As a key process subsequent to continuous casting, the cooling of cast slabs is of central importance for achieving desirably low internal stresses, thereby minimizing the risk of crack formation and structural breakage. Although the primary and secondary cooling process in continuous casting are well-established in research, studies on the thermo-metallurgical-mechanical phenomena during slab yard cooling remain critically limited. In this work, a coupled thermo-metallurgical-mechanical model is presented that elucidates the process of slab cooling, addressing the combined effects of specific alloys and cooling conditions. Three universal stages of stress accumulation are identified: the pre-transformation stage (1), the transformation stage (2), and the post-transformation stage (3). Specifically, the early ferrite transformation—which is key to many concepts of cracking susceptibility—is carefully analyzed. While stress accumulation in the transformation stage is substantially driven by the intrinsic material physics, it is shown that the potential for reducing room-temperature residual stresses resides in the application of innovative process designs in the post-transformation stage. Accordingly, a stress reduction of 50% can be achieved in critical locations. The developed model represents a versatile tool for process design and optimization, thereby contributing to the production of advanced, next-generation high-strength steels.

With the growing demand for single-crystal and semiconductor materials, the design and control of defect-free single crystals have become a central focus in both research and industrial development. In this context, an established nonlocal dislocation-density-based crystal plasticity (CP) framework is extended and parameterized to simulate the evolution of dislocations in single-crystal sapphire during crystal growth and cooling. The model incorporates both mobile and dipole dislocation densities and accounts for their spatial transport, enabling an accurate description of dislocation generation, motion, and redistribution under large thermal gradients. The CP model is implemented within a thermo-mechanically coupled finite-element framework and validated against experimental measurements obtained from etched sapphire wafers. The simulations reproduce the measured dislocation-density trends and predict the formation of the characteristic dislocation pattern associated with the anisotropy of slip systems in sapphire. Using the validated model, optimized process parameters and furnace configurations are derived. The results show that a properly designed heating configuration combined with the derived growth and cooling rates can produce sapphire crystals with significantly reduced dislocation densities, minimal wafer deflection, and no cracking. The resulting nonlocal CP model thus provides a physically consistent and computationally efficient design tool for optimizing manufacturing processes in sapphire and other single-crystal semiconductors.

Hot-dip galvanizing lines require precise control of surface decarburization to achieve target mechanical properties in automotive steel sheets. This study presents a coupled surface-reaction and one-dimensional carbon diffusion model for predicting decarburization during non-isothermal annealing. The model incorporates thermodynamic equilibrium phase fractions from the Fe–C system to describe ferrite–austenite distribution as a function of local temperature and composition, with an effective diffusion coefficient that transitions smoothly between phase-specific diffusivities using a phase-transition parameter. Model parameters were optimized using differential evolution against Glow Discharge Optical Emission Spectroscopy measurements from nine annealing experiments at 750 ^∘ C to 850 ^∘ C with varying p_H_2O/p_H_2 ratios (0.0077 to 0.1268). Leave-one-out cross-validation yielded a symmetric mean absolute percentage error of 14.6 pct [95 pct CI: 10.0 to 19.3 pct], while in-sample fitting achieved 10.6 pct. Statistical analysis revealed that decarburization depth was primarily influenced by the p_H_2O/p_H_2 ratio, with soaking temperature showing only a slight effect within the investigated range. The model successfully captures temporal evolution of carbon concentration profiles during heating and cooling cycles, providing insights into diffusion-limited regimes at elevated temperatures. Limitations include exclusion of oxidation effects and indirect treatment of phase transformation kinetics through empirical phase-transition parameters. This framework enables cost-effective prediction of decarburization under various process conditions while identifying key atmospheric parameters for process optimization in hot-dip galvanizing lines.

