Physical Model Parameters Research Articles

Dynamics and hazards of pyroclastic avalanches at Etna volcano (Italy)

We present a multidisciplinary research aimed at quantifying the conditional probabilities for hazards associated with pyroclastic avalanches at Etna, which combines physical and numerical modeling of granular avalanches and probabilistic analysis. Pyroclastic avalanches are modeled using the depth-averaged model IMEX-SfloW2D, which is able to simulate the transient propagation and emplacement of granular flows generated by the collapse of a prescribed volume of granular material. Preliminary sensitivity analysis allowed us to identify the main controlling parameters of the dynamics, i.e. the total avalanche mass, the initial position of the collapsing granular mass (and the associated terrain morphology), the initial avalanche velocity, and the two rheological parameters which determine the mechanical properties of the flow. While the first two parameters can be considered as “scenario parameters” in the definition of the hazards, the initial velocity and the rheological parameters need to be calibrated. We therefore adopted a methodology for the statistical calibration of the physical model parameters based on field observations. We used data from the pyroclastic avalanche that occurred on February 10, 2022 at Etna, for which we had an accurate mapping of the deposit and some estimates of the total mass and the initial volume. We then run a preliminary ensemble of numerical simulations, with fixed initial volume and position, to calibrate the other input parameters. Based on the accuracy of the matching of the simulated and observed deposits (measured by the Jaccard Index), we extracted from the simulation ensemble a subsample of equally probable combinations of initial velocities and rheological parameters. We then built an ensemble of model input parameters, with varying (i) avalanche volumes, (ii) initial positions, (iii) velocity, and (iv) rheological coefficients. The initial volume range was chosen within the range of observed pyroclastic avalanches at Etna (i.e., between 0.1 and 3 × 106 m3), using a prescribed probability distribution extracted from the literature data. The initial positions have been chosen on the flanks of the South East Crater of Etna, with homogeneous spatial distribution. The initial velocity and the rheological coefficients were chosen from the subsample created with the calibration. Finally, a semi-automatic procedure (digital workflow) running the Monte Carlo simulation allowed us to produce the first probabilistic map of pyroclastic avalanche invasion at Etna. Such a map, conditional to the occurrence of a pyroclastic avalanche event, can be used to identify the hazardous areas of the volcano and to plan mitigation measures.

Exploring Optimal Complexity for Water Stress Representation in Terrestrial Carbon Models: A Hybrid‐Machine Learning Model Approach

AbstractTerrestrial biosphere models offer a comprehensive view of the global carbon cycle by integrating ecological processes across scales, yet they introduce significant uncertainties in climate and biogeochemical projections due to diverse process representations and parameter variations. For instance, different soil water limitation functions lead to wide productivity ranges across models. To address this, we propose the Differentiable Land Model (DifferLand), a novel hybrid machine learning approach replacing unknown water limitation functions in models with neural networks (NNs) to learn from data. Using automatic differentiation, we calibrated the embedded NN and the physical model parameters against daily observations of evapotranspiration, gross primary productivity, ecosystem respiration, and leaf area index across 16 FLUXNET sites. We evaluated six model configurations where NNs simulate increasingly complex soil water and photosynthesis interactions against test data sets to find the optimal structure‐performance tradeoff. Our findings show that a simple hybrid model with a univariate NN effectively captures site‐level water and carbon fluxes on a monthly timescale. Across a global aridity gradient, the magnitude of water stress limitation varies, but its functional form consistently converges to a piecewise linear relationship with saturation at high water levels. While models incorporating more interactions between soil water and meteorological drivers better fit observations at finer time scales, they risk overfitting and equifinality issues. Our study demonstrates that hybrid models have great potential in learning unknown parameterizations and testing ecological hypotheses. Nevertheless, careful structure‐performance tradeoffs are warranted in light of observational constraints to translate the retrieved relationships into robust process understanding.

