MATLAB Program Research Articles

The study of mechanical properties and fracture evolution of coal-rock masses under hard roof-soft floor conditions

As the depth of coal mining in China continues to increase, the fracturing of coal rock masses has an increasingly complex impact on the surrounding rock roadways. The majority of the mine’s roadways run through coal rock masses with hard roofs and soft bottoms, which typically exhibit complex dynamic behaviour. To further research the mechanical behaviour and fracture evolution of coal rock masses under hard-roof and soft-floor conditions, the study is based on the majority of working faces in a mine, which have hard roofs and soft floors. Uniaxial compression tests were utilized to study the mechanical properties of coal rock masses under hard-roof and soft-floor circumstances, using acoustic emission monitoring, whole-process imaging technologies, and fractal dimension analysis. The experimental results are as follows: The uniaxial compressive strength of the coal rock mass is significantly higher than that of its weakest component. The results of the experiment are as follows: The uniaxial compressive strength of coal rock mass is significantly higher than that of its weakest component. Samples with different soft rock strengths exhibited dissipated energy greater than the accumulated energy before the stress maximum, accompanied by volume expansion and the formation of shear surfaces. Samples with higher soft rock strengths tend to exhibit brittle failure, while weaker samples show stress-softening behaviour. Internal fracture complexity varies amongst samples with varying soft rock strengths. A fractal study of the acoustic emission parameters was carried out utilizing MATLAB programming. The fractal analysis results show that acoustic emission ringing counts and energy time series of coal rock masses under hard-roof and soft-floor settings have good fractal properties. The fractal analysis results show that acoustic emission ringing counts and energy time series of coal rock masses under hard-roof and soft-floor settings have good fractal characteristics. Acoustic emission ringing counts tend to have a larger correlation dimension than acoustic emission energy. However, while the sample is fracturing on a vast scale, the ringing count correlation dimension fluctuates very little. The correlation dimension distribution of samples with lower strength is more concentrated after the stress maximum, implying that the deformation and fracturing of the floor rock in highways under hard-roof and soft-floor circumstances are more complex. Both the correlation dimension D of acoustic emission ringing counts and energy indicate a continuous fall before peak stress, which can be used to anticipate coal rock mass fracture. This study, based on the mechanical behaviour and fracture evolution of coal rock masses under hard-roof and soft-floor conditions, provides a foundation for disaster avoidance by controlling the stability and structural deformation of floor rock in hard-roof and soft-floor highways.

A Comparative Study of Differential Quadrature Methods for METE Nanobeam Vibrations

This study investigates the use of three different quadrature schemes, as well as an iterative quadrature methodology, to analyze vibrations in magneto-electro-thermo-elastic nanobeams. Individual MATLAB programs for each method are developed with the goal of minimizing errors in comparison to accurate findings, as well as determining the execution time for each strategy. This study shows that the Discrete Singular-Convolution Differential Quadrature Method with a Regularized Shannon Kernel (DSCDQM-RSK) and specified parameters produces the best accurate and efficient results for this particular situation. A subsequent parametric study is carried out to determine the effect of various factors on the vibrated nanobeam, including boundary conditions, material types, linear and nonlinear elastic foundation properties, nonlocal parameters, length-to-thickness ratios, external electric and magnetic potentials, axial forces, and temperature variations. Important discoveries include insights into the relationship between fundamental frequency, linear elastic foundation features, axial loads, external magnetic fields, temperature fluctuations, and material types. According to this study, these findings could be critical in the development of sophisticated nanostructures made from magneto-electro-thermo-elastic materials for use in a variety of electromechanical applications. This would entail utilizing nanobeams’ unique properties in applications such as sensors, resonators, and transducers for nanoelectronics and biology.

Thermal Analysis of Eyring-Powell Hybrid Nanofluid: A Case of Combined Convective Transport and Radiative Heat Flux along Inclined Stretching/Shrinking Sheet

Hybrid nanofluids are designed to improve conventional nanofluids' stability and other thermal properties. The present work investigates the flow of combined convective transport and the influence of radiation on the studied flow. A hybrid nanofluid ( Cu Al O  2 3 /water) flows through a vertically inclined stretching/shrinking sheet. To simplify the governing equations, the deterministic two-variable differential equations (PDEs) are systematically transformed into a system of one-variable differential equations by using appropriate similarity transformations. The bvp4c function of the MATLAB program is also used to solve the simplified mathematical model. The present study investigates and presents in tabular and graphical form the effects of stretching/shrinking surfaces, suction, and volume fraction of the nanoparticles on the velocity and temperature profiles as well as on the engineering quantities. The present results are first validated and confirmed as acceptable before the full calculations are performed. Overall, the results of this study show that the investigated parameters influence the flow characteristics, which can serve as a controlling factor for heat transfer.

