Computational Accuracy Research Articles

Nonmetal-to-metal transition in liquid hydrogen using density functional theory and the Heyd-Scuseria-Ernzerhof exchange-correlation functional.

We investigate the first-order liquid-liquid phase transition in fluid hydrogen, which is accompanied by a nonmetal-to-metal transition. We use a combination of density functional theory for the electrons and molecular dynamics simulations for the ions. By employing the nonlocal Heyd-Scuseria-Ernzerhof exchange-correlation functional, we accurately determine the equation of state and the corresponding coexistence line. Additionally, we calculate the electrical conductivity using the Kubo-Greenwood formula and find jumps in the coexisting region, which is characteristic of a first-order transition. Our new predictions are compared with previous theoretical results and available experimental data. Thereby, we find that the strongly constrained and appropriately normed exchange-correlation functional provides an excellent balance between computational cost and accuracy.

Topography‐dependent eikonal solver in tilted transverse isotropic media with anelliptical factorization

AbstractIncorporating anisotropy and complex topography is necessary to perform traveltime tomography in complex land environments while being a computational challenge when traveltimes are computed with finite‐difference eikonal solvers. Previous studies have taken this challenge by computing traveltimes in transverse isotropic media involving complex topography with a finite‐difference eikonal equation solver on a curvilinear grid. In this approach, the source singularity, which is a major issue in eikonal solvers, is managed with the elliptical multiplicative factorization method, where the total traveltime field is decomposed into an elliptical base traveltime map, which has a known analytical expression and an unknown perturbation field. However, the group velocity curve can deviate significantly from an ellipse in anellipitically anisotropic media. In this case, the elliptical base traveltime field differs significantly from the anelliptical counterpart, leading to potentially suboptimal traveltime solutions, even though it helps to mitigate the detrimental effects of the source singularity. To overcome this issue, we develop a more accurate topography‐dependent eikonal solver in transverse isotropic media that relies on anelliptical factorization. To achieve this, we first define the coordinate transform from the Cartesian to the curvilinear coordinate system, which provides the necessary framework to implement the topography‐dependent transverse isotropic finite‐difference eikonal solver with arbitrary source and receiver positioning. Then, we develop a semi‐analytical method for the computation of the topography‐dependent anelliptical base traveltime field. Finally, we efficiently solve the resulting quadratic elliptical equation using the fast sweeping method and a quartic anelliptical source term through fixed‐point iteration. We assess the computational efficiency, stability and accuracy of the new eikonal solver against the solver based on elliptical factorization using several transverse isotropic numerical examples. We conclude that this new solver provides a versatile and accurate forward engine for traveltime tomography in complex geological environments such as foothills and thrust belts. It can also be used in marine environments involving complex bathymetry when tomography is applied to redatumed data on the sea bottom.

Derivation of Four-Point Integrator for the Solutions of Second-order Oscillatory Problems

The research introduces a new four-point integrator (FPI) for solving second-order differential equations characterized by oscillatory behavior. The proposed FPI is developed through a continuous scheme within a linear multistep framework, utilizing two off-step points to enhance efficiency. Unlike conventional methods that reduce higher-order equations to first-order systems, often resulting in loss of inherent characteristics, the FPI maintains essential equation properties. Through this approach, the FPI enables a self-starting, block-by-block algorithmic implementation that does not require predictor values, simplifying computation. The integrator’s properties are rigorously analyzed, confirming its consistency, zero-stability, and convergence, all of which contribute to its reliability in handling oscillatory problems. Additionally, stability analysis, including the region of absolute stability, demonstrates the A-stability of the integrator. Numerical experiments conducted on some second-order problems reveal the FPI’s computational accuracy, effectively comparing with established solvers such as ode45, ode15s and other methods. These results highlight the potential of the FPI as a viable alternative for directly solving oscillatory differential equations with damping characteristics, providing computational efficiency and accuracy.

