The present study was aimed at investigating the effect of Na₂O and B₂O₃ addition on the viscosity and electrical conductivity of slag which was used for mineral wool production. Industrial slag samples of the CaO–Al₂O₃–MgO–SiO₂ system were used to modify its composition with different Na₂O and B₂O₃ addition content and soaked at a certain temperature range (1400–1500°C). Raman spectrum was used to represent the structure of the slag system. Results showed that the Na₂O addition modified process had a larger effect on the two parameters (macro aspect) and the relative fraction of the structural units (micro aspect) compared with the results of B₂O₃ addition.

The utilization of H₂ in the ironmaking process is a potential option for a further reduction of CO₂ emission from the blast furnace (BF). H₂ promotes the reduction reaction of burden materials, but its influence on their reduction disintegration behavior remains unknown in detail. This study investigates its influence on the specified essential factors governing the reduction disintegration behavior of the iron ore agglomerates, i.e., iron ore sinters and pellets.

Reduction disintegration index (RDI) values were measured after the reduction of the agglomerate samples using the gas mixtures of CO–H₂–CO₂–N₂. The mineral textures of reduced samples were observed using an optical-microscope and an electron probe micro-analyzer for the evaluation of reaction modes. Further, Thiele modulus (ϕ), which is considered as the index of reaction modes during reduction, was calculated using the measurement results. The calculated ϕ showed reasonable correlation with RMI values, which is one index of the reaction mode evaluated by an elemental analysis using EPMA. Disintegration does not make much progress when ϕ is larger than a certain limit value, whereas it proceeds significantly when ϕ is less than that value.

Recently, additives such as CaCO₃ and Na₂CO₃ have been proven to be capable of enhancing the reduction of high-phosphorus oolitic hematite ore and obtaining high-grade direct reduction iron (DRI) with low-P by magnetic separation. In this study, the mechanisms of adding CaCO₃ during direct reduction were further studied by gas analyzer, X-ray diffraction (XRD) and scanning electron microscopy (SEM). It was found that CaCO₃ can inhibit the reduction of fluorapatite, and more P still remained as fluorapatite which can be removed by magnetic separation. In addition, CaO and CO₂ decomposed from CaCO₃ promoted reduction atmosphere, but the contribution of CO₂ to reduction of iron oxides was very limited, in fact CaO played a central role. An appropriate CaCO₃ dosage can enhance reduction of oolitic hematite. Addition of CaCO₃ led to the consumption of quartz and inhibited the generation of fayalite, which reduced FeO content in the slag, and as a result more FeO was reduced to metallic iron. A DRI with 94.51 mass% Fe, and 0.17 mass% P can be obtained at a iron recovery of 89.3 mass% by adding 10 mass% CaCO₃. However, excessive CaCO₃ reacted with gangue and FeO to generate a large amount of slag (such as kirschsteinite), which hindered the diffusion and growth of the iron grain and increased the iron loss.

The paper investigates the transformation of iron and slag phase in cohesive zone from a water-quenched blast furnace through SEM images, EDS spectra and thermodynamic calculation. The results show that the wustite structure exists as an independent interphase insoluble in slag and iron. The content of carbon keeps about 2% in iron, and the carburization function of coke is inhibited in cohesive zone. The compositions of slag phase fluctuate in cohesive zone, while the basicity maintains about 1.8, higher than that in final slag. The liquids temperature of iron in cohesive zone is about 1673 K, while that of slag phase gradually decreases from top to bottom. The separation between slag and iron is basically completed at lower part of cohesive zone. The blocked voids caused by softening and melting burden restrains the indirect reduction at lower cohesive zone, hence an apparent titanium attachment exists around iron due to the development of direction reduction.

Industrial experimental and thermodynamic analyses were carried out to investigate the evolution of oxide inclusions from consumable electrode to droplet and refined ingot during electroslag remelting (ESR) of G20CrNi2Mo carburized bearing steel. All the oxide inclusions in electrode were CaO–MgO–Al₂O₃, most of which compositions were located in the liquid region. During droplet formation, most electrode inclusions were absorbed by molten slag, and it was inferred that the Ca content in metal film obviously decreased. A few inclusions were still remained in the liquid steel mainly owing to low interfacial energy. In addition, pure Al₂O₃ inclusions smaller than 2 µm were generated in droplet, indicating that significant Al-oxidation occurred. The ingot inclusions were low-MgO-containing MgO–Al₂O₃, Al₂O₃-based irregular CaO–(MgO)–Al₂O₃ and spherical CaO–Al₂O₃, all of which compositions were outside of the liquid region, indicating that no ingot inclusions could be identified as the relics of that in electrode. Thermodynamic calculations showed that the dissolved Ca and Mg reduced by Al at slag/metal interface could not transfer into the metal pool. FactSage^TM 7.0 was used to elucidate the formation of inclusions in metal pool, and the results were basically in accordance with the experimentally observed inclusions, showing that a quasi-thermodynamic equilibrium could be established.

