Experimental Sensitivity Analysis Research Articles

Experimental study and sensitivity analysis of performance for a hydrogen diaphragm compressor

As the critical infrastructure of hydrogen in transportation, the energy consumption of hydrogen refuelling stations plays a pivotal role in the progress of hydrogen energy within the transportation sector. Volumetric and isentropic efficiencies serve as metrics for evaluating compressor performance. To investigate the extent of factors, including suction pressure, pressure ratio, overflow pressure, and rotational speed, to the efficiencies of the diaphragm compressor, an experimental rig was set up in this study. The volume and energy losses were analysed by studying pressure–volume diagrams. The result shows that elevating suction pressure results in an increased isentropic efficiency. Specifically, raising suction pressure from 0.2 MPa to 0.8 MPa yields a 10.2 % increase in isentropic efficiency. The increase in pressure ratio leads to a reduction in volumetric efficiency but an increase in isentropic efficiency. When the pressure ratio increased from 3 to 7, the volumetric efficiency decreased by 6.5 % in volumetric efficiency, but the isentropic efficiency increased by 9.8 %. Moreover, the escalation in rotational speed corresponds to a decrease in both volumetric and isentropic efficiencies. As the rotational speed increased from 420 r/min to 660 r/min, volumetric efficiency dropped by 9.6 %, and isentropic efficiency experienced a 19.2 % decrease.

Surface Mechanical Property Prediction and Process Optimization of 18CrNiMo7-6 Carburized Steel Stator Guide Based on Radial Basis Function Neural Network and NSGA-II Algorithm

The carburizing process is a key technology that affects the mechanical properties of the surface of the hydraulic motor stator guide rail, and the related process parameters have an important influence on surface hardness, the thickness of the carburized layer, and the deformation of the guide rail. However, at present, the relationship between the carburizing process parameters and the surface mechanical properties of the target is not clear. This paper proposes a “hardness prediction and process parameter optimization” method. Firstly, a finite element model is established, with carburizing time, temperature, and carbon potential as the three input factors; the optimal Latin hypercubic experimental design and sensitivity analysis are applied. Secondly, surface hardness, carburized layer thickness, and deformation are taken as the output values, and an RBF neural network is used to construct the prediction model. The results show that the RBF neural network can be accurately used for the prediction of surface hardness, the thickness of the carburized layer, and deformation, and for the optimization of process parameters. The optimized parameters of surface hardness and the thickness of the carburized layer were increased by 4.2% and 5.1%, respectively, and the deformation amount was reduced to 0.31 mm, achieving the goal of optimal design.

Uncertainty and sensitivity analysis of non-acoustic parameters on acoustic characteristics prediction models for porous foam materials

Porous foam materials are widely used in noise control applications. Their acoustic performance can be predicted by acoustic models composed of non-acoustic parameters such as flow resistivity, porosity, tortuosity, viscosity, and characteristic length. However, the influence of these parameters on model outputs varies across different frequency ranges. Therefore, when using a single model for predictions across the entire frequency range, parameters may not fully act within the frequency range where their influence is greatest. To reduce prediction errors and improve the correlation between predicted numerical results and experimental data, uncertainty and sensitivity analyses can be conducted to determine the extent of each parameter's influence at different frequency ranges. In this study, polyurethane foam materials are investigated, and uncertainty and sensitivity analyses are performed on two acoustic models. Firstly, the uncertainty of parameters is assessed using the Monte Carlo method. Secondly, Sobol index method is employed to reveal the influence of parameters across various frequency ranges. Finally, by comparing the results of both analyses, the optimal frequency ranges for each parameter can be summarized. This provides valuable reference for enhancing the accuracy of acoustic model predictions.

Examining the impact of common faults on chiller performance through experimental investigation and parameter sensitivity analysis