A Comprehensive CNN Model for Age-Related Macular Degeneration Classification Using OCT: Integrating Inception Modules, SE Blocks, and ConvMixer

Background/Objectives: Age-related macular degeneration (AMD) is a significant cause of vision loss in older adults, often progressing without early noticeable symptoms. Deep learning (DL) models, particularly convolutional neural networks (CNNs), demonstrate potential in accurately diagnosing and classifying AMD using medical imaging technologies like optical coherence to-mography (OCT) scans. This study introduces a novel CNN-based DL method for AMD diagnosis, aiming to enhance computational efficiency and classification accuracy. Methods: The proposed method (PM) combines modified Inception modules, Depthwise Squeeze-and-Excitation Blocks, and ConvMixer architecture. Its effectiveness was evaluated on two datasets: a private dataset with 2316 images and the public Noor dataset. Key performance metrics, including accuracy, precision, recall, and F1 score, were calculated to assess the method’s diagnostic performance. Results: On the private dataset, the PM achieved outstanding performance: 97.98% accuracy, 97.95% precision, 97.77% recall, and 97.86% F1 score. When tested on the public Noor dataset, the method reached 100% across all evaluation metrics, outperforming existing DL approaches. Conclusions: These results highlight the promising role of AI-based systems in AMD diagnosis, of-fering advanced feature extraction capabilities that can potentially enable early detection and in-tervention, ultimately improving patient care and outcomes. While the proposed model demon-strates promising performance on the datasets tested, the study is limited by the size and diversity of the datasets. Future work will focus on external clinical validation to address these limita-tions.

Comparative analysis of accuracy and computational complexity across 21 swarm intelligence algorithms

Nonlinear, complex optimization problems are prevalent in many scientific and engineering fields. Traditional algorithms often struggle with these problems due to their high dimensionality and intricate nature, making them time-consuming. Many researchers have proposed new metaheuristic algorithms inspired by biological behaviors in nature, which comparatively show higher performance and accuracy than traditional optimization algorithms. Nature-inspired algorithms, particularly those based on swarm intelligence, offer adaptable and efficient solutions to these challenges. In recent years, swarm intelligence algorithms have made significant advancements. Classical and CEC benchmark suits are immersively useful for studying the performance of optimization algorithms. According to our literature survey, we identified that many algorithms were evaluated based on accuracy. Currently, swarm intelligence algorithms are used in many applications, and efficiency and computational complexity need to be evaluated. A broad-level study of the computational complexity and accuracy of popular swarm intelligence algorithms has not been done recently. Therefore this study we comprehensively evaluate and compare 21 bio-inspired swarm intelligence algorithms on eight non-separable unimodal, eight separable unimodal, five non-separable multimodal, seven separable multimodal functions, and two CEC 2018 many objective functions. We study the structure and mathematical model of the selected algorithms. Then we categorized selected algorithms into six different behavioral groups. We calculated the root mean square error between expected and actual values. Then we performed an RMSE cross-validation statistical test to understand how accurately an algorithm resolves an average problem. We found that Artificial Lizard Search Optimization (ALSO) is the most prominent algorithm in accuracy and efficiency. Besides that, Cat Swarm Optimization (CSO), Squirrel Search Algorithm (SSA), and Chimp Optimization Algorithm (CHOA-B) are also considered more universal algorithms. The Squirrel Search Algorithm (SSA) is ALSO’s second-best algorithm in time complexity. Wasp Swarm Algorithm (WSO), and Bat-Inspired Algorithm (BA) presented the lowest time complexity. Finally, several important issues and research directions are discussed.

Hyperbolic Non-Polynomial Spline Approach for Time-Fractional Coupled KdV Equations: A Computational Investigation

The time-fractional coupled Korteweg–De Vries equations (TFCKdVEs) serve as a vital framework for modeling diverse real-world phenomena, encompassing wave propagation and the dynamics of shallow water waves on a viscous fluid. This paper introduces a precise and resilient numerical approach, termed the Conformable Hyperbolic Non-Polynomial Spline Method (CHNPSM), for solving TFCKdVEs. The method leverages the inherent symmetry in the structure of TFCKdVEs, exploiting conformable derivatives and hyperbolic non-polynomial spline functions to preserve the equations’ symmetry properties during computation. Additionally, first-derivative finite differences are incorporated to enhance the method’s computational accuracy. The convergence order, determined by studying truncation errors, illustrates the method’s conditional stability. To validate its performance, the CHNPSM is applied to two illustrative examples and compared with existing methods such as the meshless spectral method and Petrov–Galerkin method using error norms. The results underscore the CHNPSM’s superior accuracy, showcasing its potential for advancing numerical computations in the domain of TFCKdVEs and preserving essential symmetries in these physical systems.

