Aluminum Melt Research Articles

Evolutionary mechanism of the precipitation behavior and organization of iron-containing intermetallic phase during solidification of recycled high-Fe Al-Zn-Mg-Cu melts

The remelting of aluminum scraps can result in the accumulation of impurities, with iron being the most prevalent among them. The presence of such impurities can cause downgrading and hindered utilization of the material. Despite this, the evolution mechanism of the Iron-containing Intermetallic Phase (IIP) in recycled high-Fe and low-Si aluminum melt has received limited attention and requires further investigation. This study investigates the evolution mechanism underlying the precipitation behavior and organization of the IIP during the solidification process of recycled high-Fe Al-Zn-Mg-Cu melts, utilizing a combination of simulation and experiment. Our findings indicate that the precipitation behavior of the high-temperature precipitation phase (HPP) in the melt is influenced by the Mn and Si, which subsequently determines the organization of the IIP. Specifically, the predominant forms of IIP in the recycled high-Fe Al-Zn-Mg-Cu alloys are lamellar and hollow rod-like phases with anisotropic, as well as skeletal phases with isotropic organization. Moreover, the synergistic addition of Mn and Si can increase the precipitation temperature (PT) and precipitation temperature interval (PTI) of the Al15(Fe,Mn)4Si2 phase in the melt, leading to the transformation of the IIP into a skeletal organization that can be easily removed and has less impact on the material properties. These findings provide insights into alloy design strategies aimed at minimizing the impact of iron accumulation on the cycle life of aluminum scraps and the performance of recycled aluminum.

PENGARUH PENAMBAHAN CACO3 DARI LIMBAH KULIT TELUR DAN WAKTU PENGADUKAN PADA PEMBUATAN ALUMINIUM FOAM MENGGUNAKAN METODE MELT ROUTE

Aluminum is a lightweight material that has good corrosion resistance and electrical conductivity. It can be used for making aluminum foam. One of the methods for making aluminum foam is the melt route method. Making aluminum foam using the melt route process, is called melting aluminum metal, adding foaming agent, and stirring. This study aims to determine the effect of adding CaCO3 from eggshells and stirring time on the foaming ability of aluminum foam. The characteristics that will be observed include the type of aluminum foam, height, pore size, density, porosity, and compressive strength. This research used the melt route method with adding variations in the mass composition of CaCO3 is 4, 5, and 6 wt% on smelted aluminum with stirring times of 30, 45, and 60 seconds. The process is carried out by heating aluminum to 760 °C and adding Al2O3 as a viscosity modifier then adding variations in the mass composition of CaCO3 and stirring with a variation of stirring time. The results show that the highest aluminum foam gets a value of 75 mm. The pore sizes of aluminum foam are obtained ranged from 0.287 to 1.109 mm. The optimal value obtained from the addition of CaCO3 with a mass composition of 4 wt% with a stirring time of 45 seconds, has a density value of 0.388 g/cm3, a porosity percentage of 85.848%, and a compressive strength of 1.777 MPa.

Electrophysical Method for Identifying the Causes of Excessive Hydro Generator Vibration

This article analyzes the operation of hydro generators based on the operation modes of a hydroelectric power plant operating in the Arctic zone of the Russian Federation. The main load of the hydropower plant is an aluminum smelter. The nonlinear load of the smelter is a powerful source of harmonic disturbances. This load produces current and voltage distortions not only in the electrical networks of the smelter but also in those of the city and in generating voltage busbars of the hydropower plant. As a consequence, higher harmonics cause additional losses in the supply networks and have a negative impact on the hydro generators’ condition. The article analyzes the influence of current impacts of the smelter load on the hydro generators under imbalanced conditions by estimating torsional and tangential vibrations emerging in the generators. The tangential forces of double frequency (100 Hz) have been shown to produce practically no significant vibration displacement when detuning the natural frequency of the basket-type end-winding parts. The values of vibration and surge displacement increase significantly in the near-resonance zone. The intense impact of superimposed surge currents has been shown to result in reduction in the hydraulic turbines’ service life and increase in frequency of repairs.