GLOBAL STABILITY AND HOPF BIFURCATION OF A DELAYED PREDATOR-PREY MODEL INCORPORATING ALLEE EFFECT AND FEAR EFFECT

This paper aims to discover the impact of the fear of predators in prey, Allee effect for predator reproduction and time delay corresponding to the gestation period on the dynamics of a predator- prey model. Existence, non-negativity, and boundedness of the model solutions are guaranteed. The criteria for asymptotically stability of all the biologically feasible steady state points are determined. It is also determined a critical value for time delay, where the model under goes Hopf -bifurcation near coexistence steady state point. Finally, with the help of the MATLAB program, to confirm the analytical results and discover the impact of fear, the Allee effect, and time delay, the model was solved numerically.it is observed that fear affect negatively on both prey and predator species and the time delay may system may induce a transition of the dynamics of system from the a stability situation to the state where the populations oscillate periodically or vice versa

Velocity Analysis of a Slider Crank Mechanism for Delta Robot Arm Manipulation: A Computational Approach

In this research, a velocity analysis of the slider crank mechanism's (SCM) for the delta robot arm manipulation was carried out. For the slider crank mechanism, new velocity response models were created. Trigonometric and inverse trigonometric functions are used in the novel Akozietic mathematical method, which is appropriate for kinematic analysis of intricate mechanisms like the four-bar mechanism (slider crank). The equilibrium conditions of the forces in a four-bar mechanism are used in the Akozietic mathematical technique to create simple mathematical models that enable user-written computer programs in Matlab and other programming languages. According to the velocity profile, the mechanism is under the most stress when the crank angle exceeds 300°, and the velocity is lowest at 180° and 0°.The crank angles where the slider shifts direction are the locations where the velocity passes zero. The novel mathematical procedure created in this study outperformed the other two kinematic analysis methods that were currently in use, according to a comparison of spreadsheets and this new mathematical method for mechanism analysis (Akozietic) with standard numerical solutions completed in Mathematica.

Optimal Allocation and Sizing of Battery Energy Storage System in Distribution Network Using Mountain Gazelle Optimization Algorithm

This paper addresses the problem of finding the optimal position and sizing of battery energy storage (BES) devices using a two-stage optimization technique. The primary stage uses mixed integer linear programming (MILP) to find the optimal positions along with their sizes. In the secondary stage, a relatively new algorithm called mountain gazelle optimizer (MGO) is implemented to find the technical feasibility of the solution, such as voltage regulation, energy loss reduction, etc., provided by the primary stage. The main objective of the proposed bi-level optimization technique is to improve the voltage profile and minimize the power loss. During the daily operation of the distribution grid, the charging and discharging behaviour is controlled by minimizing the voltage at each bus. The energy storage dispatch curve along with the locations and sizes are given as inputs to MGO to improve the voltage profile and reduce the line loss. Simulations are carried out in the MATLAB programming environment using an Australian radial distribution feeder, with results showing a reduction in system losses by 8.473%, which outperforms Grey Wolf Optimizer (GWO), Whale Optimization Algorithm (WOA), and Cuckoo Search Algorithm (CSA) by 1.059%, 1.144%, and 1.056%, respectively. During the peak solar generation period, MGO manages to contain the voltages within the upper boundary, effectively reducing reverse power flow and enhancing voltage regulation. The voltage profile is also improved, with MGO achieving a 0.348% improvement in voltage during peak load periods, compared to improvements of 0.221%, 0.105%, and 0.253% by GWO, WOA, and CSA, respectively. Furthermore, MGO’s optimization achieves a reduction in the fitness value to 47.260 after 47 iterations, demonstrating faster and more consistent convergence compared to GWO (47.302 after 60 iterations), WOA (47.322 after 20 iterations), and CSA (47.352 after 79 iterations). This comparative analysis highlights the effectiveness of the proposed two-stage optimization approach in enhancing voltage stability, reducing power loss, and ensuring better performance over existing methods.