Effect of double-layer formwork curing on the early temperature field and properties of precast concrete components in environments with large diurnal temperature variations

An efficient double-layer formwork curing method using an “inner supporting formwork + outer insulation formwork” was proposed in this study to address the early cracking of precast concrete components in high altitude regions. Steel and plywood formwork were designed as inner support formwork, while polystyrene (PS) and polyurethane (PU) were used as outer insulation formwork. Indoor experiments and two finite element methods (The complete simulation method focuses on computational accuracy, and the equivalent simulation method emphasizes computational efficiency) were employed to analyze the evolution of the concrete temperature field under different double-layer formwork curing methods throughout the curing period, combined with compressive strength and pore structures testing. The results show that steel + 5-mm-thick PU insulation formwork curing method can significantly mitigate the impact of large diurnal temperature variations on the internal temperature of concrete. Unlike traditional steam-curing, this method does not deteriorate the pore structure or compressive strength of the concrete. This study is of great significance in addressing the problem of early cracking of precast concrete components exposed to large diurnal temperature vriations in high altitude regions.

Safety and accuracy assessment of static computer assisted localized piezoelectric alveolar decortication: an in vitro study

ObjectivesTo assess the safety and accuracy of static computer assisted corticotomy surgery (sCACS) in comparison with freehand piezocision.Materials and methodsA randomized in vitro study was conducted. A total of 260 interradicular corticotomies were performed in 20 identical printed models. sCACS was performed in half of the models, while the rest underwent freehand localized decortication. Accuracy was measured in the three spatial axes by overlapping the digital planning with a previous cone-beam computed tomography (CBCT) scan of the patient and a postoperative CBCT of the models. Safety was determined as the number of damaged root surfaces. Descriptive and bivariate analyses were performed.ResultsFreehand corticotomies increased the likelihood of iatrogenic root damage 2.21-fold (95%CI: 1.30 to 3.77; p = 0.004). Both groups showed some degree of deviation compared to digital planning. Nevertheless, the accuracy of sCACS was significantly greater in sagittal (B = -0.21 mm, 95%CI: -0.29 to -0.12; p < 0.001), axial (B = -0.32 mm, 95%CI: -0.48 to -0.18; p < 0.001) and angular deviation (B = -2.02º; 95%CI: -2.37 to -1.66; p < 0.001) compared to freehand surgery, with the exception of depth.ConclusionsThe precision and safety of sCACS are greater than the freehand technique.Clinical relevanceCorticotomies are performed in crowded areas where there is usually space limitation. Clinicians should consider the systematic use of surgical guides, since minimal deviations can cause iatrogenic root damage in areas where malocclusions are present.

Self-Adaptive Moving Least Squares Measurement Based on Digital Image Correlation

Digital image correlation (DIC) is a non-contact measurement technique used to evaluate surface deformation of objects. Typically, pointwise moving least squares (PMLS) fitting is applied to process the noisy data from DIC to obtain an accurate strain field. In this study, a self-adaptive pointwise moving least squares (SPMLS) method was developed to optimize the process of window size selection, thereby attaining superior accuracy in measurements. The premise of this method is that the noise in the displacement field follows white Gaussian noise. Under this assumption, it analyses the random errors and systematic errors of the PMLS method under different calculation window sizes. The optimal size of the calculation window is determined by minimizing the errors. Subsequently, the strain field is computed based on the optimized calculation window. The results were compared with a typical PMLS method. Whether calculating low-gradient strain fields or high-gradient strain fields, the computational accuracy of SPMLS is close to the optimal accuracy of PMLS. This study effectively addresses the inherent challenge of manually selecting window size in the PMLS method.

Numerical Simulation for the Wave of the Variable Coefficient Nonlinear Schrödinger Equation Based on the Lattice Boltzmann Method

The variable coefficient nonlinear Schrödinger equation has a wide range of applications in various research fields. This work focuses on the wave propagation based on the variable coefficient nonlinear Schrödinger equation and the variable coefficient fractional order nonlinear Schrödinger equation. Due to the great challenge of accurately solving such problems, this work considers numerical simulation research on this type of problem. We innovatively consider using a mesoscopic numerical method, the lattice Boltzmann method, to study this type of problem, constructing lattice Boltzmann models for these two types of equations, and conducting numerical simulations of wave propagation. Error analysis was conducted on the model, and the convergence of the model was numerical validated. By comparing it with other classic schemes, the effectiveness of the model has been verified. The results indicate that lattice Boltzmann method has demonstrated advantages in both computational accuracy and time consumption. This study has positive significance for the fields of applied mathematics, nonlinear optics, and computational fluid dynamics.