Prediction and evaluation of key parameters in coalbed methane pre-extraction based on transformer and inversion model

Accurate parameter prediction in the coalbed methane (CBM) pre-extraction process is crucial for formulating effective control measures and preventing CBM-related accidents. Traditional prediction methods rely on feature extraction or complex physical model parameter calculations, which require extensive manual intervention and have limited practical applicability. Additionally, simple neural network methods are prone to overfitting and gradient vanishing when handling parameters, and they lack the capability to dynamically monitor gas pressure during extraction, leading to inefficient and blind extraction operations. This study proposes a CBM pre-extraction parameter and completion time prediction method based on the Transformer model. By integrating autoregressive models and wavelet denoising techniques, the approach effectively captures temporal features and long-term dependencies in CBM data. Experimental results demonstrate that the proposed model outperforms traditional methods in short-, medium-, and long-term predictions, with a median R2 value of 0.99072, and 76% of the training results exceeding 0.9. Furthermore, a CBM pressure inversion model was developed, combining dimensional analysis and physical similarity principles with the Transformer model, enabling the dynamic detection of high- and low-pressure regions in coal seams. In single borehole compliance time predictions, the median compliance time for the first stage is 4 days, with an average of 49 days and a maximum of 277 days, providing adjustment guidance for boreholes with extended compliance times. The proposed model significantly improves prediction accuracy and stability, offering critical support for developing scientifically sustainable pre-extraction plans and advancing intelligent CBM management.

Equivalence Ratio-Driven Flame Response of an Industrial Premixed Burner: Experiments and Modeling

Abstract This paper presents an analysis of the unsteady heat release rate response of premixed flames to equivalence ratio perturbations for an industrial premixed swirl-based burner. During this investigation, perfectly and technically premixed flames were acoustically forced via fuel/air mixture flow and air flow modulations, respectively, at the same operating conditions. From the resulting flame transfer functions (FTFs), measured using the multimicrophone method, the equivalence ratio driven FTF was isolated and extracted by removing the velocity driven component, i.e., the measured FTF from the perfectly premixed flame, from the technically premixed FTF with two novel extraction techniques. The results are compared with FTFs obtained directly in a previous experimental campaign where the fuel flow was acoustically forced, the resulting equivalence ratio fluctuations measured via an infrared absorption technique, and the heat release rate response to the forcing was quantified using chemiluminescence measurements. The results from both measurement approaches agreed well highlighting the validity of the techniques. Further, to understand the governing features of the equivalence ratio driven FTF, a physics-based analytical model following the G-equation approach was developed. The contributions from flame surface area, flame speed, and heat of reaction oscillations were modeled to describe the heat release rate dynamics. A limited number of physical parameters in the analytical model were anchored on one test condition, optimized and restricted to values, which were all physically reasonable, and were subsequently used for model predictions at other operating conditions. The FTF model predictions compared well with experimental data across a range of different operating conditions. Finally, the relative contributions from flame surface area, flame speed, and heat of reaction oscillations on the features of the FTFs were identified and explored.

A physics-informed neural network method for identifying parameters and predicting remaining life of fatigue crack growth

Predicting the remaining life of fatigue cracks is crucial for planning maintenance and repair strategies to prevent untoward incidents. This paper proposes a novel physics-informed neural network (PINN) method for identifying parameters and predicting remaining fatigue crack growth life (FCGL). Initially, the relationship between crack length and fatigue cycles is established through a neural network, and the gradient of fatigue cycles with respect to crack length is obtained by automatic differentiation. Subsequently, a composite loss function is designed to incorporate this gradient within the confines of physical knowledge, ensuring that the established relationship not only aligns with observed data but also adheres to physical knowledge. Furthermore, during the network training, the parameters in physical models are simultaneously updated to better conform to the individuality of the monitored subject. All predicted remaining FCGLs fall within the 1.5 times error band. Compared to purely data-driven or physics-based methods, the proposed method offers more robust and accurate predictions of remaining FCGLs.