We study the growth of Fe2Al5 particles in liquid Zn with a multi-scale approach from ab initio molecular statics and dynamics to kinetic Monte Carlo (kMC) simulations. This includes computation of the transition rates, i.e. adsorption rates from diffusion of elements in liquid Zn and desorption rates from surface desorption energies and interaction energies of atoms at the surface. Adsorption and desorption rates together with the correct crystal structure are the main input for the kMC simulations. With systematic kMC simulations, we then map out the growth rates of Fe2Al5 at different temperatures and varying chemical compositions. Altogether, this constitutes an approach that is also applicable to other studies focusing e.g. on deposition processes or dissolution of particles.

In this work, selected numerical simulation aspects are analyzed in terms of their effect on predictions of the m-c interface. The fixed-grid enthalpy porosity phase change model, which is highly attractive in the field of modeling sapphire crystallization processes, is examined for its sensitivity to the mushy zone parameter as well as the grid resolution. A further focus is set to the simulation of thermal transport including internal radiation in the crystal and the melt via the finite volume method. Depending on the purpose of the investigation, different requirements on the angular resolutions are relevant. While most of the m-c interface as well as the temperature distribution remain practically unchanged at reasonable resolutions, a high sensitivity of the m-c interface in the near-wall region is demonstrated. This sensitivity is also observed in terms of radiative transport and, hence, the total heat transfer.

Multi-droplet impingement is a fundamental aspect inherent to all kinds of technical spray processes which typically aim at enhancing the convective exchange of reagents or heat at the impinged surface. In this paper, the impingement of multiple droplets onto a structured surface is investigated by a comprehensive CFD model, which resolves the dynamics of the individual droplets and the film on a micro-scale level based on the Volume of Fluid (VOF) method. The considered surface topology includes cavities and is typical for protective masks used in the spray etching of Printed Circuit Boards (PCBs). The agitation of the liquid film in terms of the convective mass transfer rates across virtual horizontal evaluation planes is studied and the influence of film height and droplet impaction velocity is elaborated. Passive tracer tracking is employed to investigate the release and re-entrainment of fluid at the surface cavities. Two modes of mass exchange between the cavities and the main flow upon droplet impingement are identified, which are central inflow accompanied by lateral outflow (1) and lateral inflow with outflow at the opposing side (2). A statistical analysis of the allocation of tracer particles shows that high impaction velocities and low film heights correlate with an enhanced decay of tracer particles within the cavities. The susceptibility to re-entrainment is also reduced by high impaction velocities, whereas increased film heights are found to promote re-entrainment.

The minimization of unwanted dross build-up formation on the sink rolls in continuous hot-dip galvanizing lines is a key goal of the industry. In this study, the CFD multi-physics modeling of the surface reaction kinetics for dross build-up growth and the coupling to the mass transfer is the basis for the evaluation of relevant process parameters. The results of a virtual Design of Experiments were processed by neural network approaches, as well as linear regression modeling to build a surrogate process model. It was found that the bath Al concentration has the highest effect (> 80 pct) on the dross build-up rate on the sink rolls. Operating the zinc bath at higher Al concentrations decreases the dross build-up reaction rate. Furthermore, it was found by the CFD multi-physics model that the local dross build-up rate increases toward the edges of the roll grooves which might lead to the occurrence of strip surface defects.

In this paper we show that the presence of liquid flow around a crystal growing from melt can induce dissymmetry in growth similar to that described by anisotropic interfacial kinetic coefficients. A front tracking interface model based on a cellular automaton approach was applied to the growth of a Fe2Al5 crystal (also known as top dross particle) in a saturated Zn melt at constant temperature. The growth rate was found to be influenced by the intensity of the melt flow and by the direction of the flow with respect to the crystal orientation. The magnitude and the direction of flow modify the diffusion boundary layer, changing the conditions (temperature and concentration) at the facet interface, therefore the mass transfer. We have shown that despite the isotropy of interfacial kinetics, hydrodynamics was able to introduce an anisotropy in the crystal growth similar to the natural anisotropy in interfacial kinetics of the facets. The facets grow rate was found to be strongly dependant on the Reynolds number as well as on the orientation of the crystalline orientation with respect to the flow direction.

