The Melting Behavior of Hydrogen Direct Reduced Iron in Molten Steel and Slag: An Integrated Computational and Experimental Study

: Direct reduced iron (DRI) and hot briquetted iron (HBI) are essential feedstocks for tramp element control in the electric arc furnace (EAF). Due to greenhouse gas (GHG) concerns related to CO 2 emissions, hydrogen as a substitute for natural gas and a reductant in DRI production is being widely explored to reduce GHG emissions in ironmaking. This study examines the melting behavior of hydrogen DRI (H-DRI) pellets in the EAF containing low-carbon (0.1 wt.%) molten steel and molten slag. A computational heat transfer model was developed to predict the melting behavior of H-DRI pellets. To validate the model, a set of experimental laboratory simulations was conducted by immersing H-DRI in a molten steel bath and slag. The temperature history at the center of the pellet during melting and the shell thickness at different melting stages were utilized to validate the model. The simulation results agree with the experimental measurements of steel balls and H-DRI in different metallic molten steel and slag baths.


Introduction
Government, industry, and society have increased focus on the global economy to achieve net zero CO 2 emissions.Since the steel industry accounts for 6% of global CO 2 emissions, there is a growing focus on researching decarbonization technologies [1].Steelmaking processes depend on the type of iron feed material used and the conversion of iron ore into metallic iron.Traditionally, this has involved using blast furnace hot metal and steel scrap [2].The blast furnace (BF)-a basic oxygen furnace (BOF)-accounts for around 70% of global steel production, involving the emission of CO 2 to the atmosphere because of the use of carbon in the process [3].
Another process to obtain metallic iron is direct reduced iron (DRI), where the reduction occurs with a series of reactions in a vertical shaft furnace between the iron ore and CO or H 2 -reducing gases generated from natural gas.These chain reactions are shown in Equations ( 1)-( 6) [4].The examination of how steel scrap melts in a molten steel bath within the steel industry has garnered considerable attention due to the significant production of steel scrap in numerous countries.Therefore, it is essential to develop methodologies for incorporating substantial amounts of steel scrap into the typical steel-making procedures commonly employed in an EAF [5].The melting behavior of scrap in the EAF compromises different variables in the system, such as its chemistry, temperature, and stirring conditions.Steel scrap is viable for making steel.However, producing steel with minimum unrefinable impurities such as copper, nickel, and tin from scrap is difficult due to accumulation of these residuals in the recycled scrap supply.Using virgin iron units such as DRI results in obtaining steels with fewer of these impurities [6].3Fe 2 O 3(s) + CO (g) → 2Fe 3 O 4(s) + CO 2(g) (1) Metals 2024, 14 The use of DRI obtained with CO is mature in EAF.On the other hand, using hydrogen as a reducing agent in DRI can be a solution to reduce CO 2 emissions.Although the implementation of hydrogen draws a new path of decarbonizing technology, there are some challenges to understand before implementing H-DRI in EAF.