Assessment of the Choked Flow Model of RELAP5 for Application of Inverse Quantification Methods

In the framework of deterministic safety analysis, best estimate plus uncertainty methodologies can provide a more informative detailed analysis of transients than conservative approaches. However, one important step in the application of such methodologies is derivation of uncertainty of the physical models. Probability density functions of the physical model parameters are obtained by applying inverse uncertainty quantification (IUQ) methods to experimental data. The present work deals with evaluation of the experimental database and assessment of the simulation model, which are required steps prior to the application of IUQ methods. The U.S. Nuclear Regulatory Commission system code RELAP5 has been applied for simulation of three experimental databases on choked/critical flow: Sozzi-Sutherland, Super MobyDick, and Marviken Critical Flow Tests. First, the adequacy of the experimental data to the specific target domain is carried out, to then proceed to calibration of the input model parameters by combining the use of Gaussian Process metamodels and optimization schemes. The assessment of the simulation models is performed by evaluating independently accuracy, precision, and consistency through four statistical indicators, including a novel indicator to evaluate the consistency of the results. The final results indicate that the model is capable of reproducing the selected experimental database and overall average accuracy, precision, and consistency below the 10% threshold and can be used for application of IUQ methods.

Ratio of physical model parameters can retrieve aggregate size from different types of soil in cultivated regions

Soil aggregate size, which is a proxy used to guide agricultural decisions and tillage management, can be estimated using optical remote sensing techniques. However, limited investigation has been conducted into the potential of using a physical model to retrieve soil aggregate size (< 2 mm) from different types of soil. This study is based on the multi-angular spectral measurements of seven soil samples from five soil types with 14 aggregate size fractions collected in Northeast China, three versions of the Hapke model were inverted using the Bayesian method. The findings confirmed that all three versions of the Hapke model can well characterize the angular reflection characteristics of all soil samples with different aggregate sizes. The inverted photometric parameters such as single scattering albedo ω, shape parameter b, and asymmetry parameter c were found to be sensitive to soil aggregate size, but the relationships rely on soil types because of the dependence of parameters related to soil composition. In order to obtain a general model that can be applied to different types of soil, the ratio of parameters (RoP) = (b + c)/ω, which is controlled by the external structure of soil aggregates, was proposed to retrieve the aggregate size from different soil types. Results show that the RoP can robustly capture the aggregate size of the soil with high accuracy and is insensitive to soil types. The combination of photometric parameters related to soil aggregate size provides a new method for retrieving the structural properties of the soil by eliminating interfering factors.

Numerical investigation of diamond complementary logic integrated circuits

Silicon complementary metal oxide semiconductor (CMOS) technology drives the integrated circuit industry due to its energy efficiency. The narrow bandgap of silicon has led to the development of wide bandgap semiconductor materials, such as diamond, favored in power electronics, radiofrequency and extreme environment applications. Here we have established a model of the diamond CMOS logic inverter for the first time and successfully simulated the static and dynamic characteristics. The simulated physical model and relevant model parameters are well calibrated with experimental data of diamond p-FET in the literature. The simulation results demonstrate that the all-diamond CMOS inverters possess rail-to-rail operation and excellent inversion characteristics, with the peak gain of 83 V/V, the transition region of 0.25 V, and the noise margins for low and high level of 2.44 V and 2.26 V under VDD = 5 V. Particularly, all-diamond CMOS inverters have improved performance compared to the diamond-GaN inverters, operating at 500 °C with well-preserved inversion characteristics. This thermal reliability indicates that diamond CMOS inverters can be better monolithically integrated for applications in high-temperature environments in the future.