Dross particle formation in the hot-dip galvanizing zinc bath and dross build-up on the sink rolls can cause surface defects on the steel-strip. State-of-the-art approaches in zinc bath dross reaction modeling in CFD simulations rely on thermodynamics considerations, where the formation or dissolution of dross occurs instantaneously whenever the system is out of equilibrium. These approaches totally ignore the finite time required for the reaction which leads to an imperfect representation of the actual spatial distribution of the concentration fields. To overcome this drawback, a reversible kinetics model for the Fe_2Al_5Zn -phase dross particles is presented that is coupled to species transport equations. Model parameters were determined by fitting with innovative lab-scale GalvaLIBS experiments.

The so-called proper orthogonal decomposition (POD) method has been used in numerous research items, mainly in the field of turbulence, as a reduced-order model to describe transient complex turbulence by a set of deterministic functions. One of the modifications of POD known as the extended POD method (EPOD) has been successfully used mainly to analyse correlations between the flow field and synchronized vector or scalar fields such as correlations between velocity and temperature fields. However, its bottleneck in the correlation identification is demonstrated in this paper, and then the issue is addressed by a suitable modification. For this, a set of unsteady fully turbulent simulation results in the presence of different arrays of vortex generators, enhancing heat transport, is analysed by POD and EPOD. As a major result, a spatial filtering procedure is proposed to be applied prior to EPOD analysis. It is demonstrated that, in contrast to a conventional application of EPOD, the proposed procedure enables correct separation of thermally active and inactive flow modes.

As a consequence of rapid development of additive manufacturing (3D printing) methods, the academic/industrial demand has been continuously increasing. One field of application is the manufacturing of heat exchanging devices using this promising method. In this regard, understanding the underlying mechanisms from a thermo-hydraulic viewpoint becomes important. Therefore, in this study, scale-resolving large eddy simulation (LES) is applied to reveal the flow details in combination with a model of roughness topology occurring in additive manufacturing. To process the transient LES results, proper orthogonal decomposition (POD) is used to extract the coherent flow structures, and the extended POD is used to rank the flow modes based on thermal importance. The main aim of the present work is to go beyond the conventionally applied methodologies used for the evaluation of surface roughness, i.e., averaged numerical study or experimental overall performance evaluation of the flow/thermal response of additively manufactured surfaces in heat exchangers. This is necessary to reveal the underlying flow mechanisms hidden in the conventional studies. In this study, the behavior of the flow over the micro-scale surface roughness model and its effects on heat transfer are studied by assuming cone-shaped roughness elements with regular placement as the dominant surface roughness structures. The major discussions reveal the footprint of flow mechanisms on the heat transfer coefficient spatial modes on the rough surface. Moreover, comparative study on the flow/thermal behavior at different levels of roughness heights shows the key role of the height-to-base-diameter ratio of the roughness elements in thermal performance.

The impact of the electric field between rough copper lines on the failure time for electrochemical migration (ECM) in printed circuit boards is analyzed by means of modeling. The understanding and assessment of the failure time and thus the reliability becomes more and more important as the dimensions in the printed circuit boards decrease and the applied voltages increase. Once the epoxy/glass fiber interface is degraded in the printed circuit board, the additional time to form either Conducting Anodic Filaments (CAF) or dendrites depends also on the electric field. This electric field, as the main driving force, was computed on virtually constructed rough surfaces to take the real copper/prepreg interface into account before the onset of corrosion. It was shown, that roughness peaks increase the local maximum electric field, which follows a E=Ud0.63-relation that is underestimated in the state-of-the-art approach. Furthermore, it was found that the material dependent parameters can be related to the tortuosity of the possible short circuit path and the ion mobility in the material. The enhanced model for the determination of the failure time will facilitate the fitting and interpretation of future testing procedures.