The Potential Utilization of Plastic Waste as a Building Material

One of the innovations in utilizing plastic waste is to process it into Plastic Blocks for Wall Pairs (BPBPD). This research aimed to analyze the temperature required in melting used plastic and cooking oil for making BPBPD mixtures. Variations in the research are temperature under the range 180°C, 200°C, and 220°C. Comparison of the proportions of the mixture of plastic, oil, and coarse aggregate 5-10 mm, namely 1.5:1:0.5, 1:1:0.5, and 1:1:0.25. The types of plastic used are plastic bags, aluminum-coated plastic, and mica plastic. The parameters in this study are the compressive strength value, the initial rate of suction (IRS) value, the porosity value, and the water absorption rate. The study results showed that the minimum temperature for melting plastic bags and aluminum is 180°C, and for melting mica plastic is 220°C. The recommended proportion for making this BPBPD is a ratio of 1.5:1:0.5. The results of the IRS test on the plastic bags BPBPD ranged from 0.037-0.057 Kg/m2, the aluminum plastic BPBPD 0.030-0.057 Kg/m2, and the mica plastic BPBPD 0.033-0.043 Kg/m2. The water absorption rate for plastic BPBPD ranges from 0.233-0.378%, aluminum plastic BPBPD 1.644-4.233%, and mica plastic BPBPD 1.233-2.756%. Porosity results from the plastic bag BPBPD ranged from 0.355-0.931%, the aluminum plastic BPBPD 10.83-12.1%, and the mica plastic BPBPD 2.25-3.9%. In general, the compressive strength of BPBPD plastic bags, both without and with immersion, meets the minimum average compressive strength according to BSN 1989 with quality IV with the highest value in the 1.5:1:0.5 mixture of 38.2 Kg/cm2.

Megaprojects on ice: lessons from the Kárahnjúkar hydropower project for a Just Transition

ABSTRACTThe Kárahnjúkar dam, power station and aluminium smelter opened in East Iceland in 2007 after many years of debate and discord. It is the largest ever industrial project in Iceland and had national as well as local implications, both responding to and in turn changing public expectations regarding participation, environmental impact assessment and community engagement. As Iceland seeks to harness an increasing supply of renewable energy, questions are raised about what constitutes a just transition in the Icelandic context. The article begins by discussing energy supply and demand, current and projected in Iceland. It then delves into theoretical accounts of just transition. It explores the decision-making process for the Kárahnjúkar project and the longer term impacts on the region before assessing these within the framework of just transition theory. A discussion follows that delivers insights into key aspects of the just transition that can be applied to new projects both in Iceland and further afield. These pertain in particular to employment and community benefits, environmental impact assessment and public participation.

Microstructure Characterization of Cement Pastes with Recycled Aluminum Spent Pot Lining

The use of locally available industrial by-products as supplementary cementitious materials and mineral fillers is vital for reducing the embodied carbon of modern concretes. Spent pot lining (SPL), a by-product of the aluminum industry, is massively produced worldwide. SPL treated with the low caustic leaching and liming process (LCLL-ash) is no more hazardous and can be used as cementitious material. This study aims to better understand the microstructure changes of cement paste incorporating aluminum smelter wastes, such as LCLL-ash and synthetic anhydrite. Ground LCLL-ash was used to partially replace cement in cement pastes with a constant water-to-binder ratio of 0.35. A small amount of anhydrite was added to some mixes. This study investigated chemo-micromechanical properties of cement paste systems through multiple techniques, including X-ray diffraction, thermogravimetric analysis, scanning electron microscopy, wavelength-dispersive spectroscopy, and microindentation test. The results showed that the reactive alumina from LCLL-ash modified the hydrated phases with the presence of the carbo-aluminate phases. The pastes containing LCLL-ash exhibited a higher CH, and C-S-H contents refer to the reference, suggesting that LCLL-ash has a slight nucleation effect. Moreover, LCLL cement paste showed an increase in the Ca/Si ratio of the C-S-H phase intermix. Finally, microindentation results revealed that adding anhydrite with 10% LCLL-ash enhanced the mechanical property of the cement paste at 28 days.