Calculating micro- and macro-scale bone quality parameters from computed tomography images using a parametric physical model and standard bone composition

Bone quality parameters (BQPs) calculated from computed tomography (CT) and micro-computed tomography (μCT) images have been applied in clinical to diagnose and prevent osteoporotic fractures. However, the BQPs calculated from CT and μCT images are at different scales and incomparable due to the differences in image resolutions and accounted bone compositions. In this study, we proposed a novel method to convert HU values of CT images into the BQPs that were originally calculated using different tools. By using the standard bone composition of human bones, the BQPs of bone volume fractions (BV/TV) and volumetric bone mineral densities (vBMD) of the bones were calculated using different accounted compositions of bones and mathematical relationships defined in this study. In addition, the HU values of the bones were estimated using a parametric physical model and spectrum characteristic parameters. Relationships for converting HU values into BQPs were determined by linear fitting the calculated BQPs and estimated HU values. Cadaveric and patient studies show that the micro-scale bone volumes and macro-scale vBMDs of vertebrae calculated from CT images using the conversion relationships determined by the proposed method were close to those calculated from the μCT images and quantitative CT, respectively, with mean percent errors lower than 5%. The proposed method could be applied in clinical to accurately compute micro- and macro-scale BQPs from CT images for assessing the bone quality of patients.

Grain boundary segregation for the Fe-P system: Insights from atomistic modeling and Bayesian inference

In this work we re-assess experimental data for grain boundary (GB) segregation of P in bcc Fe with thermodynamic and statistical methods. The data are based on Auger-Electron-Spectroscopy (AES) measurements which have provided P GB concentrations for various bulk contents and temperatures for ferrite. While in the previous investigations of this system a single-site McLean equation was used to extract segregation enthalpy and entropy, we employ multi-site segregation models as suggested by atomistic simulations. We use a recently introduced methodology based on inter-atomic potentials to calculate the segregation energy spectrum, as well as vibrational entropy and solute-solute interactions of P in polycrystalline Fe, thereby obtaining a three-dimensional distribution of energy, entropy and interactions. Using this trivariate distribution we predict P GB concentrations and compare them to the experimental measurements. Furthermore, we calibrate the parameters of physical models of increasing complexity to the experimental data with an inverse modeling approach based on Bayesian inference. While it is not possible to seamlessly link the results from AES to atomistic modeling, our investigation provides significant new insights for thermodynamic modeling of GB segregation. The vibrational entropy deduced from experiment differs from physics based atomistic simulations even when taking the spectral nature of energy, entropy and interactions into account. However, the correlations of the quantities are in good agreement when considering the trivariate model. Our investigation highlights the need for new and more accurate experimental datasets of GB segregation.

Learning to solve Bayesian inverse problems: An amortized variational inference approach using Gaussian and Flow guides

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies epistemic uncertainty. Since analytical posteriors are not typically available, one resorts to Markov chain Monte Carlo sampling or approximate variational inference. However, inference needs to be rerun from scratch for each new set of data. This drawback limits the applicability of the Bayesian formulation to real-time settings, e.g., health monitoring of engineered systems, and medical diagnosis. The objective of this paper is to develop a methodology that enables real-time inference by learning the Bayesian inverse map, i.e., the map from data to posteriors. Our approach is as follows. We parameterize the posterior distribution as a function of data. This work outlines two distinct approaches to do this. The first method involves parameterizing the posterior using an amortized full-rank Gaussian guide, implemented through neural networks. The second method utilizes a Conditional Normalizing Flow guide, employing conditional invertible neural networks for cases where the target posterior is arbitrarily complex. In both approaches, we learn the network parameters by amortized variational inference which involves maximizing the expectation of evidence lower bound over all possible datasets compatible with the model. We demonstrate our approach by solving a set of benchmark problems from science and engineering. Our results show that the posterior estimates of our approach are in agreement with the corresponding ground truth obtained by Markov chain Monte Carlo. Once trained, our approach provides the posterior distribution for a given observation just at the cost of a forward pass of the neural network.

