flow of immiscible fluids (gas, slag and iron), the existence of the dead man and the erosion of the taphole. As a tap proceeds, both the gas–slag and slag–iron interfaces gradually tilt towards the taphole. Therefore, the overall slag and iron levels are located above and below the taphole at the tap-end, respectively. This interface titling phenomenon has been investigated, and an absolute asymptotic limit has been derived and can be applied to validate the related modeling results. However, much work is still required in order to understand the effects of, e.g., local permeability changes in the dead man or local dead man motion on the drainage patterns from individual tapholes. A deeper understanding of the drainage can be the basis of a better design of the tapping operation, which can be influenced by the duration of the inter-cast period, the drill diameter and the taphole angle. The role of the taphole length, e.g., how this variable can be controlled and how it affects the dead-man state, are also factors that should be studied and clarified in the future.

**Author Contributions:** Conceptualization, L.S. and H.S.; literature review, L.S., Q.X., C.Z., Z.Z. and H.S., original draft preparation, L.S.; writing—review and editing, L.S., Z.Z. and H.S.; funding acquisition, L.S. and Z.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was partially funded by the National Science Foundation of China, grant number 51604068. The authors gratefully acknowledge the support.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study or interpretation of the results.