1.
EAF steelmaking-melting and energy consumption.As it is known, the presence of carbon in the DRI reduces the melting temperature (4.3% C-Fe: ~1403 K to pure iron: ~1811 K) [3].Therefore, using H-DRI pellets in the EAF will require more energy to melt pellets with higher melting temperatures.2.
Foaming.The reaction of carbon with FeO or O in the metallic bath in EAF produces CO gas; this CO gas cannot escape and causes foaming [7,8].Foaming in EAF is important because it reduces electric energy consumption due to better thermal efficiency.Other benefits of foaming are lower electrode consumption, reduced wall thermal stress, and reduction in harmonic electric disturbances [8].The use of H-DRI pellets reduces the presence of C in the system, and the lack of C in the system will challenge the foaming formation.3.
Stirring conditions.Previous studies have shown that the CO/CO 2 gas evolution resulting from the reaction of the C in the system promotes the stirring in the metallic bath [9].Stirring promotes heat transfer in the DRI pellets and reduces the melting time.However, with the implementation of H-DRI pellets, the stirring conditions related to CO/CO 2 gas generation will not occur, and the melting time will be extended.This factor will represent another challenge for the use of H-DRI pellets.4.
Production costs-global competition.Implementing decarbonization technology is associated with high costs [10].By 2023, the estimated levelized cost of producing renewable hydrogen for DRI was about 4.5 USD/kg to 6.5 USD/kg, and it is expected to decline to 2.5 USD/kg to 4.0 USD/kg towards 2030 [11].According to Fabian Rosner et al. [12], the price of hydrogen production must be 1.63 USD/kg or less to be competitive with natural gas.
In steelmaking, the maximum production rate of the furnace depends on the time required for the melting of steel scrap or DRI, which is related to the geometry of the feed steel scrap or DRI and their chemical composition.Several studies have been performed to shed light on this practice.Eduardo Pineda-Martinez et al. [6] analyzed a DRI pellet's melting kinetics in a non-reactive molten slag bath.The authors developed a mathematical model assuming constant thermophysical properties.The governing equation included the convection heat transfer mechanism between the metallic bath and the DRI pellet with the omission of gas generation inside the pellet.Then, the energy conservation equation was solved in the transient stage to study the shell formation around the pellet.This study showed that increasing the temperature of the molten slag bath decreases the melting time of pellets.Additionally, increasing the heat transfer coefficient decreased the melting time of the pellet and the shell thickness.
In a similar study, O. J. P. Gonzalez et al. [13] developed a computational fluid dynamics (CFD) model coupled with a Lagrangian model for understanding the melting behavior of DRI pellets in EAF.The fluid flow was characterized within a Eulerian reference frame through the solution of turbulent Navier-Stokes equations alongside continuity and energy conservation equations.The entire system is applied to a three-phase EAF, assuming constant thermophysical properties.In this study, the molten steel was considered a continuous phase, while DRI was a dispersed phase.The results revealed that the formation of the solidified layer shell plays a vital role in the melting rate of DRI, representing almost 50% of the total melting time.In both mentioned studies [6,13], the bath contained either molten steel or molten slag.Later, Marco Aurelio Ramirez-Argaez et al. [14] evaluated the melting rate of porous DRI in a pool of molten steel and slag.They assumed that the bath was composed of two condensed liquid phases with constant thermophysical properties and non-steady state conditions for the DRI system in a steel bath and molten slag; heating was the only driving force for the motion of the two fluids.The governing equations included the conservation of mass, turbulent momentum, and energy, solved according to Newton's second law of motion based on a Lagrangian framework.The momentum transfer between fluid and particles included the drag force from the liquid to the solid DRI, buoyancy, gravitational, and turbulence forces.The results demonstrated a one-order-of-magnitude difference in melting time between a solidified metallic iron shell in a steel bath and one formed in a molten slag bath.The thickness of the slag layer was three times smaller than the steel shell.The model was validated based on other works in the literature.
Different studies have examined the influence of the steel scrap shape on the melting rate.Jianghua Li et al. [15] studied the melting rate of various sizes and shapes of steel bars in a steel bath.A two-dimensional (2D) phase-field model with a constant heat transfer coefficient and an interfacial gap between the shell and the bar was considered in the heat convection model.It was found that the melting time decreases linearly with increasing the solid fraction of the steel bar.The shape of the steel scrap does not affect the melting rate of the material.Shuai Deng et al. [16] studied an experimental setup of three different steel scraps on size, length, mass, and specific surface area, preheated at temperatures from 300 • C to 800 • C. A 2D axisymmetric model was developed to understand the solidification and melting phenomena.In this simulation, it was assumed that the temperature of molten iron is constant, and thermal conductivity, specific heat capacity, and density of the scrap are temperature dependent.This study showed that increasing the specific surface area of the pellet decreases the melting rate.Additionally, preheating the scrap increased the melting rate.The heat transfer coefficient significantly influences the melting behavior of DRI pellets.To ascertain this, several scholars developed empirical correlations.R.I.L Guthrie et al. [17] developed a heat transfer model to obtain the melting time of iron spheres of 0.85 wt.% C of various sizes in an iron bath saturated with 5 wt.% carbon.They assumed that the temperature of the pellets before immersion was uniform, the thermophysical properties of the pellets were equal to those of pure iron, no chemical reactions occurred within impurities dissolved in the molten bath, and the heat conduction through a sphere was radially solved with the energy conservation equation.The fluid flow around the DRI pellet could be either laminar or turbulent according to the Prandtl number; the Prandtl number is related to the heat transfer coefficient through the Nusselt number.This study determined that the fluid flow was laminar with a Prandtl number lower than one.It was found that density gradients generated thermal convection currents near the melting sphere, which led to shorter melting times.A shorter melting time is associated with a higher Nusselt number, which is directly related to the heat transfer coefficient.This study neglected the influence of gas generation through the reaction of DRI pellets with molten steel.DRI's melting behavior was explained via a mathematical expression based on the thermophysical properties of the phases involved in the system.
Few investigations have been reported on the melting behavior of H-DRI [18].The studies in the literature are related to the dephosphorization mechanism or interaction between the metal, slag, and refractory.Joar Huss et al. [19] studied H-DRI's melting and dephosphorization mechanism at 1773 K and 1873 K.The study found that the melting rate of H-DRI varies with the reduction degree (91-99.5%)and increases with decreasing reduction degree.When the H-DRI was melting, a gradual reversion of phosphorus from the autogenous slag was observed, which was related to a higher reduction of H-DRI.A lower reduction of H-DRI with carbon additions exhibited a slower reversion of phosphorus from the autogenous slag. A. Ammasi et al. [18] analyzed the H-DRI melting behavior in slag and molten metal.They employed an induction furnace at 1600 ± 10 • C.Then, iron ore pellets were prepared and reduced under a hydrogen atmosphere at 900 • C for three hours.This study showed that with high metallization due to the reduction of iron ore pellets with hydrogen, the ratio of FeO/Fe 3 O 4 in slag is less than its counterpart in molten iron.The melting time for a single pellet with a 11 to 14 mm diameter is 13 to 15 s for reduced pellets with 90.57% metallization.Amanda Vickerfält et al. [20] worked on the reaction mechanisms during the melting of H-DRI with different degrees of reduction at different temperatures and times (1773 K to 1873 K and at 60 s to 600 s).It was found that an autogenous slag is formed inside the pellet when the FeO inside the pellet starts to melt and flow out of the iron grains, reacting with the CaO-rich silicates.By the time 60 s had elapsed, the iron had not yet reached a molten state, but a slag phase had already developed within the pellet's pore network.After a duration of 90 s, the iron reached a molten state, and little droplets of slag were present within the liquid metal phase.Andreas Pfeiffer et al. [9] studied the melting behavior of H-DRI using the hydrogen plasma smelting reduction (HPSR) reactor under inert conditions and continuous feed of slag-forming oxides.Industrial iron ore pellets were reduced in a vertical reduction furnace (VRF), and the reduced samples were melted in the HPSR.According to this study, samples containing carbon melt more quickly than those without carbon.The presence of bubbles in the system corroborates the high reactivity of carbon in DRI.A highlighted point in the article is that the presence of carbon in the DRI plus the electromagnetic stirring of the arc helps the stirring, increasing the convective heat and improving the melting behavior of the sample compared to carbon-free DRI pellets.Therefore, more studies are needed to understand the H-DRI melting behavior.
Previous modeling efforts on the melting behavior of DRI pellets, steel scrap, and steel bars in molten slag and steel baths were based on constant thermophysical properties, including thermal conductivity, specific heat capacity, and density.Some H-DRI studies were focused on the dephosphorization mechanisms or the slag interaction with metal and refractory.Therefore, this study aims to develop a computational model to understand the melting behavior of DRI pellets in molten steel and slag baths based on the heat transfer mechanism and temperature-dependent thermophysical properties under laminar flow and natural convection.To validate the model, an experimental setup was developed to measure the temperature in the middle of the steel ball by immersing it in a molten low-C steel bath and slag and performing intermediate melt studies.The validated model was applied to understand the melting behavior of DRI pellets immersed in a molten steel and slag bath.The simulation results were validated with the corresponding measured data from the experimental setup.