ВИКОРИСТАННЯ ФІЛЬТРУ КАЛМАНА У ВЕКТОРНІЙ СИСТЕМІ ЕКСТРЕМАЛЬНОГО КЕРУВАННЯ АСИНХРОННОЮ МАШИНОЮ

In the article the reactive power of an asynchronous machine (AM) in a stable mode is obtained as a function of three vari-ables: the angular speed of rotation of the AM shaft, the module of the rotor flux coupling and the moment of static load on the shaft. The AM power factor decreases in electric drives (ED) of industrial mechanisms in which the load moment while maintaining its direction of action can take a static value less than the nominal value. Therefore, in order to ensure a high power factor of an asynchronous ED in long-term operating modes with a variable load, a vector AM control system was created, in which the magnitude of the rotor flux coupling is regulated by the reactive power channel as a function of the mo-ment of static load on the shaft. To identify the moment of loading, as well as the angular speed of the rotor and its flux cou-pling, a Kalman observer is synthesized, which allows creating a vector control system with simultaneous regulation of the speed and power factor of the AM without physical sensors of the reference vector of the rotor flux coupling and its angular speed of rotation. The significant dependence of the extreme values of the rotor flux coupling for reactive power on the torque on the AM shaft and insignificant dependence on the speed has been proved. Stability and high control quality are achieved by simultaneous use of relay control laws, invariant to coordinate and parametric perturbations, and the effectiveness of the Kalman filter algorithm for identifying variable states in the feedback loop. Thus, the article theoretically substantiates the idea of creating a sensorless relay-vector control system for an asynchronous ED with simultaneous speed regulation and optimization of AM energy indicators. The mathematical model is created as a program written in the Matlab programming language. The operability of the proposed asynchronous ED control system was confirmed by the method of mathematical modeling. References 12, figures 6.

ANALYSIS FROM 1980 TO 2018 OF TIDAL OBSERVATION DATA FOR ASSESSING THE STABILITY OF TIDAL CONSTANTS FOR PRIMARY PORT

Tidal analysis involves the computation of tidal constants (phase lag (g) and amplitude (H)) of tidal constituents at a location. This study focuses on the assessment of the stability of g and H for the Bonny port which is the only standard tidal port in Nigeria. Monthly analysis of tidal observations was carried out with 1980, 1994 and 2018 year’s data using Least Squares Method (LSM) of Harmonic Analysis with MATLAB programming codes. The observation equation technique of LSM is adopted; the dimension of the Normal (N) matrix equations obtained for the monthly analysis is 72 56 i.e. 72 rows, and 56 columns. The N matrix is inverted and gave results for mean sea level (MSL) and g and H of 28 primary constituents of tide. Four major constituents of tide (M2, S2, K1 and O1) remain stable throughout the analysis. The mean of g and H obtained for each year was observed to be almost equal to the mean obtained from the three-year data. The maximum residuals and spreads of the computed g and H over the period of study show that g and H at Bonny are stable and that results from accurately analyze one-month data observation can be employed for tidal prediction for several years. Therefore, it can be concluded that the g and H for M2, S2, K1 and O1 are stable and that the type of tide (F) at Bonny port is semidiurnal since the computed F is 0.16 which is 0.25.

COMPUTER PROGRAM FOR MODELLING RAINFALL INTENSITY DURATION FREQUENCY (IDF) RELATIONSHIPS BY SHERMAN’S METHOD FOR ILORIN AREA IN NIGERIA

A computer program was developed for the modelling of rainfall data for a period of 30 years (1981-2010) for Ilorin area using a MATLAB software. The data was analyzed by sorting and ranking the maximum rainfall depths with their corresponding depths and their return periods. The rainfall depths were converted to rainfall intensities. An algorithm was developed in form of a flowchart which guided the development of computer program using Sherman’s method. Values of rainfall intensities with corresponding durations and return periods were exported to the MATLAB program for modelling of station constants and simulation of IDF curves for Ilorin area. The station constants were obtained as n = 0.5707, c = 131.0144, and m = 0.3425 for Ilorin area respectively. These were used to produce IDF curves and mathematical model for Ilorin area.

