Graphical Plots Research Articles

Assessing the impact of hard data patterns on Bayesian Maximum Entropy: a simulation study.

This study empirically tested the robustness of Bayesian Maximum Entropy (BME) in predicting spatiotemporal data, with an emphasis on skewness, sample size, and spatial dependency level. Simulated data, both Gaussian and non-Gaussian, were generated using the unconditional sequential simulation method, with sample sizes ranging from 100 to 500 at the interval length of 50 and varying skewness (0, 1, 3, 6 and 9) and spatial dependency levels (weak, moderate, and strong). Findings revealed sample size variations and spatial dependence levels did not significantly influence BME prediction's Mean Square Error (MSE) and bias. While skewness significantly impacted MSE (p-value < 0.001), bias remained unaffected. Moreover, skewness and spatial dependence interactions affected both MSE and bias. Despite this, BME proved robust to sample size and skewness, demonstrating a negligible MSE on the graphical plot (heatmap).

Significance of heat transfer in a reversible esterification of Arrhenius activation energy with partial slip

The significance of heat transfer during a reversible esterification process in a magnetohydrodynamic boundary layer Casson fluid flow along a vertical stretching plate is examined. The multi-slip conditions are considered in a porous medium. The presence of chemical process requiring an activation energy is considered in the analysis. The study also investigates the hydromagnetic boundary layer Casson fluid flow alongwith partial slip conditions across a vertical stretching plate. The incorporation of multi-slip constraints in a porous medium, alongside magnetic fields and other parameters, highlights its relevance in diverse engineering fields such as thermal engineering, polymerization, and biodiesel industries. Understanding the characteristics of such fluids under complex conditions is vital for optimizing heat and mass transfer in industrial applications, making this investigation timely and valuable. The nonlinear differential set of equations are solved numerically involving Runge Kutta based shooting approach of fourth order and the results are verified with the bvp4c tool and the findings are explored using graphical plots. The predominance of significant factors on flow configurations are analyzed and presented in graphs and tables. A comprehensive analysis is provided on the effects on velocity, concentration, and temperature of diverse parameters such as reaction rate constant, magnetic parameter, suction parameter, mass Grashof number, Prandtl number, Casson parameter, thermal radiation parameter and slip parameters. The tabular representation of the adverse effects of drag coefficient, rate of mass transfer and Nusselt number on flow configurations for various significant parameters is presented. It is inferred that for the case of reversible and irreversible flows, the shear stress rate escalates by 29% when the magnetic parameter elevates from 0.5 to 1.5 and about 35% when the Casson parameter elevates from 0.5 to 1.5. For the suction parameter, the coefficient of drag increased by 27% and 26% for irreversible and reversible flows respectively. When the reaction rate increases from 0.5 to 1.5, the rate of shear stress elevates by 0.5% and 0.02% for irreversible and reversible flows in order. The Nusselt number decreased about 7% and 8% when the magnetic parameter and Casson parameter rises from 0.5 to 1.5 respectively, for irreversible and reversible flows. It is noteworthy that the previous studies are in precise agreement with the present investigation.

Fluxfinder: An R Package for Reproducible Calculation and Initial Processing of Greenhouse Gas Fluxes From Static Chamber Measurements

AbstractFluxes of greenhouse gases are a critical component of the earth's natural climate, but anthropogenic emissions have created an imbalance and resulted in global climate change. Quantifying the emission of these gases is vital to our understanding of their sources and sinks, both natural and anthropogenic. The static chamber method, in which a system of interest is enclosed, and gas concentrations are measured over time, is widely used to estimate fluxes of greenhouse gases. With the development of instruments such as infrared gas analyzers (IRGAs) supporting high‐frequency concentration data, there is a growing need for open‐source workflows to calculate fluxes. Here we present fluxfinder, an R package designed to support reproducible calculations and processing of greenhouse gas fluxes measured with the static chamber method. The package includes raw data file parsing from widely used IRGAs, metadata matching, unit conversion, flux estimations, and initial quality assurance/quality control (QA/QC). Diagnostic graphical plots provide a transparent way to differentiate between measurement issues and nonlinear behavior. The package is also designed to be easily integrated with the gasfluxes package for further fitting of nonlinear concentration‐time models, allowing alternative or additional flux QA/QC. The fluxfinder package offers a flexible workflow that is easily adaptable to promote open and reproducible greenhouse gas flux estimations.

BioPred: An R package for biomarkers analysis in precision medicine.