Heat Transfer Model
The conduction heat transfer model, based on Fourier's law, in the solids and fluids was applied to simulate the interaction of the melting phenomena of steel balls and H-DRI pellets in molten steel and the molten slag bath: q = −k∇T (7) where q corresponds to the conductive heat flux, k is the thermal conductivity, and ∇T is the temperature gradient.Thermal conductivity can take a positive value, indicating heat flows from high-temperature to low-temperature domains.This equation is coupled with the energy conservation equation (Equation ( 8)).
In Equation ( 8), ρ is the density, C p is the specific heat capacity at constant pressure, T is the temperature, t is the time, u is the velocity, and Q contains additional heat sources.Equation ( 8) is reduced to the form of Equation ( 9) as the steel ball/pellet is suspended in Metals 2024, 14, 821 5 of 19 the bath with no velocity field u = 0, and other heat sources like radiation are neglected (Q = 0).
The mathematical model was numerically solved using COMSOL Multiphysics 6.1 [22] in a 2D axisymmetric definition, where the geometry, the loads, and boundary conditions are rotationally symmetric about an axis z.Equation ( 10) can be rewritten in the cylindrical coordinate system as Equation ( 11) [23].
where r is the radial position, z is the height, R is the steel ball/pellet's radius, R shell is the steel ball/pellet's radius plus the solidified shell thickness, and α is the thermal diffusivity.
A schematic presentation of the steel ball/pellet and the solidified shell, as well as the temperature distribution, is shown in Figure 1.
In Equation ( 8), ρ is the density, C p is the specific heat capacity at constant pressure, T is the temperature, t is the time, u is the velocity, and Q contains additional heat sources.Equation ( 8) is reduced to the form of Equation ( 9) as the steel ball/pellet is suspended in the bath with no velocity field u = 0, and other heat sources like radiation are neglected (Q = 0).
The mathematical model was numerically solved using COMSOL Multiphysics 6. 1 [22] in a 2D axisymmetric definition, where the geometry, the loads, and boundary conditions are rotationally symmetric about an axis .Equation ( 10) can be rewritten in the cylindrical coordinate system as Equation ( 11) [23].
where r is the radial position, z is the height, R is the steel ball/pellet's radius, R shell is the steel ball/pellet's radius plus the solidified shell thickness, and α is the thermal diffusivity.A schematic presentation of the steel ball/pellet and the solidified shell, as well as the temperature distribution, is shown in Figure 1.To fully understand the melting/solidification process, this model should include heat convection and the heat required for the solid/liquid phase transition.The energy needed for the solid/liquid phase transition comes from the difference between heat conduction and convection, as shown in Equation ( 12) [14].
where Q conduction is heat conduction, Q convection = h(T ∞ −T s ) is heat convection, h is the heat transfer coefficient, T ∞ is the molten bath temperature, T s is the surface temperature of the steel ball/pellet, and Q phase change is the heat required for the solid/liquid phase transformation defined in Equation ( 13).
In this equation C ′ p is the apparent heat capacity.COMSOL Multiphysics 6.1 uses the apparent heat capacity method to determine the heat required for the phase transformation, which is defined in Equations ( 14) and ( 15) [22].
At the interface of the steel ball/pellet surface and the molten bath, two cases can occur: (1) When the steel ball/pellet's surface temperature is lower than its melting point, there is no solid/liquid phase transformation; therefore, in Equation ( 12) Q phase change = 0 where r = R.
(2) When the steel ball/pellet's surface temperature equals its melting point, the heat required for solid/liquid phase transformation must be added to Equation (18).
In these equations g is gravity, β is the thermal coefficient of volume expansion, v is the kinematic viscosity, and µ is the dynamic viscosity.The relationship between kinematic and dynamic viscosity can be found in Equation (23) [24].
Equation ( 22) is valid when the fluid around the steel ball/pellet behaves under natural convection and laminar flow.The natural convection is produced by a local increase in the molten bath density close to the pellet's surface.When the pellet is heated, and the molten bath adjacent to its surface cools down, the density of the molten bath layer increases.A flow is produced due to the difference between the density of this layer and the density of the molten bath [25].Additionally, in the experimental setup, when the steel ball/pellet was immersed in the metallic bath, the induction furnace power was turned off to prevent stirring induction in the bath.Equation (24) shows the required condition in which the fluid flow is laminar around a solid sphere [24].This condition is met for this study case, and the results are shown in Table 1.