Conceptual Platform for Basic Waterfall Manufacturing System Using Simulink with Lean- Agile Measurement Criteria

This paper forms part I of two-part series that present the full path for constructing a Lean-Agile platform using Simulink and test the different criteria of such manufacturing systems. management of manufacturing systems is one of the main rules in engineering in order to reduce the waste (lean) and to fulfill the changing requirements of the market (agile). This paper describes the process of construction of the basic waterfall platform using Matlab/Simulink, and to develop the Matlab program that facilitates the input process of constants and variables into the model and then to show the results. this platform will mimic the manufacturing system of motorcycle engine that takes six parts as input and outputs four different models, Matlab/Simulink is used to construct the platform, and the library of Simscape used to model the discrete (not continuous) behavior of the system. Waterfall platform has been constructed. and simulated with the specific constants and variables from an excel file. Showing the results of workers-usage, over-processing, machine-usage,queue-usage. It shows the orders done with time of simulation, illustrating and indication of lean and agility of the proposed system. Different figures were generated and introduced to show various measuring criteria that evaluate the performance of the proposed system. The different measurement criteria drawn using a second Matlab program developed specially for this purpose. Index Terms— Lean, agile, Leagile, manufacturing system, workshop.

Role of Fear and disease on the Dynamics of two prey-one predator model with extended Holling type II functional response

This paper deals with the studying and modeling the dynamical interaction between two prey where one of the prey species behave stronger than other, and one predator species,. The influence of fear is integrated into the development rate of vulnerable prey species owing to predation, with the spread of a SI illness among robust prey species. Here it is considered that predator both prey according to Holling type II functional response for two prey species. Then the formulation of the model is described and the boundness of solution of the system is discussed. The local stability as well as global stability for each model steady states is analyzed. Finally, with the help of MATLAB program, it is performed numerical simulations to support the evidence of our analytical results. Finally, a brief conclusion on the total work is given.

Computational Behavior of Trihybrid Casson Nanofluid Blood Flow Occurring Inside the Conical Gap Between the Rotating Disk and the Cone

The investigation of the flow patterns of a trihybrid nanofluid flow situated in the conical gap that is created among a revolving disc and a stationary cone computationally examined in this study. Three different types of nanoparticles, Al2O3, TiO2 and Ag are examined with blood as the base fluid according to flow properties and energy phenomenon. While discussing the heat transfer mechanism in trihybrid nanofluid flow crossing through the disc and cone, four different types of cases are explored likewise the disc and cone may be rotating at the same rate or at different rates, or one may be stationary about the other. The numerical scheme is planted to observe the fluid flow and heat transfer patterns. In the current article, we investigated rheological parameters, including rotating speed, cone angle, and concentration of nanoparticles, and the effect of heat transfer performance over velocity and temperature patterns. The results shed light on the complex interactions between the geometric and nanofluid characteristics, providing useful information for fluid dynamics and thermal management applications. This fluid model is also useful for the study of blood pressure, arthritis, brain therapy, and malignant tumors. The graphs are plotted using the MATLAB program BVP4C to ensure convergence. Several variables, such as a magnetic parameter, Prandtl's number, and Reynold's number, have an impact on temperature and velocity profiles. It is evident that the amalgamation of the fraction of three nanoparticles reduces the velocity and enhances the temperature of the nanofluid. The momentum boundary layer expands when the cone and disc rotate in the same direction.

Computational Behavior of Trihybrid Casson Nanofluid Blood Flow Occurring Inside the Conical Gap Between the Rotating Disk and the Cone

The investigation of the flow patterns of a trihybrid nanofluid flow situated in the conical gap that is created among a revolving disc and a stationary cone computationally examined in this study. Three different types of nanoparticles, Al2O3, TiO2 and Ag are examined with blood as the base fluid according to flow properties and energy phenomenon. While discussing the heat transfer mechanism in trihybrid nanofluid flow crossing through the disc and cone, four different types of cases are explored likewise the disc and cone may be rotating at the same rate or at different rates, or one may be stationary about the other. The numerical scheme is planted to observe the fluid flow and heat transfer patterns. In the current article, we investigated rheological parameters, including rotating speed, cone angle, and concentration of nanoparticles, and the effect of heat transfer performance over velocity and temperature patterns. The results shed light on the complex interactions between the geometric and nanofluid characteristics, providing useful information for fluid dynamics and thermal management applications. This fluid model is also useful for the study of blood pressure, arthritis, brain therapy, and malignant tumors. The graphs are plotted using the MATLAB program BVP4C to ensure convergence. Several variables, such as a magnetic parameter, Prandtl's number, and Reynold's number, have an impact on temperature and velocity profiles. It is evident that the amalgamation of the fraction of three nanoparticles reduces the velocity and enhances the temperature of the nanofluid. The momentum boundary layer expands when the cone and disc rotate in the same direction.