Remarkable improvement of wettability of Cu-coated carbon nanotubes by molten aluminum

The wettability plays a decisive role in the mechanical performances of the aluminum matrix composites reinforced with carbon nanotubes (CNTs). In this paper, novel Cu nanoparticles-coated CNTs (Cu@CNTs) were prepared successfully by the liquid phase reduction method to enhance the wettability of CNTs in aluminum melt. The microstructure, contact angle, and interfacial structure of aluminum liquid on Cu@CNTs substrate at high temperature were investigated by scanning electron microscopy (SEM) and sessile drop method in detail. By incorporating Cu nanoparticles on the surface of CNTs, the contact angle was reduced from 133° to 91°, indicating a significant improvement in the wettability of CNTs in aluminum melt. The atomic diffusion of Cu and Al elements leads to a remarkable improvement of wettability for Al-Cu@CNTs model. The coating of CNTs provides a new insight for strong wettability in high-performance aluminum matrix composites.

Synthesis of Al-5Ti-1B-1Ce alloy from remelted chips and its refinement effect

The recycling of aluminum and titanium machining chips has always been a challenge. Here, a new recycling method is proposed. Al-5Ti-1B-1Ce alloy was prepared by the melt reaction method by using Al and TC4 machining chips as the main raw materials. The effects of reaction temperature and time on the phase structure were investigated. Al-5Ti-1B-1Ce prepared from remelted chips has effect refinement to pure aluminum. The addition of 0.3 wt% Al-5Ti-1B-1Ce to the aluminum melt refines the pure aluminum grains form 3000 μm to 185.2 μm and keep 60 min without growing. Besides, the addition of Ce optimizes the morphology and distribution of the second phase, which improve the refine ability of Al-5Ti-1B-1Ce.

INVESTIGATING THE POSSIBILITY OF ALLOYING AN ALLOY ALSI25CU5CR WITH CO, CR AND MO USING METAL POWDER

A base aluminium-silicon alloy AlSi25Cu5Cr was used to investigate the possibility of alloying aluminium alloys with hard-to-melt elements. The alloying elements Co, Cr and Mo were introduced into the melt using metal powder from a hard-melting dental cobalt-chromium-molybdenum alloy. The metal powder was packed in aluminium foil and introduced into the melt of the studied alloy at a temperature of 810º C. After alloying and mechanical stirring of the melt, it stood for 30 min. at a temperature, raised to 850º C and experimental castings were cast from it. After spectral analysis, the degree of absorption of the alloying elements by the aluminium melt was determined. The structure and mechanical properties of the thus obtained alloy were investigated.

Deoxidation capacity of aluminum in ferromanganese carbon-containing melts

Deoxidation (reduction of oxygen concentration dissolved in liquid metal) is an integral part of steel production technology. For obtaining deeply deoxidized metal, mainly aluminum is used at metallurgical enterprises. It should be taken into account that alloying elements of steels and alloys under certain conditions can act as deoxidizing elements, contributing to the complex nature of the deoxidation process. Almost all steels contain manganese in one concentration or another. The study of interaction processes in the Fe – Mn – Al – O – C system at steelmaking temperatures is of applied importance. In this paper, a thermodynamic analysis of the deoxidation ability of aluminum in oxygen-containing iron-manganese melts was carried out. At the same time, influence of carbon on course of the deoxidation process was taken into account. In the study, it is effective to use a technique for constructing the solubility surface of components in metal (SSCM) – a diagram that connects the compositions of liquid metal with the compositions of conjugated non-metallic phases. In the course of this work, oxygen solubility isotherms in the Fe – Mn – O system were calculated for the temperature range of 1550 – 1650 °C. For the Fe – Mn – Al – O – C (1600 °C) system, composite sections of the SSCM were constructed at fixed carbon concentrations in steel [C] = 0; 0.1; 0.4; 0.8 and 1.2 % (hereafter by weight). It is shown that with the simultaneous presence of manganese and aluminum in an oxygen–containing iron-based melt (at industrially significant concentrations [Al] = 0.001 – 0.010 % and [Mn] – less than 1.0 %), aluminum in the liquid metal will act as a deoxidizing agent, and corundum inclusions will be formed as interaction products. Complex deoxidation by aluminum and manganese with the formation of spinel is typical only for manganese-alloyed steels, where the concentration of manganese is more than 1.5 %.