A heat sink is a specific type of heat exchanger integrated with heat generating devices - mostly electronics - for the sake of thermal management. In the design procedure of heat sinks, several considerations such as manufacturing cost, reliability, thermal and hydraulic performance have to be included. In the past few decades, the prevailing trend of electronics design miniaturization has led to high-power-density systems necessitating high performance cooling concepts. This paper intends to provide a comprehensive review on various employed heat transfer enhancement techniques in cooling procedures of electronics thermal management devices, with a focus on core ideas. The main motivation is to give a rapid overview on the key concepts in different high-performance cooling designs along with a quantitative comparison between the different concepts all in one reference which is missing in literature. For this, the key idea of each design is firstly categorized, and then a detailed description is provided for each case. The discussed categories consist of concepts based on channel cooling in various scales, phase transition, jet impingement, spray cooling and hybrid design. At the end, quantitative comparison is illustrated for thermal and hydraulic performance of a selection of the reviewed references covering all these different categories. Based on this comparison, an overview on thermo-hydraulic performance of the presented categories is provided, and recommendations for future studies are given based on this and the detailed review of references.

The growth of faceted crystals occurs often in nature and industry, involving often the presence of flow. The growth of faceted crystals is the result of interface kinetics and diffusion phenomenon. The present paper presents a front tracking interface model based on a cellular automaton approach for the simulation of faceted crystal growth. The current model takes into account the interface kinetics and solute transport by diffusion and convection. The propagation of kinks is modelled by differentiating two growth velocities, one normal and one lateral at each face. The positions of the crystal corners are shifted according to growth of adjacent faces. The hydrodynamics is computed with a two-phase model using a penalty method to model the presence of growing obstacles (the crystals). This model was applied in 2D to the growth of hexagonal Fe2Al5 crystals, so called top dross particles, in a saturated liquid at constant temperature. Qualitative comparison was made between simulation and experimental observation of crystal shape and size. The growth rate was found to be strongly influenced by the flow hydrodynamic induced kinetics.

A heat sink is a specific type of heat exchanger integrated with heat generating devices – mostly electronics – for the sake of thermal management. In the design procedure of heat sinks, several considerations such as manufacturing cost, reliability, thermal and hydraulic performance have to be included. In the past few decades, the prevailing trend of electronics design miniaturization has led to high-power-density systems necessitating high performance cooling concepts. This paper intends to provide a comprehensive review on various employed heat transfer enhancement techniques in cooling procedures of electronics thermal management devices, with a focus on core ideas. The main motivation is to give a rapid overview on the key concepts in different high-performance cooling designs along with a quantitative comparison between the different concepts all in one reference which is missing in literature. For this, the key idea of each design is firstly categorized, and then a detailed description is provided for each case. The discussed categories consist of concepts based on channel cooling in various scales, phase transition, jet impingement, spray cooling and hybrid design. At the end, quantitative comparison is illustrated for thermal and hydraulic performance of a selection of the reviewed references covering all these different categories. Based on this comparison, an overview on thermo-hydraulic performance of the presented categories is provided, and recommendations for future studies are given based on this and the detailed review of references.

The focus of this ab initio study is the interaction between Fe2Al5 particles and WC surfaces in the hot-dip galvanizing processes. In a first step, we compute surface energies of Fe2Al5 to predict the morphology of the particles. In the next step, the most relevant interfaces between Fe2Al5 and WC are characterized in terms of atomic structure and energetics, where different terminations of the two phases at the interface are considered. Finally, we investigate the effect of Zn on the stability and adhesion of the interface, where we find that low Zn coverages can even increase adhesion, but for high Zn coverages the adhesion drops significantly.