Chillers are the important components across various applications, and understanding the impact of common faults on their performance is crucial for monitoring fault progression and predicting degradation. Consequently, an experimental investigation was conducted on a magnetic levitation-driven chiller across different severity levels. The quantitative influence of common faults on performance was then analyzed, with a specific focus on thermodynamic mechanism parameters. From a data variation perspective, a sensitivity analysis was implemented to identify the fault-sensitive parameters that exhibited noteworthy variations due to faults. From a classification performance perspective, the diagnosis-effective parameters were identified based on their significance in fault diagnosis. The results of this study led to several key conclusions: 1) Trends and magnitudes of changes in 38 parameters related to nine typical faults are identified in comparison to their normal levels; 2) Common faults have a significant influence on thermodynamic mechanism parameters, causing big changes in two to eight thermodynamic mechanism parameters for each fault; 3) Discrepancies between fault-sensitive parameters and diagnosis-effective parameters results in a difference of up to 64% in diagnostic performance; 4) Nine decoupling parameters are identified as pivotal in diagnosing concurrent faults, and an effective set of fault diagnosis rules is recommended. These findings provide valuable insights into the selection of sensitive parameters, identification of fault-decoupling parameters, and the development of fully interpretable and reliable fault diagnosis approaches.

Robust Consensus Modeling: Concerning Consensus Fairness and Efficiency with Uncertain Costs

Extensive uncertainty can affect the efficiency and fairness of consensus in the consensus reaching process (CRP), but few scholars have studied consensus modeling that focuses on fairness and efficiency in uncertain environments. Additionally, the weight of the decision maker (DM) in the CRP is influenced by multiple factors. Therefore, this paper proposes robust consensus models (EFCMs) focusing on fairness and efficiency under uncertain costs to address these issues. Firstly, this paper constructs multiple uncertainty sets to describe the uncertainty of the unit adjustment cost. Secondly, the fair utility level and opinion adjustment distance are used to measure the fairness and efficiency of reaching consensus, respectively. Furthermore, this paper uses a data-driven method based on the KDE method combined with trust propagation in social networks to determine the DMs’ weights jointly. Finally, this paper also applies the proposed models to the carbon emission reduction negotiation process between the government and enterprises. The experimental results and sensitivity analysis show that the consensus cost budget and the DMs’ jealous preference behavior particularly affects the efficiency of reaching consensus, which provides a theoretical basis for solving practical decision making problems.

Integrating transient pressure and flow data for determination of hydraulic permeability and specific storage of a shale sample: Experimental tests and sensitivity analysis

This paper describes a comprehensive investigation to accurately determine the hydraulic permeability k and the specific storage Ss of a shale sample. One-dimensional pressure transient tests were conducted on a cylindrical sample under various levels of pore and confining pressures. For the boundary conditions, the upstream pressure was kept constant using a syringe pump, and the downstream storage was minimized for reducing the test duration. Both the downstream pressure and the upstream fluid flow into the sample were continuously recorded throughout the transient period. To estimate the hydraulic properties, the curve fitting technique was applied to the pressure and flow data using theoretical curves. We found that the pressure curve was sensitive to the ratio of hydraulic permeability to the specific storage (k/Ss), but not sufficient to determine the individual components (k and Ss). The upstream flow curve was sensitive to the specific storage but less sensitive to the permeability. Based on our sensitivity analysis, we present a combination of two objective functions of flow and pressure data to optimize both hydraulic properties with reasonable uncertainty. An alternative is to first use the flow data to determine Ss and then use pressure data with the predetermined Ss to obtain the remaining k.

3D printed large amplitude torsional microactuators powered by ultrasound

Here, we introduce a design, fabrication, and control methodology for large amplitude torsional microactuators powered by ultrasound. The microactuators are 3D printed from two polymers with drastically different elastic moduli as a monolithic compliant mechanism, and contain precisely engineered capsules with multiple orifices that serve as stators and rotors. Secondary acoustic radiation forces generated among the encapsulated air bubbles controllably rotate the rotor that is supported and stabilized by two torsion bars. The capsules are designed according to the simulations of an analytical model that captures the dynamics of the water-air interface vibrations, which we rigorously validate using a laser Doppler vibrometer and phase-contrast imaging. An in-depth experimental sensitivity analysis is conducted to optimize the arrangement of the rotor and the stators. Integration of experimental results with finite element analysis of the twisting bars and analytical modelling of acoustic phenomena allows us to compute the secondary acoustic radiation forces and the angular displacement of the rotor for a given input pressure. The versatility of the design framework and the robust performance of the printed actuators enable the development of a new class of microscale machines and soft robotic devices that are actuated and controlled by sound waves.