TECHNOLOGICAL FEATURES OF MANUFACTURING ALLOY AK7h STRENGTHENED WITH ZIRCONIUM INTRODUCED WITH ZIRCONIUM TETRAFLUORIDE

The paper considers the important features of the technology of strengthening AK7ch aluminum alloy with zirconium introduced with its tetrafluoride. The choice of a complex flux containing zirconium tetrafluoride in its composition is justified. It is indicated that in order to recover zirconium from its tetrafluoride in the aluminum melt, it is first of all necessary to ensure the formation of sodium or potassium fluorozirconate in the strengthening mixture. The mechanism of recovery of zirconium from tetrafluoride is presented. Technological recommendations for obtaining AK7ch alloy are given. It has been established that the complex flux intended to the alloy, which is modified, must be injected into liquid aluminum before the introduction of other alloying elements, namely silicon and magnesium. The maximum appropriate temperature for injecting zirconium into the aluminum melt from the complex flux is indicated. The maximum amount of zirconium that was recovered is 0.4%. The microstructure and mechanical properties of an alloy strengthened by zirconium from its tetrafluoride, which was injected into the alloy in the amount from 0.8 to 1.2%, were studied. As a result of the modification of aluminum alloy AK7ch with zirconium, the grains of silicon solution in aluminum (α-phase) are grind. No other structural changes are observed. The value of tensile strength and relative elongation of the alloy increases by 1.3 and 1.7 times, respectively.

A STUDY OF THE PHENOMENON BUE CREATION IN TROCHOIDAL MILLING

Aluminum alloy 6061-T6 is a commonly used material in various industries, including automotive parts manufacturing. However, its machining process can be challenging due to the occurrence of build-up edge (BUE) at the cutting edges. To address this issue, this research employed trochoidal milling to machine aluminum alloy 6061-T6 specimens, utilizing a small step over and a suitable depth of cut. The engagement of the tool during the machining process generates fluctuating forces, which consequently leads to fluctuations in temperature. This phenomenon is not only observed in trochoidal milling but also in conventional machining methods. The results indicate that the calculated maximum temperature (350°C) is lower than the aluminum's melting point (652°C). Moreover, the experimental results show minimal BUE formation on the cutting edge and an improved milling process.

STIRRING OF METAL MELTS FOR IMPROVING THE EFFICIENCY OF THE “LADLE – FURNACE” UNITS Message 2. NEW METHOD FOR ELECTROMAGNETIC STIRRING OF METALLIC MELT IN “LADLE – FURNACE” UNIT

The features of refractory lining’s wear of “ladle – furnace” unit at work on metallurgical mini-plant with intensive stirring of liquid metal by gas and electromagnetic field is studied. It was established that the most affected areas are slag zone, ladle’s bottom, as well as side wall, near which the electromagnetic stirrer is located. The stability of these areas determines the duration of the ladle working between repairs. Recommendations for recovery of the lining’s working layer have been developed. Also, there are formulated the requirements for rationalization of melt stirring modes. Theoretical studying of influence of electromagnetic stirring on heat & mass transfer processes in liquid metal bath of metallurgical aggregates (in particular, during homogenization of alloy in free turbulence mode at input of additives) was investigated. New electromagnetic stirrer was designed in the PTIMA NASU, and it is proposed for technologies of melting and finishing of alloys. The stirrer creates the pulsating magnetic field, and its force lines spread equally intensively both in the horizontal and vertical planes. It is shown that design of developed stirrer, its power supply by industrial frequency 50 Hz, and physical nature of the generated field’s action provide the simplicity of its making and operation. So, new stirrer has essential technical, economic and technological advantages in comparison with known stirrers of travelling magnetic field at the same parameters of electromagnetic systems. Joint research performed by specialists of the PTIMA NASU and IED NASU with using mathematical modeling and experiments on aluminum melt showed the following. It is possible to realize a wide range of stirring modes, both intensity and melt movement directions. Thus, the application of developed electromagnetic stirrer in the “ladle – furnace” units will allow to significantly expand the possibilities for finishing liquid alloys on chemical composition and temperature, especially at small metallurgical plants.