In the solid state steelmaking process used in recent researches, pig iron was directly casted and then decarburized in an oxidizing atmosphere in order to eliminate or reduce the amount of carbon. In the present study, the feasibility of solid state steelmaking from cast iron was investigated using limestone. For this purpose, white cast iron specimens were buried in a chamber containing CaCO₃ powder. Calcination of CaCO₃ produces CO₂ which participates in cast iron decarburization. In this technique, CO₂ reacts with the carbon content of sample according to Boudouard reaction which results in carbon consumption. Furthermore, effects of temperature and time on the decarburization process were investigated. White cast iron samples were decarburized at temperatures of 800, 900 and 1000°C for 10 and 24 h in the CaCO₃ powder pack. Very fine oxide layer was also observed to form during the decarburization process. Finally, samples were studied with optical microscope and SEM to measure the depth of the decarburized layer. However, secondary graphitization was occurred during the decarburization. Results showed that decarburization at 1000°C for 24 h has led to a completely decarburized layer of 420 µm thickness. In agreement, carbon analysis showed the reduction of carbon content from 3.16 wt% to 0.012 wt%. Kinetic studies revealed activation energy of 125 KJ/mol for decarburization of white cast iron using CaCO₃ powder pack.

Fe–Cr–Ni–Mo–N super-austenitic stainless steels were processed by using twin-roll strip casting and ingot casting, and their solidification structures and segregation behaviors were comparatively studied. The results show that serious center macro-segregation and massive eutectics were detected in ingot, with the amount of eutectics being increased from surface to center. By contrast, macro-segregation and eutectics were inhibited in cast strip (CS) due to its rapid cooling rate during the solidification process. In order to obtain optimum hot workability, homogenization treatments were carried out in the temperature range from 1050 to 1200°C for different time from 30 to 480 min in CS and ingot. The results show that the homogenized temperature of CS should be higher than 1100°C to avoid the formation of precipitates, and the optimum homogenization process was 1150–1200°C for 30 min. For the ingot homogenized at 1200°C, eutectics gradually dissolved into the matrix with increasing the homogenization time, and after 4 hours, they completely dissolved. Ingot could be homogenized after more than 8 hours of homogenization, indicating that CS has intrinsic advantages in homogenization. Finally, mechanical property and pitting corrosion resistance of 1 mm-thick cold-rolled bands, fabricated from CS and ingot, were tested and compared. The results show that the overall performance of cold-rolled bands of CS was superior to that of ingot.

Surface peeling or chipping of wire rod has been one of the serious problems of hot rolling of continuously cast low carbon steel billets. This led to frequent interruption in the rolling mill production besides impairing the surface quality of the finished wire rods. Metallographic examination of wire rod samples revealed the problem was largely due to presence of gas porosity or fine blow holes close to the surface of the cast billets. Higher dissolved gases in liquid steel can lead to the formation of gas porosity during initial stage of liquid steel solidification in billet casting. For evaluating the relative contribution of different dissolved gases on the porosity formation during liquid steel solidification, a sequential microsegregation-thermodynamic calculation procedure has been developed and applied for predicting their safe limits in liquid steel. Based on model prediction appropriate countermeasures were recommended for mitigating the problem of wire rod chipping during hot rolling of continuously cast low carbon steel billets.