Influence of side channel inlet angle on energy conversion of a side channel pump

The side channel pump generates several disadvantage vortices due to abrupt structural changes at the junction of the impeller and side channel, leading to unstable flow, which may induce severe vortex cavitation at the inlet section of the side channel, its impact on the pump's unstable flow mechanism and on the energy conversion characteristics has yet to be thoroughly investigated. This paper explores the effect of backflow vortex on pump performance through optimizing side channel inlet angles by combining the Ω criterion, helicity, and entropy production methods. The computational fluid dynamics numerical simulation's accuracy has been experimentally verified. It was found that increasing the side channel inlet angle could improve internal flow, thereby suppressing backflow vortices and promoting dynamic vortices formation in the inlet section. The backflow vortex is the primary source of high localized energy loss in the inlet section, significantly influencing the reduction of flow loss. It also reduces low pressure areas caused by backflow vortices, thus, restricting cavitation origin. In addition, within a certain range, the flat side channel pump enhances its hydraulic performance, exhibiting the best performance at a 60° inlet angle with an efficiency improvement of 4.6% at the Best Efficiency Flow Point (BEP), which has the most effective backflow vortex suppression, and therefore, lowest flow losses. However, the head improvement was negligible. The performance improvement is due to complete energy conversion within the inlet section. This paper offers new insights into the mechanisms underlying internal energy loss and cavitation characteristics in refining side channel pumps.

Parallel implementation and performance of super-resolution generative adversarial network turbulence models for large-eddy simulation

Super-resolution (SR) generative adversarial networks (GANs) are promising for turbulence closure in large-eddy simulation (LES) due to their ability to accurately reconstruct high-resolution data from low-resolution fields. Current model training and inference strategies are not sufficiently mature for large-scale, distributed calculations due to the computational demands and often unstable training of SR-GANs, which limits the exploration of improved model structures, training strategies, and loss-function definitions. Integrating SR-GANs into LES solvers for inference-coupled simulations is also necessary to assess their a posteriori accuracy, stability, and cost. We investigate parallelization strategies for SR-GAN training and inference-coupled LES, focusing on computational performance and reconstruction accuracy. We examine distributed data-parallel training strategies for hybrid CPU–GPU node architectures and the associated influence of low-/high-resolution subbox size, global batch size, and discriminator accuracy. Accurate predictions require training subboxes that are sufficiently large relative to the Kolmogorov length scale. Care should be placed on the coupled effect of training batch size, learning rate, number of training subboxes, and discriminator’s learning capabilities. We introduce a data-parallel SR-GAN training and inference library for heterogeneous architectures that enables exchange between the LES solver and SR-GAN inference at runtime. We investigate the predictive accuracy and computational performance of this arrangement with particular focus on the overlap (halo) size required for accurate SR reconstruction. Similarly, a posteriori parallel scaling for efficient inference-coupled LES is constrained by the SR subdomain size, GPU utilization, and reconstruction accuracy. Based on these findings, we establish guidelines and best practices to optimize resource utilization and parallel acceleration of SR-GAN turbulence model training and inference-coupled LES calculations while maintaining predictive accuracy.

Classification of Lung Diseases in X-Ray Images Using Transformer-Based Deep Learning Models

This research evaluates the performance of two Transformer models, the Vision Transformer (ViT) and Swin Transformer, in the analysis of thoracic X-ray images. The study's objective is to determine whether Transformer models can enhance diagnostic accuracy for lung diseases, considering challenges such as early symptom variability and similar radiological signs. The dataset includes 21,165 X-ray images, featuring 3,616 COVID-19 cases, 10,192 normal images, 6,012 images of Lung Opacity, and 1,345 pneumonia images. Model development involved tuning hyperparameters such as epoch numbers and optimizer choice. The results indicate that using the AdamW and Adamax optimizers achieves an optimal balance between computational efficiency and accuracy. The Swin Transformer model, using the Adamax optimizer, reached the highest testing accuracy of 96.10% in 33,802.70 seconds, while the Vision Transformer achieved a testing accuracy of 95.10% in 33,503.10 seconds.