Chemical, Mechanical, and Durability of Composites Developed from Aluminum Slag

The research investigated the chemical, mechanical and durability of composites developed from aluminum slag. Aluminum slag is a hazardous residue product of secondary Aluminum smelting. The objective of this research was to study the chemical and geotechnical properties of Al slag. To investigate the stabilization of Al slag with fly ash and GBFS binder to enhance the pozzolanic reaction. Lastly, to study the properties of developed composites and recommend the application. Aluminum slag can be categorized as black or white, with the black dross (slag) having low metal concentration and a granular-like appearance comparable to sand. White dross (slag) has a high metal concentration and contains small quantities of oxides and salts, forming huge blocks. Aluminum slag is a by-product of the foundry industry that is deposited in landfills, causing pollution such as soil, air, and groundwater contamination, as well as affecting human health. Aluminum slag recycling has become more popular in recent years, and it can now be used to make concrete and bricks instead of cement. When compared to properties obtained from composites produced from cement, Aluminum slag improves several properties of the material in this study. Properties such as compressive strength, workability, and durability of the material are found to be improved. At 40% binder and cured at 80°C, the mortar sample made from Al slag, GBFS binder, and fly ash had the highest unconfined compressive strength (UCS) of 24 MPa. The optimum number of days for curing was found to be 14 days. Based on the overall research, it can be concluded that Aluminum slag produced from the foundry industries can be stabilized with fly ash and GBFS binder to produce bricks and concrete

Consistent histories of anthropogenic western European air pollution preserved in different Alpine ice cores

Abstract. Individual high-Alpine ice cores have been proven to contain a well-preserved history of past anthropogenic air pollution in western Europe. The question of how representative one ice core is with respect to the reconstruction of atmospheric composition in the source region has not been addressed so far. Here, we present the first study systematically comparing longer-term ice-core records (1750–2015 CE) of various anthropogenic compounds, such as major inorganic aerosol constituents (NH4+, NO3-, SO42-), black carbon (BC), and trace species (Cd, F−, Pb). Depending on the data availability for the different air pollutants, up to five ice cores from four high-Alpine sites located in the European Alps analysed by different laboratories were considered. Whereas absolute concentration levels can partly differ depending on the prevailing seasonal distribution of accumulated precipitation, all seven investigated anthropogenic compounds are in excellent agreement between the various sites for their respective, species-dependent longer-term concentration trends. This is related to common source regions of air pollution impacting the four sites less than 100 km away including western European countries surrounding the Alps. For individual compounds, the Alpine ice-core composites developed in this study allowed us to precisely time the onset of pollution caused by industrialization in western Europe. Extensive emissions from coal combustion and agriculture lead to an exceeding of pre-industrial (1750–1850) concentration levels already at the end of the 19th century for BC, Pb, exSO42- (non-dust, non-sea salt SO42-), and NH4+, respectively. However, Cd, F−, and NO3- concentrations started surpassing pre-industrial values only in the 20th century, predominantly due to pollution from zinc and aluminium smelters and traffic. The observed maxima of BC, Cd, F−, Pb, and exSO42- concentrations in the 20th century and a significant decline afterwards clearly reveal the efficiency of air pollution control measures such as the desulfurization of coal, the introduction of filters and scrubbers in power plants and metal smelters, and the ban of leaded gasoline improving the air quality in western Europe. In contrast, NO3- and NH4+ concentration records show levels in the beginning of the 21th century which are unprecedented in the context of the past 250 years, indicating that the introduced abatement measures to reduce these pollutants were insufficient to have a major effect at high altitudes in western Europe. Only four ice-core composite records (BC, F−, Pb, exSO42-) of the seven investigated pollutants correspond well with modelled trends, suggesting inaccuracies of the emission estimates or an incomplete representation of chemical reaction mechanisms in the models for the other pollutants. Our results demonstrate that individual ice-core records from different sites in the European Alps generally provide a spatially representative signal of anthropogenic air pollution trends in western European countries.

Improving the properties of nickel/graphene oxide coated copper plate by changing the electroplating process conditions

One of the attractive ways to improve the mechanical properties and prevent damage to the surface of the copper plate is to create a nickel/graphene coating on it. In this work, the effect of bath type and process conditions on mechanical and wettability properties of nickel/graphene oxide coated copper plate via electroplating, has been investigated. Ultrasonic stirring of the bath with a power of 200 W increased the hardness of the coating to 747 Vickers and the wetting angle with molten steel to 125° by uniformly distributing the graphene oxide layers among the nickel grains and preventing the growth of the grains. By using a chloride bath instead of a Watts bath, due to the adhesion and delamination mechanism, a slight weight loss occurred in the pin-on-disk wear test. The coating obtained by electroplating in a chloride bath containing 20 cc of colloidal graphene oxide had a structure with a thickness of 12–15 μm consisting of large and compact masses of cauliflower with a uniform distribution of graphene layers. This sample shown a contact angle of 130° with the surface tension of 25 × 10−6 N/m to the aluminum melt drop and a 135° and 120 × 10−6 N/m to the steel melt drop.