Theoretical derivation of super-ellipse model as approximation of physics-based implicit model for solar PV

Recently, it has been shown that the super-ellipse model can be used to represent the voltage-current characteristics of illuminated solar PV modules. Since the model is claimed to be empirical in nature, this paper demonstrates that the super-ellipse model can be derived as a theoretical approximation of the physics-based implicit model of solar PV. Further, the model parameters used in the super-ellipse model can be approximated to the physical parameters of the implicit model of solar PV. Here, it is also shown how the model parameters of the super-ellipse model vary with the ambient temperature and solar irradiance. The super-ellipse model is compared with other explicit models for different solar modules and shows satisfactory results in representing the voltage-current (current–density) curve of the solar PV module.

Effect of polarized colliding beam on Higgs boson production at the lepton collider

Different production processes involving the Higgs boson, such as annihilation and W/Z boson fusion, will be observed in the International Linear Collider (ILC). The ILC operates at a center-of-mass (CM) energy of [Formula: see text]–1000[Formula: see text]GeV. The study reveals that the production cross-section can either be enhanced or reduced depending on the CM energy and the specific combination used, which has implications for selecting appropriate production processes. Additionally, this investigation highlights that by polarizing beams, the number of measurable observables increases. These observables, such as left–right asymmetry, detailed effective polarization, and adequate effective luminosity, are crucial to ascertain contemporary physical parameters in physics models absurdly the Standard Model (SM).

Calibration Method of PFC3D Micro-Parameters under Impact Load

Micro-parameter calibration is essential in constructing an accurate and reliable numerical model of particle discrete element PFC3D 6.0 software. Micro-parameter calibration is mainly accomplished according to the macro-parameters obtained from static or quasi-static laboratory tests such as UCS. However, there is little current research concerning the calibration method under impact load. An SJM micro-parameter calibration method, based on the SHPB rock test and the FLAC3D/PFC3D coupling method, is proposed to solve this problem. Firstly, UCS, SHPB, and other laboratory rock tests were carried out to determine the rock sample’s macroscopic physical and mechanical parameters. Secondly, the FLAC3D/PFC3D numerical coupling model of the SHPB test was established, and the single-factor and double-factor orthogonal numerical simulation was carried out. Then, the main micro-parameters that affect the macroscopic physical and mechanical parameters of the SJM particle discrete element model were proposed. Finally, the quantitative relationship between the model’s macro-parameters and micro-parameters was established through multiple linear regression. A set of PFC3D micro-parameter calibration processes under impact load was established. The relative errors of the macro-parameters obtained from laboratory and numerical tests totaled less than 5%, which further verifies the rationality of the calibration method. This method provides some reference values for PFC3D micro-parameter calibration under impact load.

Dynamic modelling and a dual vector modulated improved model predictive control with auto tuning feature of active front‐end converters for distributed energy resources

AbstractThe operational performance of grid‐connected active front‐end converters (AFEs) faces challenges arising from the intricate interplay among phase‐locked loop (PLL) non‐linearities, grid impedance, and conventional control strategies, resulting in compromised stability. This study introduces a refined approach to dynamic model predictive control (MPC) by integrating recursive least squares (RLS) for the precise estimation of physical model parameters, thereby addressing stability concerns. Unlike conventional methodologies, the proposed enhanced RLS‐based MPC approach, equipped with an auto‐tuning feature, allows for the design of controllers without a prerequisite understanding of exact external dynamics. Notably, this technique exhibits exceptional disturbance rejection capabilities. The evaluation of the cost function at each sampling interval facilitates the determination of optimal switching states based on predicted variables. Gate pulses for the switches of the AFEs are generated accordingly. Employing a simulation platform, the proposed control structure's performance across varied conditions is comprehensively assessed, encompassing alterations in grid impedance and system non‐linearities. The method adeptly integrates inherent non‐linearities within the system, showcasing exceptional robustness in diverse dynamic scenarios. To further substantiate the efficacy of the proposed control system over conventional approaches, simulation results are validated using a laboratory hardware platform equipped with Typhoon HIL and dSPACE real‐time emulators, providing tangible evidence of the proposed control system's effectiveness in real‐world hardware setups. The multifaceted approach, encompassing precise parameter estimation, predictive control, auto‐tuning, disturbance rejection, robust design, and real‐time evaluation, collectively establishes a resilient foundation for enhancing and maintaining the overall stability of the system across diverse operating scenarios.