Porosity-Dependent Thermophysical Properties
The H-DRI pellets have porosity and were determined using Archimedes' principle based on the ASTM C20 method [26].The apparent porosity is determined using Equation (25).
where W is the saturated weight, D is the dry weight, and S is the suspended weight.The measured open porosity was 60 ± 3% for H-DRI pellets.Arizona State University provided these H-DRI pellets, which were reduced at 700 • C under hydrogen.Studies performed by Yuri Korobeinikov et al. [27] on these pellets showed a total porosity (open porosity + closed porosity) of 64%.Therefore, the closed porosity was considered negligible in this study.

Density, ρ
When the pellet's porosity increases, the pellet's density decreases.The density of the pore can be neglected, and the H-DRI pellet density can be determined as a linear function of density shown in Equation (26) [6].ρ s is the density of the solid phase.
The specific heat capacity is calculated by weighted volume defined by "the mixture rule" shown in the Equation ( 27) [28].
In this equation, V f is the volume of the fluid in the pores, C p,f is the specific heat capacity of the fluid, V m is the volume of the metal in the matrix, C p,m is the specific heat capacity of the metal in the matrix.For the thermal conductivity, an empirical correlation is used to calculate the effective thermal conductivity using the equation proposed by Koh and Fortini [29], where n is a constant equal to 11 for sintered metal powders determined in Equation (28).
k m is the thermal conductivity of the metal in the matrix, and e is the porosity of the pellet.

Boundary Conditions
The geometry of the domain for the pellet and bath based on the experimental setup is shown in Figure 2. A thermal resistance with a thermal conductivity of 0.04 [W m −1 K −1 ] is considered between the thermocouple and the H-DRI/steel ball [30].This thermal resistance is due to a thin layer of the high-temperature aluminum silicate adhesive that sticks the thermocouple in the H-DRI pellet.According to the designed experiment, the temperature in the chamber's walls was fixed to 1602 • C. Convective heat flux between the steel ball/pellet's surface and the metallic bath was defined based on the heat transfer coefficient calculated using the dimensionless numbers in Equations ( 20)-( 22), as shown in Figure 2. The bath temperature was fixed to 1602 • C, and the initial temperature for the steel ball/pellet was 77.3 • C. The free triangular mesh with linear Lagrangian shape functions was considered in the simulations.The entire domain was meshed with three different sizes: 0.03 mm for the area close to the melting interface (between the molten bath and H-DRI pellet/steel ball) and the pellet/steel ball domain, 0.05 mm for the thermocouple and thermal resistance between the thermocouple and pellet/steel ball, and 3 mm for the rest of the domain.A mesh quality study was performed for the entire mesh, and it showed an average element quality of 0.937 with 1,143,150 and 527,386 elements implemented for the steel ball and H-DRI in a metallic bath model.The mesh element quality is a dimensionless number between 0 and 1, where 1 represents a perfectly regular element [22].This simulation considers an adaptive time step with a maximum of 0.05 s, the parallel direct sparse solver for clusters (PARADISO), and a linear solver method.

Thermal Conductivity, k
For the thermal conductivity, an empirical correlation is used to calculate the effective thermal conductivity using the equation proposed by Koh and Fortini [29], where n is a constant equal to 11 for sintered metal powders determined in Equation (28).
k m is the thermal conductivity of the metal in the matrix, and e is the porosity of the pellet.

Boundary Conditions
The geometry of the domain for the pellet and bath based on the experimental setup is shown in Figure 2. A thermal resistance with a thermal conductivity of 0.04 [W m −1 K −1 ] is considered between the thermocouple and the H-DRI/steel ball [30].This thermal resistance is due to a thin layer of the high-temperature aluminum silicate adhesive that sticks the thermocouple in the H-DRI pellet.According to the designed experiment, the temperature in the chamber's walls was fixed to 1602 °C.Convective heat flux between the steel ball/pellet's surface and the metallic bath was defined based on the heat transfer coefficient calculated using the dimensionless numbers in Equations ( 20)-( 22), as shown in Figure 2. The bath temperature was fixed to 1602 °C, and the initial temperature for the steel ball/pellet was 77.3 °C.The free triangular mesh with linear Lagrangian shape functions was considered in the simulations.The entire domain was meshed with three different sizes: 0.03 mm for the area close to the melting interface (between the molten bath and H-DRI pellet/steel ball) and the pellet/steel ball domain, 0.05 mm for the thermocouple and thermal resistance between the thermocouple and pellet/steel ball, and 3 mm for the rest of the domain.A mesh quality study was performed for the entire mesh, and it showed an average element quality of 0.937 with 1,143,150 and 527,386 elements implemented for the steel ball and H-DRI in a metallic bath model.The mesh element quality is a dimensionless number between 0 and 1, where 1 represents a perfectly regular element [22].This simulation considers an adaptive time step with a maximum of 0.05 s, the parallel direct sparse solver for clusters (PARADISO), and a linear solver method.