A novel semi-analytical approach based on scaled boundary finite element method for fluid-structure coupling analysis of liquid sloshing in 3D containers

In this paper, a novel semi-analytical approach is proposed for the three-dimensional fluid-structure coupling analysis of liquid sloshing in elastic containers subjected to harmonic and seismic loading in the horizontal direction, based on the scaled boundary finite element method (SBFEM). A modified SBFEM model, referred to as the scaling surface-based SBFEM, is developed to simulate the container wall, which is treated as a thin shell structure. Within the framework of the scaling surface-based SBFEM, the geometry of the shell structure is entirely determined by scaling one surface of the structure. This approach differs significantly from the standard SBFEM, where approximation is achieved through coordinate mapping based on a scaling center, thereby enhancing the modeling accuracy and efficiency. Hydrodynamic pressure is treated as an independent nodal variables in the governing equations of the fluid domain, which is modeled using the standard scaling centre-based SBFEM. The coupled fluid-structure system is assembled by applying equilibrium and compatibility boundary conditions to ensure the balance of interaction forces. A synchronous solution algorithm, combined with the implicit-implicit scheme of the Newmark method, is used to determine the dynamic responses of the coupled system. The main advantage of this novel approach is that it meshes and discretizes the boundaries instead of the entire structural and fluid domains, thereby reducing computational costs. Additionally, analytical solutions can be obtained along the radial direction of the interior domain, enhancing the accuracy and convergence of the results. Another advantage is the approach's ability to provide a unified modeling framework for structures of any shape. Furthermore, the asymmetry issue of the coefficient matrix can be effectively avoided by using a synchronous solution algorithm. Benchmark examinations confirm the superior computational accuracy and robustness of the proposed approach. A comprehensive parametric study is conducted, focusing on the effects of liquid filling levels, as well as geometric and material parameters, on the transient vibration and distribution behaviors of the fluid-structure coupling system.

A pseudo-density conjugate heat transfer method and its application to simulating the quasi-steady temperature field of a compressor cylinder

The substantial disparity in time scales between heat conduction and convection requires extremely tiny time steps in simulations, leading to significant computational demands when using current-tightly coupled methods to solve the temperature field of cylinders at the quasi-steady stage. A new pseudo-density method is proposed to accelerate the heat conduction rate. The influence of solid density on transient temperature under the periodic third-type boundary conditions is analyzed in a one-dimensional model by analytical methods and verified in a three-dimensional structure by numerical methods. It is found that reducing solid density can accelerate the heat conduction rate and increase the fluctuation amplitude of solid temperature. Therefore, a variable pseudo density is adopted for solids in the simulation of the transient heat transfer characteristics between the compressed gas and the cylinder. The results show that the pseudo-density method provides similar computational accuracy to the current tightly coupled methods, but at significantly lower computational cost. The fluctuation amplitude of the cylinder's temperature decreases rapidly in the wall thickness direction. The distribution of the convective heat transfer coefficient on the inner wall of the cylinder is extremely transient and highly non-uniform, which is consistent with the distribution of gas velocity near the cylinder wall.

A simplified interpolation algorithm for the numerical simulation of the consolidation in composite foundation containing group of stone columns

Based on Biot consolidation theory, a simplified interpolation algorithm under the finite element method and a corresponding modeling method for group of stone columns are proposed to solve the consolidation simulation problem of composite foundation containing group of stone columns. The correctness of the modeling method and computational program is confirmed by comparing the results from the unit cell model with those from axisymmetric model and analytical solution. Subsequently, the composite foundation model is used to verify the accuracy of this method in calculating the settlement change and consolidation time under load for composite foundation containing group of stone columns. Compared to detailed modeling, this method gets satisfactory results with simpler modeling and less computation time. In comparison to homogenization method, this method offers better computational accuracy and enables the stress analysis of stone column. Additionally, discussions on mesh sensitivity, number of stone columns and the influence of the upper structure provide guidelines for the application of this method in practical engineering projects.