Bayesian physical–statistical retrieval of snow water equivalent and snow depth from X- and Ku-band synthetic aperture radar – demonstration using airborne SnowSAr in SnowEx'17

Abstract. A physical–statistical framework to estimate snow water equivalent (SWE) and snow depth from synthetic aperture radar (SAR) measurements is presented and applied to four SnowSAR flight-line data sets collected during the SnowEx'2017 field campaign in Grand Mesa, Colorado, USA. The physical (radar) model is used to describe the relationship between snowpack conditions and volume backscatter. The statistical model is a Bayesian inference model that seeks to estimate the joint probability distribution of volume backscatter measurements, snow density and snow depth, and physical model parameters. Prior distributions are derived from multilayer snow hydrology predictions driven by downscaled numerical weather prediction (NWP) forecasts. To reduce the signal-to-noise ratio, SnowSAR measurements at 1 m resolution were upscaled by simple averaging to 30 and 90 m resolution. To reduce the number of physical parameters, the multilayer snowpack is transformed for Bayesian inference into an equivalent one- or two-layer snowpack with the same snow mass and volume backscatter. Successful retrievals meeting NASEM (2018) science requirements are defined by absolute convergence backscatter errors ≤1.2 dB and local SnowSAR incidence angles between 30 and 45∘ for X- and Ku-band VV-pol backscatter measurements and were achieved for 75 % to 87 % of all grassland pixels with SWE up to 0.7 m and snow depth up to 2 m. SWE retrievals compare well with snow pit observations, showing strong skill in deep snow with average absolute SWE residuals of 5 %–7 % (15 %–18 %) for the two-layer (one-layer) retrieval algorithm. Furthermore, the spatial distributions of snow depth retrievals vis-à-vis lidar estimates have Bhattacharya coefficients above 94 % (90 %) for homogeneous grassland pixels at 30 m (90 m resolution), and values up to 76 % in mixed forest and grassland areas, indicating that the retrievals closely capture snowpack spatial variability. Because NWP forecasts are available everywhere, the proposed approach could be applied to SWE and snow depth retrievals from a dedicated global snow mission.

Dynamics of pollutant dispersion and solid–fluid interfacial layer in Jeffrey nanofluid flow subjected to waste discharge concentration: Implementation of probabilists’ Hermite polynomial collocation method

The current study explores the flow of a Jeffrey nanofluid with the impact of a non-uniform heat source/sink and magnetic effects over a stretching sheet by accounting for a pollutant’s transient dispersion after being released from a source outside the system. The need to enhance the efficiency of prospective future technologies, including heat exchangers, solar collectors with nanoscale solid particles suspended in the base fluid, powered engines, pharmaceutical procedures, and hybrid microelectronics, has grown recently. Graphene is treated as a nanoparticle and NaA lg as a base liquid. To emphasize the thermal integrity of the flow that is now taken into consideration, the influence of the diameter of the nanoparticle and the liquid–solid interfacial layer is also shown at the molecular level. The modeled equations are transformed into ordinary differential equations by means of the appropriate similarity transformations. Probabilists’ Hermite polynomial collocation technique is employed to solve these nonlinear dimensionless ODEs, and the graphical representations are created for certain significant values of the underlying physical parameters in the flow model. The result reveals that as Deborah number increases, velocity upsurges but temperature declines. A rise in concentration is observed when the local pollutant external source variation parameter rises. The temperature is enhanced with the advanced values of non-uniform heat source/sink parameters.