A Numerical and Experimental Sensitivity Analysis on Electrochemical Neutral Pickling for Stainless Steel Using Secondary Current Distribution

Electrochemical neutral pickling (ENP) is an extended process used in the stainless steel industry to remove the oxide surface layer formed during the annealing process. The absence of strong acids such as nitric acid results in a minimum loss of base material, improve operators working conditions, and reduces the pickling environmental impact, while keeping relatively low operation and maintenance costs. However, despite its multiple benefits, ENP may become the bottleneck for integrated annealing and pickling line, especially when processing thin austenitic and duplex steels. Fortunately, there is room for improvement as the total Faradaic efficiency of the process in typical operation is in general low (around 20 – 30 % for austenitic materials) [1]–[3], while estimations of the energy efficiency are as low as to 1 - 2 % [4].This work provides guidelines to the design and operation of ENP cells to increase the oxide removal rate. We focus on the effect of the geometry and some operational parameters, using secondary current distribution. The simulations are validated against experimental, and a sensitivity analysis of the oxide removal rate with respect to the geometry and some key operational parameters is performed. The electrode-to-strip and the inter-electrode distances were found to have a determining effect on the total cell resistance and on its so-called geometric efficiency (relative current reaching the strip). Moreover, an optimal range for the ratio of these distances is proposed. In addition, the strip thickness and width were found to significantly affect the cell performance, especially for the thinnest gauges.

Current Signature Modeling of Surface-Mounted PMSM Drives With Current Sensors Faults

This paper presents the closed-form analytical determination of the current signature of a surface-mounted permanent magnet synchronous motor drive controlled by means of field oriented control strategy, when a fault occurs in one or more current sensors. Both DC offset and gain fault for all phase current sensors are considered. The proposed model includes the response of the control loop and related gains, eliminating the need for phase voltage sensors and complicated state estimation. However, the proposed approach requires the solution of an overdetermined system of equations. Then a new methodology of solution is proposed to save computing time, as an alternative to the classical one based on the Moore-Penrose pseudoinverse matrix. Experimental results and sensitivity analysis to parameter variations confirm the validity of the proposed model.

Experimental study and sensitivity analysis on the rheological treatment of MWCNT-CuO/SAE50 non-Newtonian hybrid nanofluid to show the usability in industrial applications

The dynamic viscosity of MWCNT-CuO(40–60 %)/SAE50 hybrid nanofluid (NF) is investigated experimentally. This experiment was performed in T = 25–50 °C, SR = 7998–666.5 s−1, and SVF = 0.0625–1 %. Examining NF’s rheological behavior shows NF's behavior was non-Newtonian and independent of time. The power-law index values illustrate viscosity of NFs reduces with a temperature rise. Furthermore, viscosity has an inverse relation with SR. NF is also a shear-thinning type. Experimental consequences indicate that viscosity also changes with variation of SVF. The largest rise in viscosity was 19 % at SVF = 1 % and T = 25 °C. The lowest reduction of viscosity is observed at 10 % in SVF = 0.0625 %. Due to the appropriate changes in the NF viscosity in various SVFs, this NF can be used in thermal applications in the industry. This NF is recommended for use in industrial cooling due to its good performance. Also, correlation coefficient R2 = 0.998 for RSM was considered to predict NF viscosity. The margin of deviation (MOD) data is in the range of 5 %<MOD< +7 % and this indicates the good accuracy of the proposed data.

Application of samarium doped lanthanum nickel oxide perovskite nanocatalyst for biodiesel production

The catalytic performance of the synthesized LaNiO3 (LNO) and LaSmNiO3 (L1-xSxNO) perovskite structures as novel efficient catalysts for the conversion of waste cooking oil (WCO) to biodiesel was evaluated. The synthesized heterogeneous catalysts of LNO and L1-xSxNO were characterized via Scanning Electron Microscopy (SEM), Energy-Dispersive X-ray Spectroscopy (EDX), Transmission Electron Microscopy (TEM), Brunauer, Emmett, and Teller (BET), inductively coupled plasma-optical emission spectrometer (ICP-OES), and Power X-ray diffraction (XRD). The crystal size of LNO was obtained to be around 31 nm at 2θ of 47.31° using Scherrer's equation. Catalysts characterization revealed that doping Sm with LNO (L0.9S0.1NO) enhanced the surface area from 7.71 to 15.75 m2/g, and thus may provide more active sites for transesterification reaction. Also, the Sm doping causes numerous oxygen vacancies in the structure of perovskite, improving the catalyst's ability to catalyze reactions. To determine the optimum conditions in the WCO transesterification process, the response surface methodology (RSM) based central composite design (CCD) was applied. The influences of key parameters including MeOH/WCO ratio (5–20 mol/mol), reaction duration (1–5 h), catalyst mass fraction (1–5 wt%), and reaction temperature (60–120 °C) were explored on the behavior of the reaction. It is inferred that the L0.9S0.1NO catalyst has excellent catalytic activity in converting WCO to biodiesel. The experimental and modeling sensitivity analysis indicated that the application of L0.9S0.1NO catalyst led to the WCO conversion of 95.14 % to biodiesel at MeOH/WCO ratio of 9.07, reaction duration of 3.02 h, catalyst mass fraction of 3.08 wt%, and reaction temperature of 80.07 °C.