In this paper we develop a new hybrid Mixed Integer Linear Programming/Constraint Programming (MILP/CP) decomposition method to solve a parallel Continuous Galvanizing Line (CGL) scheduling problem. The objective of the problem is to minimize the total production cost. Unlike common parallel scheduling problems, in this problem sequencing on each CGL is difficult because of the complex production rules of CGLs. Furthermore, all coils are required to be delivered on time, which means an assignment between coils and CGLs may not result into feasible scheduling. The problem is formulated as an integer programming model, but its structure is not suitable for optimization software package to solve. That is the reason why a new hybrid MILP/CP decomposition method is developed. To accelerate the method and reduce the computational time, a heuristic which tries to find the nature of infeasible assignments and obtain more effective cuts is embedded into the framework of the hybrid method. Some properties and a heuristic are employed to tell why the assignment is unfeasible and to derive more effective cuts. 60 instances are randomly generated to simulate actual production data. The new hybrid method is compared with the basic hybrid method without any features proposed in this paper. Numerical results show that the new hybrid method solves all instances in much less computation time than the basic one, especially for large scale instances.

An excitation source driven by pulsed discharge voltage of a two-step waveform, comprising a short higher-voltage pulse and a subsequent main pulse, is suggested for the depth profiling in glow discharge optical emission spectrometry (GD-OES). Pulsation of a DC voltage can be applied effectively for analysis of several specified samples, such as a ultra-thin layer to suppress the sputtering rate; however, it might worsen the in-depth resolution due to a decrease in the sputtering rate. The main reason for this degradation is that the switching-on period of the pulsed discharge may not follow the waveform of the timing pulse and then it is delayed and distorted, due to the capacity component of the plasma itself. In the dual-step pulse method, the first-step pulse would work as a trigger for start of the switching-on period, and thus the response of the resulting plasma could be less delayed even when the duty ratio becomes smaller. As a result, the sputtering conditions were suitable for the in-depth analysis with better interface resolution as well as larger information depth. Depth profiling of an electro-plated nickel layer on a steel substrate was carried out comparatively between a conventional single-step pulse and the dual-step pulse method, yielding better interface resolution by a factor of 1.5–2 with the sputtering rate to be 2–4 times reduced.

A steelmaking slag is one of the main by-products of iron and steel. The slag has been reused as aggregate for road and civil constructions. However, the slags may contain free magnesia (f-MgO) that can cause expansive self-destruction by reactions with water and carbon dioxide in the air. It is thus very important in evaluating the quality of the slags as raw materials to develop an accurate and precise method for determination of f-MgO in the slag. However, a reliable analytical method for determination of f-MgO in slag samples has not been reported yet. In the present work, we developed a method for determination of f-MgO in the slags by hydration of f-MgO with microwave digestion followed by thermogravimetry (TG). The microwave assisted hydration with hot water over 100°C makes f-MgO to rapidly and completely convert into Mg(OH)₂, the amount of which, in turn, can be determined by TG. The developed method was successfully applied to the determination of f-MgO in synthetic and real steelmaking slag samples.

In the present investigation, the plastic flow curves and work softening behaviour of a dual phase Fe–Cr–Ni alloy during hot deformation (low to intermediate temperature range, 948 K (675°C) to 1248 K (975°C)) along with concurrent microstructural development were investigated. The flow stress increased with the increase in strain rate and decreased with the increase in deformation temperature. The single peak characteristic appearing in all the flow curves indicated that dynamic recrystallization (DRX) was the dominant softening mechanism in the later stage of deformation. The critical strain for DRX initiation was ε_c = 0.632ε_p and the peak strain (ε_p) were expressed through the Zener-Hollomon parameter (Z). For flow stress modelling, an Arrhenius type constitutive model was established to predict the flow stress behaviour during hot deformation. The results showed that the calculated flow curves agreed reasonably well with the experimental results. The microstructural analysis using optical microscopy indicated that all the deformed structures exhibited elongated grains similar to that of parent microstructure and some equiaxed grains (resulting from DRX in the austenite phase). The fraction of equiaxed grains (in austenite) increased with the deformation temperature. At low Z, the ferrite phase accommodates the strain and dynamic recovery was the prominent restoration process. At high Z, austenite controlled the deformation mechanism and DRX was the likely cause for microstructural refinement. The iso-strain rate sensitivity (m) contour map was used to determine the optimum regime of high temperature workability.

The effect of the Mn addition on the oxidation resistance of high purity Nb containing 19% Cr ferritic stainless steels has been studied using specimens isothermally oxidized in air at temperatures from 1073 to 1273 K. The structures of the scale and the scale/metal interface were investigated in detail by means of FE-SEM, SEM-EBSD and FE-TEM.