Physical model-based ArF photoresist formulation development

Since the logic 28 nm technology and beyond, ArF immersion lithography has been widely used in manufacturing. To fully utilize the potential of the lithographic resolution, process simulation has been used since the lithography process setup step. The accuracy of the model prediction can be a key factor in the process stability, defectivity, and yield of the final product. To get better model prediction, it is very important to develop a process model with as many parameters as possible with physical meanings. Since the analysis of exposure data with a physical model can provide insights into the process and the photoresist material, it may greatly accelerate the photoresist formulation development or improvement process. From another aspect, as the function of the photoresist is to record the aerial image information on wafer, theoretically, the photoresist image should not deviate much from the aerial image or it will inevitably reduce the information content of the aerial image, i.e., through various kinds of averaging, mixing, etc. Since the emergence of Optical Proximity Correction (OPC), the time that takes to finalize a photolithography process has been significantly lengthened and made more complicated. To make the OPC model more reliable and less dependent on patches, a more physical OPC model is necessary. Therefore, it is clear that if we can develop a photoresist formulation to realize a more physical photoresist image, or a photoresist image closer to the aerial image, we can greatly improve the photolithography process performance and the time consumed for the process setup including OPC. In this paper, we focus on several physical model parameters for photoresist, especially the effective photoacid diffusion length and photo decomposable base parameters. We will show that these two parameters can provide a good description of photoresist imaging behavior, and the resist formulation can be improved to match the physical model prediction with more accuracy.

Computational investigation of thermal process in radiated nanofluid modulation influenced by nanoparticles (Al2O3) and molecular (H2O) diameters

Abstract The study of variety of Newtonian nanofluids subject to various physical model parameters gained much interest of engineers and scientists. Owing to their coolant and absorption characteristics, these are broadly found in chemical engineering, biomedical engineering (expansion and contraction of veins and arteries), detection of cancer cells through magnetic nanoparticles, microchips, and particularly in petroleum industry. This study focuses on investigation of nanofluid heat transfer applications inside a channel formed by expanding/contracting walls. A new heat transport model is introduced by adding the effects of nanoparticles and molecular diameters, thermal radiations, and walls permeability. Then, numerical code for the model is developed and executed to analyze the dynamics of the model from physical aspects. For expanding (${\alpha }_1 = 1.0,2.0,3.0,4.0$) and contracting (${\alpha }_1 = - 1.0, - 2.0, - 3.0, - 4.0$) walls, the velocity is examined maximum in the channel center. However, the fluid movement in the working domain is in reverse proportion for ${Re} = 1.0,3.0,5.0,7.0$. Further, high absorbent walls (${A}_1 = 0.1,0.3,0.5,0.7$) controlled the motion for both ${\alpha }_1 &amp;gt; 0$ and ${\alpha }_1 &amp;lt; 0$, respectively. The addition of thermal radiation number ${Rd} = 0.1,0.3,0.5,0.7$ played the role of catalytic parameter which imperatively increased the fluid temperature. Further, contracting walls and temperature ratio number ${\theta }_r = 0.1,0.3,0.5,0.7$ reduced the temperature and this decrease is rapid in conventional fluid.

Mathematical modeling and extraction of parameters of solar photovoltaic module based on modified Newton–Raphson method

This paper presents a numerical method for estimating four physical parameters of a single-diode circuit model based on manufacturer’s datasheet. A system of four non-linear equations are formed based on three key points of PV characteristics. The photocurrent, saturation current, ideality factor and the series resistance are solved iteratively using the proposed method. The suggested method is validated using RTC France solar cell, Chloride CHL285P and Photowatt PWP210 modules and the results are verified with respect to the in-field outdoor measurements. The proposed method shows a good agreement with the experimental data. Lastly, The model chosen is simulated under MATLB environment to assess the effects of external physical weather conditions, that is, temperature and solar irradiance. The advantage of the proposed method with respect of existing numerical techniques is that it converged faster than the widely used Newton method. Modeling of PV cell/module is essential in predicting performance of photovoltaic generators at any operating condition.