This paper presents a new computational framework to investigate the driving force for the formation of intermetallic dross particles in the zinc bath and dross build-up on the bath hardware. This is a major problem in continuous hot-dip galvanizing lines. The Computational Fluid Dynamics (CFD) model calculates the turbulent thermo-chemical flow conditions within the liquid melt. A detailed modeling of the steel strip–liquid interface enhances this approach, by means of a conjugated heat transfer calculation and a spatially resolved, temperature- and concentration-dependent iron dissolution and aluminum uptake. The heart of the computational framework is a thermodynamic model, which assesses the driving force for the formation or dissolution of dross particles in the bath and dross build-up on stationary and rotating equipment. The simulation results are validated with temperature and species depth profile measurements. The applicability of the CFD model is shown by investigating the locally resolved aluminum uptake and iron dissolution at the steel-strip surface, and the multi-physics conditions in the region near the roll. The novel approach of evaluating the thermodynamic driving force enables the assessment of the formation of dross build-up at the roll surface.

In addition to corrosion resistance and processing properties, high coating uniformity is a key quality criterion for galvanized steel sheets. Hydrodynamic gas jet wiping has proved to be an efficient method to control the coating thickness. However, the occurrence of non‐uniformities is attributed to the unsteadiness of the impinging jet. For the first time, vertical surface non‐uniformities resulting from the interaction of the impinging jet with the liquid coating are numerically predicted under industrial boundary conditions using the ANSYS Fluent®. The turbulent flow field of the compressible wiping gas is accomplished by the LES (Large‐Eddy‐Simulation) turbulence model, whereas the interphase between the wiping gas and the liquid coating is modeled by the VOF (Volume‐of‐Fluid) method. It is found that the liquid coating reacts relatively slowly to the high frequent flapping gas jet. Only, when the jet is deflected for a comparatively long period, significant waves are able to develop. The waviness predicted by the simulation model is in good agreement with experimental results. Thus, the model enables a careful study of process settings on the vertical coating uniformity characteristics. For the studied case, an increase of nozzle inclination is found to enhance the performance in terms of coating uniformity significantly.

Accelerated cooling is a decisive process step since it enables the precise adjustment of mechanical material properties such as yield strength and fracture toughness. At the same time, by applying optimized cooling strategies, plates with minimized distortion are obtained at the end of the cooling step. Modelling accelerated cooling involves dealing with complex material phenomena which are a source of significant nonlinearities. Above all, the phase transformation from the austenitic parent phase to the bainitic product phase has to be taken into account [1]. It causes not only release of latent heat but also a significant change of the physical material properties [2]. Moreover, transformation induced plasticity occurs.

Heavy steel plates are among the most essential construction elements for plant and heavy machinery. Their production involves hot rolling, followed by accelerated cooling and leveling. In this work, the focus is put on modelling the accelerated cooling step. It is the goal to build an algorithm which can be used for a virtual design of the accelerated cooling process in order to minimize distortion. Simulation of accelerated cooling requires a complex material model since various physical effects are involved, when plates are cooled down from 850°C to room temperature. Above all, the material undergoes a phase transformation from the austenitic parent phase to the bainitic product phase. The phase transformation is accompanied by metallurgical strains as well as transformation induced plasticity [1]. The highly nonlinear material behavior calls for implicit local integration. To this end, an implicit procedure is formulated within the plane stress theory accounting for plasticity and TRIP. Moreover, it provides the consistent elasto-plastic material stiffness. The global level normally requires an excessive number of DOFs for reliable predictions. It is a challenging task to make accurate predictions about the plate behavior (especially curvature) at the same time avoiding an excessive number of DOFs. A 3D calculation (Fig. 1) is still needed to verify the assumptions that are permitted to reduce the number of DOFs without losing accuracy. Eventually, the fast computation algorithm describes the approximate deformation of the plate by 3 DOFs only, enabling a reduction of computation time by several orders of magnitude. Due to its speed the algorithm can be used as an efficient tool for a virtual process design to obtain minimized distortion at the end of the cooling step (Fig. 2).