A conditional branch predictor based on weightless neural networks

Conditional branch prediction allows the speculative fetching and execution of instructions before knowing the direction of conditional statements. As in other areas, machine learning techniques are a promising approach to building branch predictors, e.g., the Perceptron predictor. However, those traditional solutions demand large input sizes, which impose a considerable area overhead. We propose a conditional branch predictor based on the WiSARD (Wilkie, Stoneham, and Aleksander’s Recognition Device) weightless neural network model. The WiSARD-based predictor implements one-shot online training designed to address branch prediction as a binary classification problem. We compare the WiSARD-based predictor with two state-of-the-art predictors: TAGE-SC-L (TAgged GEometric-Statistical Corrector-Loop) and the Multiperspective Perceptron. Our experimental evaluation shows that our proposed predictor, with a smaller input size, outperforms the perceptron-based predictor by about 0.09% and achieves similar accuracy to that of TAGE-SC-L. In addition, we perform an experimental sensitivity analysis to find the best predictor for each dataset, and based on these results, we designed new specialized predictors using a particular parameter composition for each dataset. The results show that the specialized WiSARD-based predictor outperforms the state-of-the-art by more than 2.3% in the best case. Furthermore, through the implementation of specialized predictor classifiers, we discovered that utilizing 90% of the specialized predictor for a specific dataset yielded comparable performance to the corresponding specialized predictor.

Optimization of heat transfer nanofluid blood flow through a stenosed artery in the presence of Hall effect and hematocrit dependent viscosity

The heat transfer rate of the MHD nanofluid blood flow through a stenosed composite artery with hematocrit-dependent viscosity and Hall effect is optimized by using the response surface methodology (RSM). An experimental design and sensitivity analysis based on RSM are employed to examine the impact of different physical parameters and how changes to these parameters affect the response factors of interest. RSM is utilized in the process of constructing the model dependencies between the output response variables, such as the skin friction coefficient and the local Nusselt number, and the independent input parameters, such as the magnetic field parameter, the Hall parameter, and the Brinkman number. These model dependencies are used to determine the relationship between the output response variables and the independent input parameters. For medical applications, the effects of the aforementioned parameters on the velocity and temperature along the radial axis have been examined and physically interpreted. Shear stress and Nusselt number are analyzed using graphs for several physical factors in addition to stenosis height. The increases in the hematocrit parameter are accompanied with a decrease in velocity profile, as it enhances the fluid viscosity that reduces the fluid motion. The sensitivity of Nux (Nusselt number) and τ (shear stress profile) are positive for Br, while negative for M and Be. In addition, current research may be helpful in biomedical by detecting the abnormalities in the artery with the help of the artery image, also known as magnetic resonance angiography (MRA).

Experimental and parametric sensitivity analysis of a novel indirect evaporative cooler for greener cooling

Energy-efficient space cooling is one of the biggest challenges because of high energy consumption and emissions and exponentially growing demand. Besides, the use of high global warming potential chemical-based refrigerants in the conventional system is stressing the need for a sustainable and economical alternative. Owing to these reasons, water-based cooling systems have gained significant attention because of their simple operation, low energy consumption, easy manufacturing, and benign environmental footprints. However direct evaporative cooling systems usage is limited by high humidity issues because such levels of humidity are incompatible with human comfort and certain industrial needs such as electronics cooling. Regarding the existing indirect evaporative cooling systems, they have design limitations that have hindered their commercial development. These include multilayer heat transfer walls, complex manufacturing, heavyweight, microbial growth on hydrophilic surfaces, and water management issues. The proposed innovative indirect evaporative cooling system addresses the major limitations in existing systems such as water management and wet channel surface development. A prototype has been fabricated and tested. Experimental investigation showed that the system achieved competitive performance with a maximum temperature drop of 18 °C, a coefficient of performance of 31, and wet bulb efficiency of 93%. Besides, the system also offers several advantages like high operational life, low maintenance, low cost, and resilient design which can lead to commercial scale development for greener cooling.