The R package BioPred offers a suite of tools for subgroup and biomarker analysis in precision medicine. Leveraging Extreme Gradient Boosting (XGBoost) along with propensity score weighting and A-learning methods, BioPred facilitates the optimization of individualized treatment rules (ITR) to streamline subgroup identification. BioPred also enables the identification of predictive biomarkers and obtaining their importance rankings. Moreover, the package provides graphical plots tailored for biomarker analysis. This tool enables clinical researchers seeking to enhance their understanding of biomarkers and patient population in drug development. The package is available at CRAN and https://github.com/deeplearner0731/BioPred. Supplementary data are available at Bioinformatics online.

Corrosion of Copper, Cupronickel, Nickel Aluminium Bronze and Super-Duplex Stainless Steel Rotating Cylinder Electrodes in Seawater under Turbulent Flow Conditions

The corrosion of uncoated metals in a marine environment restricts the choice of suitable engineering metals and alloys. Anodic dissolution of metal and cathodic reduction of oxygen are important processes and formation of a surface oxide film can affect both electrode reactions. Charge transfer and mass transfer data can provide information on corrosion rate and mechanism. Several metals and alloys having a history of use in marine engineering are considered, including copper, two copper alloys (cupronickel and nickel aluminium bronze) plus a more recent addition to strong, corrosion resistant alloys (a super duplex stainless steel). The rotating cylinder electrode offers the benefits of a controlled, turbulent flow of electrolyte, facilitating controlled mass transfer in a compact cell geometry which is well-suited to bench-top operation. These features are illustrated using a variety of electrochemical techniques, including open-circuit potential vs time monitoring, linear sweep voltammetry, rotation speed step- or potential step current transients and linear polarisation resistance measurements. Seawater taken from Langstone Harbour, Hampshire, UK, was filtered, air-saturated, pH 8.0 and maintained at 25 °C. Dimensionless group correlations and graphical plots (using an analogous approach to the Koutecky-Levich equation for an RDE) enabled contributions of charge transfer-, mixed- and mass transfer- controlled data to be appreciated, allowing the Tafel slopes of electrode reactions, the diffusion coefficient of dissolved oxygen, the mass transfer coefficient for oxygen reduction and the mean corrosion rate to be estimated.

Community-level dietary intake of sodium, potassium, and sodium-to-potassium ratio as a global public health problem: a systematic review and meta-analysis

Background: Widespread adoption of a westernized diet represents a major lifestyle change characterized by substantially higher sodium consumption and lower potassium intake, which is related to cardiovascular morbidity. Methods: We performed a systematic review and meta-analysis over published studies in accordance with quantifying the dietary intake of sodium and potassium of the universal population across the world. The PubMed, EMBASE, Cochrane Library, and Google Scholar databases were used to find research that pronounced 24-hour urinary sodium or potassium excretion (reference period: 2014–2021). The effect size was estimated using the fixed-effect model; sub-group analysis become accomplished to determine urinary sodium and potassium excretion disaggregated by geographical location. Publication bias became evaluated the usage of graphical funnel plot. Data analysis was performed using STATA 16. Results: Forty-three studies (n= 62,940) qualified the selection criteria. The mean urinary excretion of sodium and potassium was 156.73 mmol/24h [95% confidence interval (CI), 148.98–164.47] and 48.89 mmol/24 h (95% CI, 43.61–54.17), respectively; the mean urinary sodium/potassium ratio was 3.68 (95% CI, 2.96–4.40). Conclusions: This updated systematic review highlights excessively high dietary intake of sodium and low intake of potassium at the community level in most parts of the world. The urinary Na/K ratio exceeded the level recommended by the WHO guidelines.

On the analysis and deeper properties of the fractional complex physical models pertaining to nonsingular kernels.

This study solves the coupled fractional differential equations defining the massive Thirring model and the Kundu Eckhaus equation using the Natural transform decomposition method. The massive Thirring model is a dynamic component of quantum field theory, consisting of a coupled nonlinear complex differential equations. Initially, we study the suggested equations under the fractional derivative of Caputo-Fabrizio. The Atangana-Baleanu derivative is then used to evaluate the comparable equations. The results are significant and necessary for exploring a range of physical processes. This paper uses modern approach and the fractional operators in this situation to develop satisfactory approximations to the offered problems. The proposed approach combines the natural transform technique with the efficient Adomian decomposition scheme. Obtaining numerical findings in the form of a fast-converge series significantly improves the scheme's accuracy. Some graphical plot distributions are presented to show that the present approach is very simple and straightforward. We performed a fractional order analysis of assumed phenomena to demonstrate and validate the effectiveness of the future technique. The behaviour of the approximate series solution for several fractional orders is shown visually. Additionally, the nature of the derived outcome has been observed for various fractional orders. The derived results demonstrate how simple and efficient the proposed method is to apply for analysing the behaviour of fractionally-order complex nonlinear differential equations that arise in related fields of engineering and science.