Experimental Setup
The physical model includes an induction furnace provided by Inductotherm Corp., Rancocas, NJ, USA, with an alumina crucible provided by Eastern Crucibles, Groton, MA, USA, and a capacity of 90 kg.The crucible's diameter is 240 mm and its height is 360 mm.Arizona State University provided the H-DRI pellets with a 95% reduction, as studied by A. Meshram et al. [31] in Tempe, AZ, USA, and Nucor, Convent, LA, USA.The mass percentage composition of the iron ore is as follows: iron in the hematite 67.2%, SiO 2 1.98%, Al 2 O 3 0.47%, CaO 0.99%, MgO 0.062%, S 0.004%, P 0.02%, and Mn 0.077%.
For the computational simulation, thermal physical properties were considered close to pure iron without considering the presence of gangue in the sample.Steel Supply, Houston, TX, USA, provides spherical steel balls with a diameter of 20 mm.Samples of H-DRI and steel balls were immersed 18 cm in molten steel and molten slag using a pneumatic frame.The experimental matrix for the immersion time of the samples is shown in Table 2.It should be noted that some of these samples fell into the metallic bath, and the information could not be recorded.When the samples were immersed, the furnace was turned off to prevent inductive stirring in the metallic bath.Based on the chemical compositions, thermophysical properties were calculated using JmatPro-v14 [32], and are shown in Tables 3-7 and Figures 3-5.
1046 1213 ρ (kg m −3 ) 2900 2900 T m 1803 [32] 1805 [32] Latent heat of fusion [kJ kg −1 ] L f 271 [32] 257 [32] * Based on experimental measurement.The samples were weighed, and diameter measurements were recorded before the experiments.Using titanium-coated 1/8-inch drill bits, the samples were bored to the center using a milling machine.K-type thermocouples were employed for this study using alumina tubes.The thermocouple was pressed into the bored pellet to ensure perfect contact.Alumina-silicate refractory cement was employed to fix the thermocouple in the sample.A zircon wash was then added to the alumina tube to prevent fracture from thermal shock upon immersion.This setup is shown in Figure 6.L f 270 [32] 858 [25] * Based on experimental measurement.T m 1803 [32] 1805 [32] Latent heat of fusion [kJ kg −1 ] L f 271 [32] 257 [32] * Based on experimental measurement.
The samples were weighed, and diameter measurements were recorded before the experiments.Using titanium-coated 1/8-inch drill bits, the samples were bored to the center using a milling machine.K-type thermocouples were employed for this study using alumina tubes.The thermocouple was pressed into the bored pellet to ensure perfect contact.Alumina-silicate refractory cement was employed to fix the thermocouple in the sample.A zircon wash was then added to the alumina tube to prevent fracture from thermal shock upon immersion.This setup is shown in Figure 6.Nine identical fixtures were used for the experimentation, each of which could hold three samples at the same deep height immersion of 18 cm in the metallic bath.The alumina tubes were cemented to the steel fixtures.The metallic bath temperature was held at 1600 • C and was constantly measured using a temperature probe provided by Heraeus electronite company, Hartland, WI, USA.The temperature in the center of the samples was recorded using a GL220 midi data logger provided by Graphtec Corporation, Irvine, CA, USA, connected to a thermocouple K-type provided by OMEGA TM , Norwalk, CT, USA.A similar procedure was reported by Joe Govro et al. [35].The setup is shown in Figures 7 and 8.
1600 °C and was constantly measured using a temperature probe provided by Heraeus electronite company, Hartland, WI, USA.The temperature in the center of the samples was recorded using a GL220 midi data logger provided by Graphtec Corporation, Irvine, CA, USA, connected to a thermocouple K-type provided by OMEGA TM , Norwalk, CT, USA.A similar procedure was reported by Joe Govro et al. [35].The setup is shown in Figures 7 and 8.This study used steel balls in a metallic bath to validate the model, as the steel balls' physical properties are well known.The validated model was subsequently employed to predict the melting behavior of H-DRI pellets.

Temperature Profiles
Figure 9 shows the experimental result and the corresponding computational calculation for the temperature profile in the center of the steel ball immersed in the molten steel and slag bath.These results show that the time required for the complete melting of the steel ball in molten slag is longer than its counterpart in the molten steel bath.This can be explained based on the difference in the calculated heat transfer coefficient summarized in Table 7 and the overall lower thermal diffusivity of the slag compared to steel.
Figure 9a shows that the melting behavior in experiments 3 and 4 deviates from both the other experiments and the model at the initial stage.This can be explained because these were a new set of experiments, and it is possible that the thermocouple was not precisely in the center.This could mean that the thermocouple was closer to the steel ball's walls, which is the reason for the high heating rate.Figure 9b shows that the calculated temperature using the developed model matches the experimental results for tempera- This study used steel balls in a metallic bath to validate the model, as the steel balls' physical properties are well known.The validated model was subsequently employed to predict the melting behavior of H-DRI pellets.