Response surface optimization for the electromagnetohydrodynamic Cu-polyvinyl alcohol/water Jeffrey nanofluid flow with an exponential heat source

This article examines the sensitivity analysis of Jeffrey fluid flow in the presence of copper nanoparticles with polyvinyl alcohol water serving as the base fluid under the influence of source terms like Joule heating, viscous dissipation, exponential heat source, and Arrhenius activation energy via a non-linear vertically elongating surface of non-uniform thickness. Governing PDEs are first converted into ODEs using a suitable similarity transformation. The resulting coupled ODEs are converted into a system of first-order ODEs and then solved using the shooting iteration technique with the RK-4th order method. The remarkable impacts of numerous parameters like Deborah number, Hartmann number, electric field parameter, thermal and solutal Grashof number, Prandtl and Eckert numbers, exponential heat source parameter, Lewis number, chemical reaction parameter, and activation energy parameter associated with the flow properties are discussed graphically. The effects of various physical parameters and the dependence of the response factors on the input parameter are explored using an experimental design and sensitivity analysis based on Response Surface Methodology. Response Surface Methodology is utilized to determine the output response variables of model dependencies, such as the drag coefficient and Nusselt number on the independent input parameters, namely the electric field parameter and Deborah numbers for the drag coefficient, and electric field parameter, thermophoresis diffusion parameter, and exponential heat source parameter for the Nusselt number. Local Nusselt number enhances with increment in the electric field parameter and thermophoresis diffusion parameter values, whereas it decelerates with the rise in exponential heat source parameter. The non-Newtonian nanofluids have proven their great potential in thermal transportation which has a diverse range of applications in thermal energy technologies such as lubrication, natural gas networks, spray processes, and cooling of nuclear reactors, spinning of fibers, cryopreservation, drawing of copper wires, nano-drug delivery, electronics, and many more.

Experimental study, prediction modeling, sensitivity analysis, and optimization of rheological behavior and dynamic viscosity of 5W30 engine oil based SiO2/MWCNT hybrid nanofluid

In this paper, the rheological performance and dynamic viscosity of hybrid nanofluid containing SiO2 and multi-walled carbon nanotubes (MWCNTs) nanoparticles (90:10) with 5W30 engine oil as base fluid is experimentally evaluated under different shear rates (SRs) in the range of 50–1000 rpm. The hybrid nanofluid volume fractions (VFs) and temperatures are considered in the ranges of 0.05–1.00 vol% and 5–65 °C, respectively. It was found that the hybrid nanofluid under study behaves as a non-Newtonian fluid. In addition, the calculated power law index was lower than unity, resulting in pseudoplastic features of hybrid nanofluid in all VFs and temperatures. It was observed that the rise of nanofluid temperature from 5 to 65 °C leads to the dynamic viscosity reduction (a 93% decrease in viscosity was observed in a VF of 0.2%), while the increase of nanofluid VF brings about the dynamic viscosity elevation (By increasing VF from 0.05% to 1% at SR of 800 rpm and temperature of 25 °C, the viscosity increases by 29.21%). Based on measured data, an innovative three-variable correlation was established that can more accurately estimate the experimental data than published correlations in the literature. Moreover, the capabilities of GMDH-type neural network (NN) and response surface methodology (RSM) to predict the relative viscosity of the hybrid nanofluid were evaluated. It was concluded that both NN and RSM approaches have a superior ability to forecast the dynamic viscosity behavior of the corresponding hybrid nanofluid, having R2 values of 0.999656 and 0.9955. Furthermore, the optimization was performed and the best solution for achieving the minimum dynamic viscosity with the maximum desirability (1.00) was obtained. Eventually, the dynamic viscosity sensitivity to changes in VF, temperature, and SR was evaluated. It was observed that the dynamic viscosity sensitivity increases as the nanofluid temperature and concentration increase considering a constant SR of 800 rpm.