The addition of Mn was confirmed to impair the oxidation resistance. Moreover, the scale structure was significantly affected by the addition of Mn. After oxidizing, 1%Mn steel in air for 720 ks at 1123 K, 5-µm thick oxidation scale formed. The Mn rich (Mn, Cr)₃O₄ spinel formed in the upper most layer following MnCr₂O₄ just above 3-µm thick Cr₂O₃ scale. Beneath the Cr₂O₃ scale, another MnCr₂O₄ spinel layer formed. The grain size of Cr₂O₃ of 1%Mn steel was surprisingly fine with approximately 200 nm and it turned out to be much smaller than that of the Mn-free steel where the 2-µm thick Cr₂O₃ monolayer consisting of the similar size of Cr₂O₃ formed. Such a difference is postulated to be related to the oxidation resistance. These effects of the Mn addition are inferred to stem from the fast diffusion of Mn through the grain boundaries of the very fine Cr₂O₃ scale. Furthermore, the scale of 1%Mn steel has a tendency to be bent into folds after long oxidation.

The usefulness of a new approach to detecting the distribution of hydrogen absorbed into pure iron utilizing a WO₃ thin film was demonstrated in this study. A WO₃ film with an electrochromic property was formed on the hydrogen detection side of iron sheet by reactive magnetron sputtering. After hydrogen was absorbed into the iron sheet by cathodic polarization on the hydrogen absorption side, the color of the WO₃ film corresponding to the electrode area changed from light blue to dark blue. The WO₃ film was found to reflect the distribution of hydrogen absorbed into the pure iron sheet. No color change occurred on the hydrogen detection side unless a Pd film was inserted between the WO₃ film and the iron specimen. The reflectance of the WO₃ film in the visible region was reduced by hydrogen charging, with a marked reduction in the RGB color values after the start of hydrogen charging. The results of an XPS analysis suggested that the phase transition from WO₃ to H_xWO₃ resulted in the color change of the WO₃ film during hydrogen charging. Because of the simplicity of this approach to detecting hydrogen compared to other hydrogen detection methods, it is expected to have various applications.

In this study, several single chemical and double thermal-chemical etching techniques have been used in order to identify in details the prior austenite grain boundaries (PAGBs) with a good contrasting resolution in an ultra cleaned high strength low alloy Cr bearing microalloyed steel. The general chemical etching techniques are based on the various conventional metallographic reagents involving: Picral; 60°C hot Picral; and Vilella solutions; while the double stage of thermal-chemical procedures have been classified into 400°C low and 650°C high temperature thermally treated for 3 hours followed with general chemical etching. Light and scanning electron microscopic observations have been supplemented with energy dispersive X-ray spectroscopy to follow the PAGBs detection in conjunction with that of carbide precipitation. Evidences are presented which indicate that only a tracing detection of PAGBs can be identified with general single metallography using conventional chemical etching reagents, while the double stage of thermal-chemical etching treated samples are associated with sharp contrasting resolution of PAGB areas. These observations are rationalized in terms of higher stimulation of chromium rich carbide formation and consequently the higher dilution of solute chromium at grain boundary areas of thermal-chemical treated samples. The PAGBs are considerably enriched from solute chromium in the direct water quenched fresh martensitic samples, while the thermal-chemical treated samples have been associated with chromium rich carbide precipitation at grain boundaries causing a higher sensitivity of grain boundaries to general chemical etching solutions, resulting the higher contrasting resolution of grain boundary areas.

Four different isothermal treatment processes were designed to investigate the effect of isothermal treatment parameters on the comprehensive property in an ultrafine bainite steel. Four different isothermal treatment processes, including two kinds of one-step bainite transformation procedures at temperature above M_S and below M_S, respectively, and two kinds of two-step isothermal processes, were employed in this study. The results indicate that compared with the one-step bainite transformation at temperature above M_S, the comprehensive property of ultrafine bainite steel was not improved by austempering at temperature below M_S. However, it was improved by the two-step isothermal process. In addition, at the condition that the total transformation time of multi-step isothermal process was the same, the product of tensile strength and elongation (PSE) of sample increased with the decrease of transformation time at the first stage. At the same time, the transformation kinetics of the second stage transformation was significantly accelerated with the decrease of transformation time at the first stage.