Temperature Profiles
Figure 9 shows the experimental result and the corresponding computational calculation for the temperature profile in the center of the steel ball immersed in the molten steel and slag bath.These results show that the time required for the complete melting of the steel ball in molten slag is longer than its counterpart in the molten steel bath.This can be explained based on the difference in the calculated heat transfer coefficient summarized in Table 7 and the overall lower thermal diffusivity of the slag compared to steel.
bath to explain the variation with the previous results shown in Figure 12.Density, specific heat capacity, and thermal conductivity for the small air gap between the pellet and thermocouple were extracted from the COMSOL Multiphysics library and ASHRAE Handbook of Fundamentals [36].    Figure 9a shows that the melting behavior in experiments 3 and 4 deviates from both the other experiments and the model at the initial stage.This can be explained because these were a new set of experiments, and it is possible that the thermocouple was not precisely in the center.This could mean that the thermocouple was closer to the steel ball's walls, which is the for the high heating rate.Figure 9b shows that the calculated temperature using the developed model matches the experimental results for temperatures below 1100 • C.There is a variation between the computational simulation model and the experimental result above 1100 • C. It is expected that if the experiment is run for more than 100 s, the experimental temperature should get closer to the computational simulation temperature result.This is like Figure 10b, and because of the complexity of the experiment in molten slag, some experimental results were taken from the literature to validate the computational simulation model.
bath to explain the variation with the previous results shown in Figure 12.Density, specific heat capacity, and thermal conductivity for the small air gap between the pellet and thermocouple were extracted from the COMSOL Multiphysics library and ASHRAE Handbook of Fundamentals [36].Similar results were included regarding the melting behavior of H-DRI in molten steel and slag bathes, as shown in Figure 10. Figure 10a shows that all the experiments match the computational simulation model from 0 to 10 s, with only experiment 1 presenting a variation.This can be explained because the H-DRI pellets are not perfectly spherical, and it is possible that the thermocouple's location is close to the pellet's border, allowing the temperature profile to increase faster than in the other experiments.
More experiments on H-DRI were carried out in a steel bath; however, the results varied from the previous one.The cross-section of the H-DRI pellet after 1 s immersion in the molten steel bath showed a thin layer of air between the thermocouple and the H-DRI pellet (see Figure 11).This gap is considered in the simulation of H-DRI in a molten steel bath to explain the variation with the previous results shown in Figure 12.Density, specific heat capacity, and thermal conductivity for the small air gap between the pellet and thermocouple were extracted from the COMSOL Multiphysics library and ASHRAE Handbook of Fundamentals [36].The experimental data from [25] were utilized to corroborate the accuracy of veloped model.Table 8 summarized the thermophysical properties of an iron ball a different H-DRIs.
IR-1B-1 [25].LR-2J-1 The experimental data from [25] were utilized to corroborate the accuracy of the developed model.Table 8 summarized the thermophysical properties of an iron ball and two different H-DRIs.Figures 13 and 14 compare the temperature profile in the center of the iron ball and two types of H-DRI from [25] calculated from the developed computational model and the measured experimental result, showing a good agreement.Figure 13 shows the temperature profile of a pure iron ball in a molten slag; the experimental results match the computational simulation results.After 150 s, the temperature profile approximated 1300 • C, and the slope of the curve became flat.Something similar occurs in Figure 14 above 60 s, which is expected in Figures 9b and 10b.Therefore, the computational simulation model developed works for the temperature profiles for steel balls and H-DRI in different metallic baths (molten steel and slag).

Shell Thickness
The steel balls/H-DRI pellets were removed from the metallic bath and cooled at room temperature.They were then cut in the middle and mixed with epoxy resin for 24 h; after polishing, the sample radius plus the shell thickness was measured using the software ImageJ-v14, as shown in Figure 15. Figure 16 shows the experimental measurements

Shell Thickness
The steel balls/H-DRI pellets were removed from the metallic bath and cooled at room temperature.They were then cut in the middle and mixed with epoxy resin for 24 h; after polishing, the sample radius plus the shell thickness was measured using the software ImageJ-v14, as shown in Figure 15. Figure 16 shows the experimental measurements

Shell Thickness
The steel balls/H-DRI pellets were removed from the metallic bath and cooled at room temperature.They were then cut in the middle and mixed with epoxy resin for 24 h; after polishing, the sample radius plus the shell thickness was measured using the software ImageJ-v14, as shown in Figure 15. Figure 16 shows the experimental measurements and computational modeling results of the shell thickness for a steel ball and an H-DRI in molten steel.The experimental results match the computational simulation results.The steel ball takes more time to fully melt than the H-DRI pellet as the steel ball diameter was 20 mm and larger than the H-DRI pellet diameter (10-12 mm).According to Figure 16, the shell thickness formation is higher for the steel ball than for the H-DRI pellet and it is possible to determine that the melting temperature for the steel ball and H-DRI pellet is higher than that of the molten steel.This is because the steel ball and H-DRI pellet radius remain constant after the shell fully melts and shrinks after two seconds.The melting temperatures of the steel ball and H-DRI pellet are 1530 • C and 1532 • C, respectively.Meanwhile, the melting temperature for the steel bath is 1521 • C. That explains why the steel ball and H-DRI pellet require some time before they start to melt.The steel ball contains 0.1 wt.% carbon, and the H-DRI is essentially carbon-free with a metallization above 95%, according to analysis performed at Arizona State University [31].Therefore, the melting temperature will be close that of pure iron and higher than that of the steel ball.according to analysis performed at Arizona State University [31].Therefore, the melting temperature will be close to that of pure iron and higher than that of the steel ball.Figure 17 shows the melting behavior of a steel ball at different times.This figure presents a visualization of the process depicted in Figure 16a.Meanwhile, Figure 18 represents the melting behavior of an H-DRI pellet at different times.As discussed before, the H-DRI pellet melts faster than the steel ball in a uniform path due to geometrical conditions and thermophysical properties.according to analysis performed at Arizona State University [31].Therefore, the melting temperature will be close to that of pure iron and higher than that of the steel ball.Figure 17 shows the melting behavior of a steel ball at different times.This figure presents a visualization of the process depicted in Figure 16a.Meanwhile, Figure 18 represents the melting behavior of an H-DRI pellet at different times.As discussed before, the H-DRI pellet melts faster than the steel ball in a uniform path due to geometrical conditions and thermophysical properties.