Numerical solution of multi-dimensional time-fractional diffusion problems using an integral approach.

This paper presents a significant scheme to drive the numerical solution of multi-dimensional diffusion problems where the fractional derivatives are taken in Caputo sense. The Mohand homotopy integral transform scheme (MHITS) is the composition of Mohand integral transform (MIT) and the homotopy perturbation scheme (HPS) which can be used to investigate the numerical solution in the form of convergence series. This approach does not require any presumptions, limitations on elements, or any other hypothesis. The primary objective of this strategy is to perform its direct implementation to the recurrence relation. This method produces results in the form of a convergent series, which accurately predicts the exact results. Graphical results and plot error distribution show an excellent agreement between MHITS results and the exact solution.

Exergy and Energy Analysis of Forced Convective Thin-layer Solar Drying of Tiger Nuts (Cyperus esculantus L.)

Aims: To study the exergy and energy analysis for thin-layer solar drying of tiger nuts; and also to determine the drying kinetics for the thin-layer solar drying of tiger nuts. Study Design: Yellow variety of tiger nuts were dried in a forced convection solar dryer to determine the exergy and energy indices. Place and Duration of Study: Federal University of Technology, Owerri, Nigeria between October, 2022 to March, 2023. Methodology: The experiment was conducted at three different air velocities of 1.5, 2.5, and 3.5 m s-1 and two different loads of 70 and 140 g. The tiger nuts were dried from average initial moisture content of 52% (wb) to final moisture content of 10.2% (wb), at an average temperature range of 50.5 to 51.2 ºC. Energy utilization, exergy loss rate, exergy efficiency, improvement potential, and sustainability index were determined. Results: The results of energy utilization, exergy loss rate and improvement potential ranged from 2.1 to 5.09 W, 0.25 to 0.93 W and 0.08 to 0.54 W respectively; however, these values increased with increasing air velocities and loads. The results of exergy efficiency and sustainability index ranged from 41.8 to 68.49% and 1.72 to 3.17 respectively; these values increased with decreasing air velocities and loads. Graphical plots of moisture content with drying time showed that the moisture content of the tiger nuts decreased with increasing drying time. The characteristic nature of the curve is indicative of the fact that there was an initial higher rate of drying, which gradually declined with drying time. The results also showed that the drying rates of the tiger nuts ranged from 6.03 to 8.44 %MC/hr; and these values varied with the different air velocities and loads. Conclusion: The results from this research will serve as a guide in reduction of energy costs for the optimum design of convective dryers.

The Detailed Axial Compression Behavior of CFST Columns Infilled by Lightweight Concrete

The utilization of lightweight aggregate concrete (LWC) plays a major role in reducing the self-weight of CFST (concrete-filled steel tube) columns, which is reflected in the behavior of the structural system. This paper aims to investigate the characteristics of lightweight concrete-filled steel tubular (LWCFST) columns under an axial compressive load, using a total of (48) LWCFST column models. The simulated models were divided into four groups with different concrete compressive strength, length-to-diameter ratios (L/D), and diameter-to-thickness ratios (D/t). Four concrete compressive values were examined (30, 40, 50, and 60) MPa, three length-to-diameter ratios short (L/D = 3), medium (L/D = 6), and long (L/D = 9), and four diameter-to-thickness ratios (36, 31, 26, and 21). The method of nonlinear finite element analysis (NLFEA) was used to fulfill the objective of this study where results were presented as graphical plots between the compressive loading versus the axial and lateral strains along with the failure modes. In addition, the results were compared with the AISC360-16 and EC4 codes predictions to examine their applicability on the LWCFST columns where the AISC was overpredicted in most cases with higher percentages under lower (L/D) values, whereas the EC2 was underestimated in most cases with high percentages up to 28%, which become closer to the NLFEA predictions at higher (L/D) values. It has been revealed that the utilization of steel tubes significantly improves the LWCFST column’s mechanical performance, ductility, compressive strength, and toughness. Moreover, the structural behavior of the LWCFST columns and their associated failure modes was found to be highly affected by the geometrical properties of the CFST column (i.e., L/D ratio and D/t ratio) where specimens with small tube thickness show bad behavior. Finally, the utilization of high-strength concrete has a favorable performance compared to the utilization of thick steel tubes.