The effect of the two-stage continuous cooling process with different finish cooling temperatures (FCTs) after 950°C high temperature finish deformation on microstructural evolution, precipitation and mechanical properties of V–N alloyed steel has been investigated under the simulated and pilot-scaled thermomechanical condition. Microstructural observation of dilatometry specimens indicates that FCT should be above 600°C to obtain microstructure composed of polygonal ferrite (PF), pearlite (P), and less than 5 vol. pct bainite (B) in steel. Based on the simulation result, three pilot-scaled cooling paths with FCTs of 950, 750 and 600°C are designed and all microstructure consists of PF + P. The decreased FCT contributes to a refinement in the effective ferrite grain size and interlaminar spacing of pearlite, coupled with a decrease in PF content. Conversely, the amount of high misorientation angle boundary (above 15°) is increased. Moreover, the lower FCT promotes the precipitation of refined nano-scaled V(C,N) particles including interphase and random precipitates. Furthermore, an optimal combination of strength, ductility and toughness has been acquired at 600°C, of which the yield strength, tensile strength, total elongation, uniform elongation, and impact energy at room temperature are 769 MPa, 935 MPa, 23 pct, 11 pct and 30 J, respectively. The negligible variation of mechanical properties after artificial ageing exhibits that the addition of 0.024 mass% N in vanadium alloyed steel is available.

Recrystallization and grain growth are important phenomena for controlling the mechanical and magnetic properties of steels through texture. Only a limited number of studies have been carried out on texture evolution during recrystallization and grain growth in heavily cold-rolled Si steel. The present study first focuses on clarifying the texture evolution during normal grain growth, followed by an investigation into the development of the {411}<148> component during recrystallization. The {411}<148> component is remarkably developed during normal grain growth after the completion of recrystallization. At just fully recrystallized stage, the diameters of the {411}<148> grains were larger than that of the grains with other orientations. Therefore, the {411}<148> grains significantly grew owing to the size advantage.

Just at the commencement of recrystallization, differences in grain diameter of recrystallized grains in terms of crystal orientation were not detected. However, it is worthwhile to mention that the nucleation of {411}<148> recrystallized grains is unexpectedly fast in heavily cold-rolled Si steel. Recrystallized {411}<148> grains were observed to nucleate in the deformed α-fiber grains, especially near the grain boundaries. Nuclei with {411}<148> orientation grow easily due to the high mobility of the interface between the recrystallized/non-recrystallized grains and the high driving force. Consequently, the diameter of a {411}<148> recrystallized grain becomes relatively large upon the completion of recrystallization. This contributes to the selective grain growth during the normal grain growth stage because of the size effect.

The effect of boron (B) on the recrystallization behavior, in particular the growth of the recrystallized grain into the unrecrystallized grain, of titanium (Ti) added interstitial atom free (IF) steel sheets was studied from the viewpoint of the solute-drag effect considering the interaction between B and Ti atoms. The growth rate of the recrystallized grain at 5% fraction recrystallized decreased with increasing the B content. Furthermore, the decrease became more pronounced in the B added steels with the higher Ti content. The interaction energy between B and Ti atoms at the grain boundary was evaluated by the first-principles calculation in the bcc-Fe(111)Σ3[110] symmetrical tilt grain boundary. The attractive interaction between B and Ti atoms was obtained in most of the grain boundary atom sites examined. B segregation at the interface between recrystallized and unrecrystallized grains was concluded to induce Ti segregation through the attractive interaction between B and Ti atoms during interface migration. The mechanism for the suppression in the growth of the recrystallized grains was proposed to be caused by the decrease in the interface mobility caused by the enhanced Ti segregation.

Fatigue properties of Fe-19Cr-8Ni-0.05C and Fe-19Cr-8Ni-0.14C steels were investigated using a rotating bending fatigue test machine. Fatigue limit of both of the steels were dominated by critical stress amplitude for crack initiation. Because of the austenite stability, the fatigue limit of the Fe-19Cr-8Ni-0.05C steel was 200 MPa higher than that of the Fe-19Cr-8Ni-0.14C steel. Although occurrence of dynamic strain aging in the Fe-19Cr-8Ni-0.14C was expected to improve fatigue limit, the effect did not appear due to the remarkable increase of phase stability that deteriorates positive effects of transformation-induced plasticity and transformation-induced crack closure.

In this study, the effect of aging treatment at 373 K on Hall–Petch coefficient (k_y) was investigated by considering the change in friction stress associated with carbide/nitride precipitation in ferritic steels containing 60 mass ppm carbon or nitrogen (C60 and N60). Tensile tests revealed that the k_y monotonously increased with increasing aging time in both steels. Additionally, C60 exhibited a k_y value exceeding that of N60 with respect to the same aging time. The results of the 3DAP analysis and theoretical calculation for the grain boundary segregation of carbon and nitrogen indicated that the k_y corresponded to the amount of carbon and nitrogen existing at the grain boundary. No difference in the effect on increments in k_y between the two elements was observed. The increase in k_y in C60 under the same aging condition was due to the higher amount of segregated carbon when compared with that of nitrogen.