Numerical Solution of Elliptic Partial Differential Equation: Method of Lines and Crank-Nicholson Method

The method of lines (MOL) is a solution procedure for solving partial differential equation (PDE) and the Crank-Nicholson method (CNM) is an implicit finite difference method, used to solve the elliptic equation and similar partial differential equations numerically. In this study, the numerical techniques were introduced to solve elliptic partial differential equation (PDE) together with initial and boundary conditions. The Poisson equation was considered as an elliptic PDE. Particularly, two methods were used to solve a two-dimensional Poisson equation numerically, such as the method of lines (MOL) and Crank-Nicholson method (CNM). The implementation of the solutions was done using Microsoft office spreadsheet and MATLAB programing language. Lastly, the numerical solutions were presented graphically which was obtained with method of lines along with Crank-Nicholson method.

RESIDUAL DISPLACEMENT DUE TO ARBITRARY PLASTIC STRAINS

The displacement of the boundary of an elastic body in which inelastic strains exist or initiate due to various conditions can affect the intended functioning of the machine element and thus the service life of the assembly. Plastic strains are often initiated when the body is loaded beyond the elasticity limit of its material. The subsequent deformation of the boundary may affect the interaction with the coupling elements, resulting in further perturbations of the contact conditions. This is especially true when load is transmitted through a small contact region, such as in gears or bearings. Assessment of this permanent deformation is thus essential to predict and prolong the service life of various machine elements working under severe contact loads. The mathematical model employed in this work is built around the Betti’s reciprocal theorem, which exposes a property of the Elasticity equations in the presence of inelastic strains. The resulting equations prove that the residual displacement due to plastic strains in the bulk of the body can be expressed by superposition of effects, as a convolution product. The Green’s functions for the latter convolution are integrated to derive the influence coefficients needed in the numerical approach. The model discretisation is rectangular, with the volume of plastic strains approximated with a reunion of adjacent cuboids with uniform strains. The contributions of each elementary cuboid to the displacement components in a specific point from the boundary, i.e., the influence coefficients, are derived and expressed analytically. With these elements, an acceleration technique for the computation of elastic displacement can be extended to residual displacement. Calculations are performed with the aid of a Matlab computer program developed based on the newly derived relations. Five configurations of plastic strains are considered and the program predictions are compared with existing results from the literature. The good agreement gives confidence in the advanced computer tool and encourages its implementation in a more complex program for the simulation of the elastic-plastic contact.

Developing new solar radiation estimation models with machine learning techniques and testing their efficiency in various places

ABSTRACT Renewable energy sources have garnered significant global attention in terms of cost-effectiveness, efficiency and minimal environmental impact. Among these, solar energy has emerged as one of the most critical and widely applied renewable energy sources. As the utilization of solar energy sources ascends, modeling the solar radiation (SR) which is costly and challenging to measure has become an essential area of research. The main aim of this study is to determine the Angstrom coefficients for SR estimation using machine learning (ML) techniques. The linear regression and support vector machine (SVM) regression approaches were implemented in the MATLAB program to determine the Angstrom coefficients. In order to analyze the regional variations in the performance of this novel approach, four separate regions were determined. Furthermore, four distinct statistical tests were employed to assess the performance of the developed models. According to these test results, it has been concluded that the developed models with the SVM approach in SR estimation have superior performance overall, effectively capturing the relationship between the estimated and observed SR values across all regions. Upon the comprehensive evaluation of the results, it was concluded that method SVM regression has superior performance Region 1 and Region 4, while linear regression performed better in Region 2 and Region 3.