Enhancing Radiological Biomedical Natural Language Processing Tasks with Radiology-Specific Word Encodings: A Comparative Analysis of Word Embeddings Sources

Background: Machine Learning (ML)-based Biomedical Natural Language Processing (BNLP) techniques have garnered attention in radiology. However, these models typically depend on Word Encodings (WE) trained on generic datasets, as radiology-specific word libraries are limited. Objective: This study aimed to investigate the potential of radiography as a comprehensive database for generating Radiology-Specific Word Encodings (RSWE), enhancing the efficiency of BNLP tasks, especially in processing radiological texts. Methods: A systematic evaluation was conducted using WE derived from four databases: medical records, biomedical journals, Wikipedia, and news sources. Unstructured Electronic Medical Record (EMR) data from the Mayo Clinic and PubMed Central publications were used to train WE for medical-specific sources, while GloVe and Google News represented publicly available pre-trained WE for generic sources. Analytical evaluation employed medical keywords in three categories (illness, symptoms, drugs), and a 2-D graphical plot was created for 380 medical words. Numerical evaluation consisted of internal and external assessments. Results: Findings revealed that RSWE derived from EMR and PubMed Central outperformed generic WE, better capturing medical word meanings and identifying medically essential terms, aligning more closely with expert assessments. Conclusion: The study demonstrates the value of radiography as a radiology-specific resource for generating RSWE, with promising implications for improving BNLP in radiology.

Is dark energy necessary for the sustainability of traversable wormholes?

Abstract Dark energy is usually the principal ingredient needed for traversability of wormholes by providing the negative gravity effect to keep the throat open. But can the same be achieved without dark energy? It turns out that if we couple the trace of energy-momentum with the standard Einstein-Hilbert Lagrangian and utilise a specific equation of state then dark energy may be obviated. The Casimir stress energy is known to result in the violation of the null energy condition (NEC) on the energy momentum tensor. This phenomenon makes such an equation of state (EoS) an ideal candidate to generate traversable wormhole (WH) geometries. The laboratory proven phenomenon provides a natural mechanism to sustain an open WH throat without having to appeal to dark energy. We generate two classes of WH solutions with this in energy-momentum trace-coupling gravity.&amp;#xD; For the specific choice of the Casimir EoS relating the energy-momentum tensor components [ Kar and Sahdev: Phys. Rev D {\bf 52} 2030 (1995)] and different choices for redshift functions, we determine the WH geometry completely. The obtained WH solutions violate the NECs and all qualitative constraints demanded of physically realisable WHs are satisfied. This is demonstrated via graphical plots for a suitably chosen range of values of the coupling parameter. Furthermore, our study involved an investigation into the repulsive effect of gravity, which revealed that its presence leads to a negative deflection angle for photons traveling along null geodesics. Notably, we observed a consistent pattern of negative values for the deflection angle across all values of $r_0$ in the three scenarios considered, thus indicating the clear manifestation of the repulsive gravity effect. All of this is possible without invoking the existence of dark energy.

Investigation of Space-Time Dynamics of Akbota Equation using Sardar Sub-Equation and Khater Methods: Unveiling Bifurcation and Chaotic Structure

This paper focuses on obtaining exact solutions of nonlinear Akbota equation through the application of the modified Khater method and Sardar sub-equation method. Renowned as one of the latest and precise analytical schemes for nonlinear evolution equations, this method has proven its efficacy by generating diverse solutions for the model under consideration. The equation is crucial in the study of optical solitons, which are stable pulses of light that maintain their shape over long distances. The Akbota equation helps in understanding the behavior and stability of these solitons. The governing equation undergoes transformation into an ordinary differential equation through a well-suited wave transformation. This analytical simplification paves the way for the derivation of trigonometric, hyperbolic, and rational solutions through the proposed methods. To illuminate the physical behavior of the model, the study presents graphical plots of the selected solutions of Khater and Sardar sub-equation method. This visual representation, achieved by selecting appropriate values for arbitrary parameters, enhances the understanding of the system’s dynamics. All calculations in this study are meticulously conducted using the Mathematica and Maple software, ensuring accuracy and reliability in the analysis of the obtained solution. Furthermore we investigate the sensitivity analysis of the dynamical system.