Mathematical modeling and simulations using software like MATLAB, COMSOL and Python

This study explores the application of MATLAB, COMSOL, and Python in mathematical modeling and simulation within precision engineering. These tools are analyzed for their strengths in handling various engineering challenges, from control systems to multiphysics simulations and custom algorithm development. The study also investigates the role of artificial intelligence (AI), in supporting mathematical modeling tasks by automating coding, providing concept explanations, and aiding model structuring. By comparing computational performance, accuracy, and usability, the research aims to identify the best-suited software for different simulation types, such as thermal-fluid dynamics and structural analysis. The findings underscore the significance of choosing appropriate software for optimizing computational resources, validating models, and achieving reliable, efficient simulations. This study contributes practical guidelines for bridging the gap between theoretical models and practical applications, enhancing productivity, and fostering innovation in precision engineering.

Integrating AlphaFold pLDDT Scores into CABS-flex for enhanced protein flexibility simulations

CABS-flex is a well-established method for fast protein flexibility simulations, offering an effective balance between computational efficiency and accuracy in modeling protein dynamics. To further enhance its predictive capabilities, we propose incorporating AlphaFold's predicted Local Distance Difference Test (pLDDT) scores into CABS-flex simulations. The pLDDT scores, which reflect the confidence of AlphaFold's structural predictions, were integrated with secondary structure information to refine the restraint schemes used in the simulations. We tested this approach on the ATLAS database, which includes molecular dynamics (MD) simulations of nearly 1400 proteins. The results showed improved alignment of flexibility predictions with the MD data compared to previous restraint schemes. The integration of pLDDT scores also offers a new perspective on protein flexibility by incorporating structural confidence into the analysis. This development enhances the utility of CABS-flex for investigating protein dynamics and motion.

Innovative vacuum distillation technology for preparing refined Al from Al–Mg alloy

This study presents an advanced approach utilizing vacuum distillation (VD) to purify Al from Al–Mg alloys. The activity coefficients of Al-Mg binary alloy components were meticulously determined by applying the molecular interaction volume model (MIVM), non-random two-liquid (NRTL) model, and Wilson equation. Comparative analysis between experimental data and calculated activity coefficients enabled the selection of an optimal model exhibiting high computational accuracy and extensive applicability. The NRTL model, chosen for its precision, was then employed to compute the activity coefficients of Al-Mg alloy across various temperatures, leading to the development of a vapor-liquid equilibrium (VLE) diagram. This VLE diagram provides a robust quantitative foundation for assessing the purification limits of Al within the temperature range of 973–1373 K in the distillation process. Theoretical analyses underscore that VD offers a rapid and efficient method for Al purification. Experimental verification at a kilogram scale, conducted at 1373 K for 120 min, achieved an Al purity level of 99.9989% with a direct recovery efficiency of 97.98%. Notably, this VD process aligns with environmental standards for sustainable metallurgical practices, as it prevents the release of gaseous emissions or effluents, thereby meeting the industry’s growing demand for eco-friendly Al recycling methods.

Soret and Dufour effects in two-phase boundary layer flow of non-Newtonian and Newtonian fluids with uniform shear strength ratio

BackgroundThis study numerically investigates heat and mass transfer in two-phase boundary layer shear flows, focusing on a non-Newtonian Casson fluid interacting with an adjacent Newtonian fluid under the influence of thermal radiation. By incorporating both Soret and Dufour effects, we examine how temperature gradients influence mass flux and how concentration differences affect energy flux. These coupled effects are essential for applications involving simultaneous heat and mass transport, such as chemical reactors, separation processes, and thermal management systems. MethodsThe analysis explores boundary layer convergence with varying shear intensities, utilizing the MATLAB solver “bvp4c” with appropriate similarity transformations for computational accuracy. The resulting numerical data are presented in graphical form to illustrate the impact of key parameters on flow characteristics. Additionally, variations in the Sherwood number, Nusselt number, and interfacial shear stress are depicted for each fluid across different parameter values. To evaluate the accuracy of our numerical method, we conducted a comparative analysis with the results reported by Weidman and Wang [4] and Wang [2]. This comparison demonstrated an excellent match, confirming the reliability of our approach, as shown in Table 1 and Fig. 2. Significant findingsThe results demonstrate that the fluid temperature increases with the Dufour number, while the concentration rises with the Soret number. Higher Casson parameter values lead to a reduction in interfacial shear stress in both fluids. Furthermore, the Nusselt and Sherwood numbers increase with an enhanced radiation parameter, highlighting the influence of thermal radiation on heat and mass transfer. These insights offer a valuable understanding of flow behavior in systems with coupled thermal and concentration gradients.