Conclusions
A computational heat transfer model was developed using COMSOL Multiphysics 6.1 to predict the melting behavior of steel balls and H-DRI pellets immersed in a steel bath and molten slag.The model is validated based on a set of experimental tests and available data from the literature.This study showed the following:

Conclusions
A computational heat transfer model was developed using COMSOL Multiphysics 6.1 to predict the melting behavior of steel balls and H-DRI pellets immersed in a steel bath and molten slag.The model is validated based on a set of experimental tests and available data from the literature.This study showed the following: Figure 17 shows the melting behavior of a steel ball at different times.This figure presents a visualization of the process depicted in Figure 16a.Meanwhile, Figure 18 represents the melting behavior of an H-DRI pellet at different times.As discussed before, the H-DRI pellet melts faster than the steel ball in a uniform path due to geometrical conditions and thermophysical properties.

Conclusions
A computational heat transfer model was developed using COMSOL Multiphysics 6.1 to predict the melting behavior of steel balls and H-DRI pellets immersed in a steel bath and molten slag.The model is validated based on a set of experimental tests and available data from the literature.This study showed the following: • The developed computational model can reproduce the melting behavior of steel balls and H-DRI pellets in a steel bath and molten slag.• The heat transfer coefficient calculated using the Nusselt number correlation for natural convection can predict the melting behavior of steel balls and H-DRI pellets.

•
Steel balls and H-DRI pellets melt faster in a steel bath than in molten slag, as the thermal conductivity and specific heat capacity of the steel bath are higher than molten slag's.
• The porosity has a strong influence on the melting behavior of H-DRI pellets through its effect on the thermophysical properties and pellet mass.

Figure 1 .
Figure 1.A 2D schematic of the temperature profile for a steel ball/pellet in a molten steel/slag.The dot lines denote R-sample's radius and Rshell-sample's radius + shell thickness.

Figure 1 .
Figure 1.A 2D schematic of the temperature profile for a steel ball/pellet in a molten steel/slag.The dot lines denote R-sample's radius and R shell -sample's radius + shell thickness.

Figure 2 .
Figure 2. Mesh distribution for the simulation: (a) thermal resistance between the thermocouple and the pellet (the arrows are pointing the thermal resistance in blue and the thermocouple in the center), (b) boundary between the pellet and the metallic bath, and (c) initial temperature conditions and geometry.

Figure 2 .
Figure 2. Mesh distribution for the simulation: (a) thermal resistance between the thermocouple and the pellet (the arrows are pointing the thermal resistance in blue and the thermocouple in the center), (b) boundary between the pellet and the metallic bath, and (c) initial temperature conditions and geometry.

Figure 3 .
Figure 3. Calculated thermal conductivity of the steel ball and the H-DRI pellet using JmatPro-v14.

Figure 4 .
Figure 4. Calculated specific heat capacity of the steel ball and the H-DRI pellet using JmatPro-v14.

Figure 3 .
Figure 3. Calculated thermal conductivity of the steel ball and the H-DRI pellet using JmatPro-v14.

Figure 3 .
Figure 3. Calculated thermal conductivity of the steel ball and the H-DRI pellet using JmatPro-v14.

Figure 4 .
Figure 4. Calculated specific heat capacity of the steel ball and the H-DRI pellet using JmatPro-v14.

Figure 4 .
Figure 4. Calculated specific heat capacity of the steel ball and the H-DRI pellet using JmatPro-v14.

Figure 4 .
Figure 4. Calculated specific heat capacity of the steel ball and the H-DRI pellet using JmatPro-v14.

Figure 5 .
Figure 5. Calculated density of the steel ball and the H-DRI pellet using JmatPro-v14.Figure 5. Calculated density of the steel ball and the H-DRI pellet using JmatPro-v14.

Figure 5 .
Figure 5. Calculated density of the steel ball and the H-DRI pellet using JmatPro-v14.Figure 5. Calculated density of the steel ball and the H-DRI pellet using JmatPro-v14.

Figure 6 .
Figure 6.Thermocouple fixed to the H-DRI pellet.Figure 6. Thermocouple fixed to the H-DRI pellet.

Figure 6 .
Figure 6.Thermocouple fixed to the H-DRI pellet.Figure 6. Thermocouple fixed to the H-DRI pellet.

Figure 9 .
Figure 9.The temperature profile in the center of a steel ball (a) in a steel bath with a 5100 W m −2 K −1 heat transfer coefficient, and (b) in a molten slag with a 185 W m −2 K −1 heat transfer coefficient.

Figure 10 .
Figure 10.Temperature profile in the center of an H-DRI (a) in a steel bath with an 8500 W m −2 K −1 heat transfer coefficient, and (b) in a molten slag with a 283 W m −2 K −1 heat transfer coefficient.

Figure 11 .
Figure 11.A cross-section of the H-DRI mounted on a resin epoxy shows a solidified thin shell around the pellet after 1 s of immersing it in the steel bath.

Figure 9 .
Figure 9.The temperature profile in the center of a steel ball (a) in a steel bath with a 5100 W m −2 K −1 heat transfer coefficient, and (b) in a molten slag with a 185 W m −2 K −1 heat transfer coefficient.

Figure 9 .
Figure 9.The temperature profile in the center of a steel ball (a) in a steel bath with a 5100 W m −2 K −1 heat transfer coefficient, and (b) in a molten slag with a 185 W m −2 K −1 heat transfer coefficient.