Lie symmetry analysis, exact solutions and conservation laws of (3+1)-dimensional modified Wazwaz-Benjamin-Bona-Mahony equation

In this paper, we study the (3+1)-dimensional modified Wazwaz-Benjamin-Bona-Mahony equation using Lie symmetry analysis. An optimal system is constructed with the help of a commutator table and an adjoint table. Similarity reductions are obtained on the basis of the optimal system, and the governing partial differential equation is transformed into another partial differential equations with a smaller number of independent variables. The solutions of these reduced partial differential equations give invariant solutions of the (3+1)-dimensional modified Wazwaz-Benjamin-Bona-Mahony equation. The 3D graphical plots are used to describe the dynamical characteristics of the solutions. Hence, by employing these graphs, physicists and mathematicians can more efficiently and successfully follow complex physical processes. Finally, self-adjoint is checked, and conservation laws are also deducted corresponding to each infinitesimal generator.

Investigating optical soliton pattern and dynamical analysis of Lonngren wave equation via phase portraits

This study focuses on finding effective solutions to a mathematical equation known as the Lonngren wave equation. The solutions from the Lonngren wave equation can be used to evaluate electromagnetic signals in cable lines and sound waves in stochastic systems. The main equation is transformed into an ordinary differential equation by utilizing a suitable wave transformation, allowing for the exploration of mathematical models by using the modified Khater technique to detect the exact solution of a solitary wave. We use the provided method to derive the trigonometric, rational, and hyperbolic solutions. To illustrate the model’s physical behavior, we also present graphical plots of selected solutions to illustrate the physical behavior of the model. By choosing appropriate values for arbitrary factors, the visual representation enhances the understanding of the dynamical system. Furthermore, the system is transformed into a planar dynamical system, and phase portrait analysis is conducted. Additionally, the sensitivity analysis of the dynamical system confirms that slight changes in the initial conditions will have minimal impact on the stability of the solution. The existence of chaotic dynamics in the Lonngren wave equation is explored by introducing a perturbed term in the dynamical system. Two and three-dimensional phase portraits will be used to demonstrate these chaotic behaviors.

Quantifying the Impact of Siderite Composition and Reservoir Resistivity (Rt) on Water Saturation Estimation in Low-Resistivity Sideritic Sandstone Reservoirs Using the Graphic Plot Method

Quantifying the Impact of Siderite Composition and Reservoir Resistivity (Rt) on Water Saturation Estimation in Low-Resistivity Sideritic Sandstone Reservoirs Using the Graphic Plot Method

A novel relative-equilibrium graphical plot for rapid reversible tracer studies in dynamic PET imaging

Objective. This study aims to address the issue of long scan durations required by traditional graphical analysis methods, such as the Logan plot and its variant, the reversible equilibrium (RE) Logan plot, for dynamic PET imaging of tracer kinetics. Approach. We propose a relative RE Logan model that builds on the principles of the Logan plot and its variant to significantly reduce scan time without compromising the accuracy of tracer kinetics analysis. The model is supported by theoretical evidence and experimental validations, including two computer simulations and one clinical data analysis. Main results. The proposed model demonstrates a significant linear relationship between the variable x and the slope DVT of the RE Logan plot, and the variable x′ and the slope DVT′ of the relative RE Logan plot. The Pearson correlation coefficients (r) of the linear fitting of the x′ to the x equal 0.9849 in the simulated data and 0.9912 in the clinical data. Similarly, the r values for the linear fitting of DVT′ to DVT equal 0.9989 and 0.9988 in the simulated data, and 0.9954 in the clinical data. Significance. These results demonstrate the model’s capability to maintain strong linear relationships and produce parametric images comparable to the traditional RE Logan plot, but with the considerable advantage of shorter scan durations. This innovation holds significant potential for enhancing the efficiency and feasibility of PET imaging in clinical settings.