Properties of various CaO-Al2O3-TiO2 refractories and their reaction behaviours in contact with Ti6Al4V melts

Vacuum induction melting technology is an important method for producing high-quality titanium alloy. The key challenge lies in the development of refractories with excellent chemical stability for titanium alloy corrosion. In this work, CaO-Al2O3-TiO2 refractories are proposed as the potential materials for Ti6Al4V alloy smelting. Four CaO-Al2O3-TiO2 refractories with different TiO2 contents were prepared and their reaction behaviours in contact with titanium aluminum melts were investigated in detail. When the refractory has a suitable content of CaTiO3 phase, it promotes the diffusion and mass transfer rate of ions and improves the sintering reaction activity, leading to good high temperature mechanical properties and corrosion resistance to titanium aluminum alloy. However, when the TiO2 component is excessive, CA6 has been completely wrapped by CaTiO3, and some CA6 grows abnormally, resulting in a decrease in high temperature mechanical properties of the refractory. Moreover, during the smelting of Ti6Al4V alloy, Al component reacts with CaTiO3 to produce metallic Ti and calcium aluminate phase with low melting point, resulting in degradation of refractory.

Strategic Marketing Approach of Indonesia Aluminium Mineral Industry: Upstream and Downstream Analysis

The research aimed to determine the causes of imports by analyzing the upstream and downstream sides of the existing aluminium industrial chain. The research applied a descriptive-exploratory approach by collecting secondary data from credible sources. Interviews and focus group discussions with appropriate experts were also conducted to obtain supporting data. Research shows that aluminium imports will continue both in the short and long term. It is due to the upstream supply, especially in aluminium smelters, which cannot keep up with the increasing demand. Even though the market opportunity, especially in the automotive, construction, and power cable segments, is enormous and continues to grow, if there is not enough supply, the deficit of aluminium metal will continue to occur. It takes encouragement from the Government's political will to provide ease of electricity sources, increase production capacity and technology, change the mindset from relying on traders solely towards the mindset of the industrialist.

On the Pressure and Rate of Infiltration Made by a Carbon Fiber Yarn with an Aluminum Melt during Ultrasonic Treatment

The effect of the infiltration time of a carbon fiber yarn in the range of 6 to 13.6 s on the infiltrated volume under the cavitation of an aluminum melt has been studied. When the infiltration time was more than 10 s, the carbon fiber was completely infiltrated with the matrix melt, and a decrease in the infiltration time led to a monotonous decrease in the fraction of the infiltrated volume. Based on the experimental data, the infiltration rate and the pressure necessary to infiltrate a carbon fiber yarn with an aluminum melt were estimated. The infiltration rate was 20.9 cm3/s and was independent of the infiltration depth. The calculated pressure necessary for the complete infiltration of a carbon fiber yarn at this rate was about 270 Pa. A comparison of the pressure values calculated according to Darcy’s and Forchheimer’s laws showed that the difference between them did not exceed 0.01%. This indicates that a simpler Darcy’s law could be used to estimate pressure.

Analysis of the melting and solidification process of aluminum in a mirror furnace using Fiber-Bragg-Grating and numerical models

In the search of an adequate real time strain measurement method in aluminum casting, the use of Fiber-Bragg-Grating (FBG) is being investigated with great interest. In order to do so, the behaviour of glass fiber sensors in a liquid aluminium alloy at temperatures up to 750°C is experimentally analysed in a laboratory environment. For better process understanding a simulation of the fiber alloy composite is conducted. FBG is an optical measurement method, which uses engraved Bragg reflectors in a 125 µm in diameter thick glass fiber. This reflector transmits most of the wavelengths but only reflects one specific wavelength. This specific wavelength can be measured and changes due to the axial strain on the grating by the fluid alloy reaction and by the changes in temperature. Using a so-called mirror furnace, several experiments with the fiber alloy composite are evaluated. These measurements are also the basis for the further understanding of hot tearing. The data gathered during the measurement campaign - both numerical and experimental - is used to parameterize a simulation. As a result, the understanding of the fiber alloy composite behaviour is expanded and a digital twin is modeled with MATLAB’s partial differential equation toolbox.