Effect of ferrite grain size on dislocation strengthening was investigated in low carbon steels (0.006%C-0.15%C) with various grain sizes from 1 to 100 µm. In specimens with slight deformation, dislocation density increases in proportion to the inverse of ferrite grain size. In the dislocation density range below 2×10¹⁴/m², dislocation density increases linearly against deformation strain but it tends to level off due to the dynamic recovery of dislocations when dislocation density has exceeded it. On the other hand, tensile tests revealed that yield stress follows the Hall-Petch relation for as-annealed specimens but follows the Bailey-Hirsch relation for cold rolled specimens. This means that flow stress depends on only the dislocation density regardless of grain size. As a result, it was concluded that the introduction of dislocations has been promoted with decreasing ferrite grain size and this results in the increase of flow stress in the uniform deformation region.

To develop a slag reduction process (IBX process: Iron Bath for X), three kinds of slag reduction tests were carried out using different pilot scale and commercial scale DC arc furnaces. The goals are to recover the valuable elements such as Fe or P from the steelmaking slag and to modify the slag composition. The main target is to use molten slag directly in the reduction process and to establish a stable operation for improving the energy consumption, productivity, and processing cost. In the present paper, we describe the results obtained in a pilot scale closed-type 2 MW DC arc furnace (Test 1), commercial scale open-type 30-MW DC arc furnace (Test 2), and newly designed closed-type 4-MW DC arc furnace (Test 3). Reduction efficiency and the metallurgical properties in DC arc furnaces, the mechanism of slag foaming, and the influence of the atmosphere in the furnace were discussed based on the experimental results. Finally, model calculations of the flow patterns in the furnace were carried out for further comprehension of the metallurgical phenomena. From these results, it was confirmed that the closed-type DC arc furnace can achieve efficient and stable reduction of steelmaking slag with hot charging.

To recover valuable elements such as Fe or P from steelmaking slag and to modify the slag composition, a molten slag reduction process (IBX process: Iron Bath for X) has been developed. So far, pilot and commercial scale test operations have been carried out and it has been clarified that closed-type DC arc furnaces are desirable for the slag reduction process with hot slag charging. In the present work, issues and solutions of the actual operation are discussed. One issue is the optimization of the material feeding method. A hollow electrode, top lance, and injection pipe method were tested in the same furnace and the performance of each was investigated. The second issue is slag boiling and solidification at hot slag charging. To establish stable operation, use of a bottom block to avoid the formation of an emulsion at slag charging and off-gas combustion for heating the slag were proposed and tested. Finally, thermal aspects were discussed and the required energy consumption was estimated to show the effect of hot slag charging. Through these studies, it was confirmed that stable operation of slag reduction with hot slag charging can be attained in closed-type DC arc furnace, representing a great step for realizing of complete utilization process of BOF slag.

Cui et al.¹⁾ proposed a methodology for the fluid flow characterization of asymmetric tundishes that does not rely on any idealized flow model. First, the E curves of each tundish strand is obtained through the pulse input experiment. Subsequently, the E curves are converted into F curves by integration. Then, the dead volume fraction of the entire tundish (V_d /V) is calculated so as to evaluate the overall tundish performance. Finally, the flow uniformity among tundish strands is assessed through quantities obtained from the strand F curves (i.e. maximum difference between strand F curves for two-strand tundishes or maximum standard deviation among strand F curves for multi-strand tundishes). In the present work, the calculation procedure for the methodology of Cui et al.¹⁾ is discussed in detail. It was identified a problem in the obtention of F curve by Cui et al.¹⁾ that modified the actual formulas of V_d /V. In addition, this work presents new equations that facilitate the calculation of V_d /V when physical and mathematical models are employed. Moreover, the most convenient definition of the dead volume fraction is studied. It was found that V_d /V can distinguish different flows more effectively if it is based on one dimensionless residence time rather than two. Furthermore, some parameters for assessing the flow uniformity among tundish strands were compared. The area metric described by Oberkampf and Roy¹¹⁾ is the recommended one.