QSPR Analysis of Kidney Infection (Pyelonephritis) Drugs by Entropy Graphs Weighted with Topological Indices, and MATLAB Programming

The entropy of the chemical graph primarily measures the complexity of chemical structures. In this study, Shannon’s entropy approach was utilized to calculate entropies for chemical graphs with degree-based topological indices, predicting the physicochemical correlation capability of 12 drugs for kidney infection and its implications for physicochemical aspects. Entropy can help identify important correlations between the structure and function of compounds, which in turn can aid in developing QSPR models. A computer-based computing technique and algorithm were employed to simplify calculations and data analysis. Degree-based topological indices, along with the entropy graphs weighted with indices, were calculated using the MATLAB program and used to measure entropy. This research aims to predict the physicochemical characteristics of these drugs based on the entropy of topological indices. Several regression models were used to analyze drugs’ quantitative structure-property relationship (QSPR) and predict their physicochemical properties. Effective predictors were identified in this study, and optimal equations were introduced to evaluate the physicochemical characteristics based on the highest correlation coefficient and Fisher’s statistical test. Interestingly, in some cases, the entropy of degree-based indices showed a stronger correlation with drug characteristics. In conclusion, the optimal equations for estimating molar refractivity (MR) and polarizability (P) using the ENT RR − 1 / 2 , ENT SC , and ENT ABC indices incorporate compound, growth, and exponential factors. Meanwhile, the optimal equations for estimating molar volume (MV) with the ENT F index are quadratic and cubic.

METHODOLOGY OF ROTATION OF GENERAL SURFACES

When parts are machined, especially on heavy machine tools, an accurate description of the rotations around the geometric axes is required. The work adds the concept of rotation around the machine and the workpiece axes. Both types of rotation in mechanics are related to internal and external rotations, which we describe in detail. We show how both types convert to each other and how conversion formulas are derived. The resulting conversions are formalized as functions in the C and MATLAB programming languages. The result of this mathematical description will be transferred to a new transformation cycle that can be used on machines as a standard.

Finite element analysis of stress concentration singularities in orthotropic/isotropic hole plates on an aircraft wing

The cutouts in the ribs of aircraft wings create stress concentrations. Stress concentrations in an elastic body are very important in structural design and are mainly caused by two mechanisms: the concentration of force acting on a body and geometric discontinuities in the object, such as holes or sudden changes in the geometry of the object's surface. To obtain equivalent stresses and strains for a wing rib without a cutout and with a circular cutout, we considered a perforated plate as the test piece. We studied the stress concentration factor (SCF), around a circular central hole in isotropic and orthotropic rectangular plates subjected to tensile loading using the finite element model, and validated it by comparing the constitutive analytical equations of Heywood and Howland for orthotropic and infinite isotropic plates and with the Matlab program. Next, we analyzed the overall and net stress concentration factor around the hole as a function of different variables: the plate diameter-width ratio (d/W), the effect of the fiber orientation angle (θ°),and the effect of the length/width ratio (L/W). Abaqus was used as design software to extract stress concentration factors for materials such as Al 2024-T3, Glass/Epoxy, and Carbon/Epoxy. These results were then compared with the analytical formula using Matlab as the programming software, the statistics showed that there was good agreement between the stress concentration factor around the hole using Abaqus and the Matlab program formula. It can be concluded that the application of Matlab software for SCF estimation is faster than Abaqus software.

Evaluation of Microwave Heating Uniformity for Ready-to-Eat Rice in Metalized Packaging Structure.

Microwave energy utilization undergoes two stages via absorption and conversion inside ready-to-eat rice (RER) under microwave reheating. The reasonable utilization of microwave energy inside the processed material may enhance the uniformity of the temperature distribution. To analyze the uniformity changes inside RER, the effects of microwave reflection, refraction, and absorption by a metal aluminum film were studied through the thermodynamic properties. A simulation model was developed using the co-simulation method of COMSOL Multiphysics with MATLAB programming to analyze the mechanism of material properties and electromagnetic distribution on temperature distribution uniformity, as well as the formation mechanism of the temperature distribution uniformity of microwave-reheated RER. Based on models of the designed package boxes covering the metal film, the optimal structure was developed to include a metal aluminum film with a width of 5 mm and a thickness of 0.30 mm, which was sprayed on the edges and corners of a rectangular packaging box. The packaging boxes covering the metal films may reduce the average temperature of the upper and lower layers in RER by 8.03 °C and 7.42 °C, respectively, while the temperature distribution uniformity increased by 35.71% and 72.22%. The introduction of a metalized package significantly enhances the temperature uniformity inside RER under microwave reheating.