Wide-field optical tracking of LEO objects: Theoretical assessment and observing strategy

The main technical and strategic aspects related to Space Surveillance and Tracking (SST) with optical sensors are set in context in this study to lead to an efficient inventory of the active satellites and un-cooperant space debris population at Low-Earth orbital regimes (LEO). In particular, special emphasis is devoted to the combined interplay between timing of observations, target illumination conditions, instrumental fine tuning and data acquisition mode (surveying vs. active tracking).At LEO altitudes, satellites are seen to cross the sky at very high angular velocity, in excess to 0.5–1.5 deg/sec, always making their positional measurements (and the inferred dynamical properties) a challenging task for ground telescopes. To this aim, objective criteria have to be identified for a best trade-off between instrument field of viev (FOV), CCD/CMOS platescale, telescope aperture and exposure time in order to maximize target(s) detection and reference grid of stars valuable for astrometry. Many counter-intuitive aspects are discussed in this regard, compared for instance with a more classical “astronomical” approach, delving in particular the widely recognized inherent link between time-tag accuracy and resolving power of optical imagery to track LEO objects.A number of tables and graphical plots are provided for practical use to the reader.

Unveiling the influence of end-capped acceptors modification on photovoltaic properties of non-fullerene fused ring compounds: a DFT/TD-DFT study.

Herein, unique A-D-A configuration-based molecules (NBD1-NBD7) were designed from the reference compound (NBR) by utilizing the end-capped acceptor modification approach. Various electron-withdrawing units -F, -Cl, -CN, -NO2, -CF3, -HSO3, and -COOCH3, were incorporated into terminals of reference compound to designed NBD1-NBD7, respectively. A theoretical investigation employing the density functional theory (DFT) and time-dependent DFT (TD-DFT) was performed at B3LYP/6-311G(d,p) level. To reveal diverse opto-electronic and photovoltaic properties, the frontier molecular orbitals (FMOs), absorption maxima (λ max), density of states (DOS), exciton binding energy (E b), open-circuit voltage (V oc) and transition density matrix (TDM) analyses were executed at the same functional. Moreover, the global reactivity parameters (GRPs) were calculated using the HOMO-LUMO energy gaps from the FMOs. Significant results were obtained for the designed molecules (NBD1-NBD7) as compared to NBR. They showed lesser energy band gaps (2.024-2.157 eV) as compared to the NBR reference (2.147 eV). The tailored molecules also demonstrated bathochromic shifts in the chloroform (671.087-717.164 nm) and gas phases (623.251-653.404 nm) as compared to NBR compound (674.189 and 626.178 nm, respectively). From the photovoltaic perspectives, they showed promising results (2.024-2.157 V). Furthermore, the existence of intramolecular charge transfer (ICT) in the designed compounds was depicted via their DOS and TDM graphical plots. Among all the investigated molecules, NBD4 was disclosed as the excellent candidate for solar cell applications owing to its favorable properties such as the least band gap (2.024 eV), red-shifted λ max in the chloroform (717.164 nm) and gas (653.404 nm) phases as well as the minimal E b (0.126 eV). This is due to the presence of highly electronegative -NO2 unit at the terminal of electron withdrawing acceptor moiety, which leads to increased conjugation and enhanced the intramolecular charge transfer (ICT) rate. The obtained insights suggested that the designed molecules could be considered as promising materials for potential applications in the realm of OSCs.

Performance assessment of a sample nanorefrigerant cooling process as a function of flow Reynolds number, evaporator and ambient temperatures

In this paper available experimental data of nanorefrigerant, NRF cooling process are processed using MATLAB to determine the coefficient of performance COP as a function of Reynolds number, Re of NRF, evaporator and ambient temperatures, Te and Ta as a novelty. The cooling process performance assessment of NRF is provided in comparison with a pure refrigerant, R through relative COP term, COPr. The used data ranges with 20–70 nm of Al2O3 in R134a are at varying volume fraction, φ of 0.075–0.303% and volumetric flow rate, Q of 6.5–11 L/h for Ta in 294–306 K and Te in 288–309 K. Re calculations are based on the thermophysical parameters evaluated at Te not only in the cited experimental ranges of Q, φ but also extrapolated for the extended range of Q of 15–25 L/h for a generalization purpose. Since data processing is under the interactive influence of the parameters the functional relationships of COP, Re, φ, Te are expressed as 3D graphical plots which are the start of a trial-error procedure. The experimental data are expressed in terms of fitted equations for functional relationships between various non-dimensional parameters as Re, COP, (COP*φ), (COP*Te/Ta*φ), (Re*Te/Ta*φ), (Re*Te/Ta), and COPr to provide a practical assistance for whom designing and using NRF cooling. A functional relationship of Re*(Te/Ta) with COPr at varying φ is found as the most critical output of the study due to the practice of the appeared parameters in cooling performance assessment. COPr>1 corresponds to φ>0.151% for the processed data ranges.