Figure 10 .
Figure 10.Temperature profile in the center of an H-DRI (a) in a steel bath with an 8500 W m −2 K −1 heat transfer coefficient, and (b) in a molten slag with a 283 W m −2 K −1 heat transfer coefficient.

Figure 10 .
Figure 10.Temperature profile in the center of an H-DRI (a) in a steel bath with an 8500 W m −2 K −1 heat transfer coefficient, and (b) in a molten slag with a 283 W m −2 K −1 heat transfer coefficient.

Figure 10 .
Figure 10.Temperature profile in the center of an H-DRI (a) in a steel bath with an 8500 W heat transfer coefficient, and (b) in a molten slag with a 283 W m −2 K −1 heat transfer coeffic

Figure 11 .
Figure 11.A cross-section of the H-DRI mounted on a resin epoxy shows a solidified around the pellet after 1 s of immersing it in the steel bath.

Figure 11 .
Figure 11.A cross-section of the H-DRI mounted on a resin epoxy shows a solidified thin shell around the pellet after 1 s of immersing it in the steel bath.Metals 2024, 14, x FOR PEER REVIEW

Figure 12 .
Figure 12.The experimental measurement and computational calculation of the temperatur in the center of an H-DRI.The model incorporated the small gap between the thermocouple H-DRI pellet.

Figure 12 .
Figure 12.The experimental measurement and computational calculation of the temperature profile in the center of an H-DRI.The model incorporated the small gap between the thermocouple and the H-DRI pellet.

20 Figure 13 .
Figure 13.Temperature profile in the center of an iron ball with a heat transfer coefficient of 209 W m −2 K −1 .Adapted from Ref. [25].

Figure 13 . 20 Figure 13 .
Figure 13.Temperature profile in the center of an iron ball with a heat transfer coefficient of 209 W m −2 K −1 .Adapted from Ref. [25].

Figure 15 .
Figure 15.Steel ball radius plus shell thickness after immersed time of (a) 7 s and (b) 17 s.

Figure 16 .
Figure 16.Shell thickness measurement in molten steel: (a) steel ball with a 5100 W m −2 K −1 heat transfer coefficient and (b) H-DRI pellet with an 8500 W m −2 K −1 heat transfer coefficient.The melting behavior at different times (I) to (VI) is shown in Figures 17 and 18.

Figure 15 .
Figure 15.Steel ball radius plus shell thickness after immersed time of (a) 7 s and (b) 17 s.

Figure 15 .
Figure 15.Steel ball radius plus shell thickness after immersed time of (a) 7 s and (b) 17 s.

Figure 16 .
Figure 16.Shell thickness measurement in molten steel: (a) steel ball with a 5100 W m −2 K −1 heat transfer coefficient and (b) H-DRI pellet with an 8500 W m −2 K −1 heat transfer coefficient.The melting behavior at different times (I) to (VI) is shown in Figures 17 and 18.

Figure 16 .
Figure 16.Shell thickness measurement in molten steel: (a) steel ball with a 5100 W m −2 K −1 heat transfer coefficient and (b) H-DRI pellet with an 8500 W m −2 K −1 heat transfer coefficient.The melting behavior at different times (I) to (VI) is shown in Figures 17 and 18.

Figure 17 .
Figure 17.Melting behavior of a steel ball in molten steel at different times.(I) 0 s shows the steel ball's initial diameter, (II) 5 s shows the formation of the shell thickness, (III) 10 s shows the shell's melting process, and (IV) 15 s, (V) 20 s, and (VI) 25 s show the steel ball's melting behavior.

Figure 18 .
Figure 18.Melting behavior of an H-DRI in molten steel at different times.(I) 0 s shows the pellet's initial radius, (II) 2 s shows the shell's melting, and (III) 4 s, (IV) 6 s, (V) 8 s, and (VI) 10 s show the pellet's melting behavior.

Figure 17 . 20 Figure 17 .
Figure 17.Melting behavior of a steel ball in molten steel at different times.(I) 0 s shows the steel ball's initial diameter, (II) 5 s shows the formation of the shell thickness, (III) 10 s shows the shell's melting process, and (IV) 15 s, (V) 20 s, and (VI) 25 s show the steel ball's melting behavior.

Figure 18 .
Figure 18.Melting behavior of an H-DRI in molten steel at different times.(I) 0 s shows the pellet's initial radius, (II) 2 s shows the shell's melting, and (III) 4 s, (IV) 6 s, (V) 8 s, and (VI) 10 s show the pellet's melting behavior.

Figure 18 .
Figure 18.Melting behavior of an H-DRI in molten steel at different times.(I) 0 s shows the pellet's initial radius, (II) 2 s shows the shell's melting, and (III) 4 s, (IV) 6 s, (V) 8 s, and (VI) 10 s show the pellet's melting behavior.

Table 2 .
Experimental matrix for immersion time of H-DRI and steel balls in a steel bath.

Table 3 .
Chemical composition of steel balls, steel bath, and molten slag.

Table 4 .
Thermophysical properties of the slag.

Table 5 .
Thermophysical properties of the steel bath and the molten slag.
* Based on experimental measurement.

Table 6 .
Thermophysical properties of the steel ball and the H-DRI pellet.

Table 6 .
Thermophysical properties of the steel ball and the H-DRI pellet.

Table 8 .
Thermophysical properties of iron and H-DRI.

Table 8 .
Thermophysical properties of iron and H-DRI.