Experimental evaluation, modeling and sensitivity analysis of temperature and cutting force in bone micro-milling using support vector regression and EFAST methods

Experimental evaluation, modeling and sensitivity analysis of temperature and cutting force in bone micro-milling using support vector regression and EFAST methods

Experimental investigation on 3D printed lightweight sandwich structures for energy absorption aerospace applications

One of the ongoing challenges in aeronautics is the development of increasingly lighter structures. This has become a crucial goal because structural lightening means improving aircraft performance in terms of speed, manoeuvrability, fuel efficiency, and at the same time reducing manufacturing and service costs. The aerospace industry continues to focus more and more on this goal and every improvement in technology and materials can bring significant advantages in performance, efficiency, and safety of aircraft. The present work is part of this framework, as it analyses the feasibility of achieving very high weight reduction in sandwich panels using a new manufacturing approach. It introduces an experimental limited sensitivity analysis on the mechanical responses of composite sandwich structures for shock-absorption applications lightened by appropriately setting a specific additive manufacturing process parameter: the infill value. The investigated sandwich structures are characterised by a core Designed for Additive Manufacturing (DfAM) in order to maximise their performance in terms of energy-to-weight ratio and damping of impact loads. The material chosen for the inner part of the sandwich structure (core and internal face sheets) is polypropylene (PP) while the external face sheets are in Carbon Fibre Reinforced Polymers (CFRP).By comparing the post-impact responses at 20 J impact of three sandwich configurations with the same external shape but different material layer densities related to different setting of the infill parameter in the frame of the printing process, the work proves that this approach leads to lightening of this specific sandwich structures by up to 28% and at the same time improves their structural effectiveness in terms of energy absorption characteristics.The comparison was made by relating specific absorption indices, force-time and force-displacement graphs and CT scans.

Do voters prefer educated candidates? How candidate education influences vote choice in congressional elections

Previous research shows that democracies are more likely to produce educated politicians, but is this because voters prefer educated representatives or because of other features of the democratic process? Education may serve as a signal of candidate quality to voters or it may simply be associated with other factors, such as access to campaign funds, that help candidates win elections. We address this puzzle by analyzing head-to-head matches between candidates in US House elections from 2002 to 2012 along with a conjoint experiment. We find evidence that candidates with higher levels of education win more votes than candidates with lower levels of education, even after we account for standard indicators of candidate quality and campaign spending. This education premium not only garners more votes, but it also translates into higher probabilities of winning. The experimental results and sensitivity analyses show that it is unlikely that these results are explained by a hidden confound. The experiment also illuminates that the education premium flows from perceptions of candidate qualification and ability to pursue respondent interests.

A novel temperature prediction method without using energy equation based on physics-informed neural network (PINN): A case study on plate- circular/square pin-fin heat sinks

This study introduces a new physics-informed neural networks (PINN)-based prediction method to determine the temperature pattern of fluid and fins when flow passes over plate-circular/ plate-square pin fin heat sinks (PCPFHS / PSPFHS). The proposed method is based on calculating the velocity pattern on the fins' surface. For this target, a training algorithm based on the feed-forward neural network (FNN) (110 layers of learnable weights and 16 neurons in each layer), a nonlinear activation function (rectified linear unit, "ReLU") and the Adam method for optimization is used. The training algorithm is fed by transient large eddy simulation (LES) results at every 0.01 s time step for the total physical time of 100 s. According to the input parameter type, the training:validation ratio is varied between 70:30 and 90:10 in order to keep the coefficient of determination (R2) at its maximum. The automatic differentiation employed the forward accumulation approach to reduce calculation costs, while the transient training matrix fed the neural network. The adaptive gradient (AdaGrad) method is also to improve convergence process and its speed up. Based on the developed calculation tools, the temperature pattern for the flow and over the fins are calculated according to the energy balance on the fin surface and the transient pattern of velocity predicted by PINN. After careful validation with experimental data and sensitivity analysis on the number of neurons and layers, the thermal behavior of PCPFHS and PSPFHS are determined using the conduction heat transfer equation inside the fins via the finite element method and by assuming a heat balance between the fins' surface and airflow. As a result of the proposed method, it is possible to reduce the number of equations in the calculation process of these parameters. According to the results, it is found that PSPFHS has an average Nusselt number which is 9.63% greater than the one in PCPFHS. However, compared to PCPFHS, PSPFHS shows a -17.78% reduced vorticity ratio at Re = 4,865. The results indicated that, for long calculation times (for instance, at 2,000 s physical time), the PINN method reduces calculation costs up to 35% compared to the technique that directly solves the energy conservation in the whole domain.