State-of-the-Art Review on the Application of Membrane Bioreactors for Molecular Micro-Contaminant Removal from Aquatic Environment.

In recent years, the emergence of disparate micro-contaminants in aquatic environments such as water/wastewater sources has eventuated in serious concerns about humans' health all over the world. Membrane bioreactor (MBR) is considered a noteworthy membrane-based technology, and has been recently of great interest for the removal micro-contaminants. The prominent objective of this review paper is to provide a state-of-the-art review on the potential utilization of MBRs in the field of wastewater treatment and micro-contaminant removal from aquatic/non-aquatic environments. Moreover, the operational advantages of MBRs compared to other traditional technologies in removing disparate sorts of micro-contaminants are discussed to study the ways to increase the sustainability of a clean water supplement. Additionally, common types of micro-contaminants in water/wastewater sources are introduced and their potential detriments on humans' well-being are presented to inform expert readers about the necessity of micro-contaminant removal. Eventually, operational challenges towards the industrial application of MBRs are presented and the authors discuss feasible future perspectives and suitable solutions to overcome these challenges.

Numerical investigation of ibuprofen removal from pharmaceutical wastewater using adsorption process.

In the present study, a mathematical modelling was developed to investigate ibuprofen adsorption from pharmaceutical wastewater into activated carbon and sonicated activated carbon. The developed model was dissolved based on the finite element method. Effect of different operating parameters including particle porosity and diameter as well as ibuprofen diffusion coefficient in solution on the amount of ibuprofen adsorption at different time point and position in the particle were evaluated. It was found good agreement between experimental values and modelling results in terms of ibuprofen adsorption as a function time. The 84.5% and 92.5% of maximum adsorption was achieved for the AC and SAC at the centre of particle after 150 min. Increasing the particle porosity and ibuprofen diffusion coefficient was improved the ibuprofen adsorption into the adsorbent. However, the particle diameter had negative impact on the system performance. There was a decrease in solute adsorption from 84.10 to 7.30 mg/g and from 106 to 15.73 mg/g for the AC and SAC respectively with increasing the particle radius from 173 to 500 µm. Finally, it was concluded that the particle specifications play important role in the adsorption process as it was observed considerable change in the amount of adsorption at different positions in the particle with changing the particle specifications.

Ability of neural network cells in learning teacher motivation scale and prediction of motivation with fuzzy logic system.

We employed a new approach in the field of social sciences or psychological aspects of teaching besides using a very common software package that is Statistical Package for the Social Sciences (SPSS). Artificial intelligence (AI) is a new domain that the methods of its data analysis could provide the researchers with new insights for their research studies and more innovative ways to analyze their data or verify the data with this method. Also, a very significant element in teaching is teacher motivation that is the trigger that pushes the teachers forward, depending on some internal and external factors. In the current study, seven research questions were designed to explore different aspects of teacher motivation, and they were analyzed via SPSS. The current study also compared the results by using an adaptive neuro-fuzzy inference system (ANFIS). Due to the similarity of ANFIS to humans' brain intelligence, the results of the current study could be similar to humans regarding what happens in reality. To do so, the researchers used the validated teacher motivation scale (TMS) and asked participants to fill the questionnaire, and analyzed the results. When the inputs were added to the ANFIS system, the model indicated a high accuracy and prediction capability. The findings also illustrated the importance of the tuning model parameters for the ANFIS method to build up the AI model with a high repeatability level. The differences between the results and conclusions are discussed in detail in the article.

Thermal prediction of turbulent forced convection of nanofluid using computational fluid dynamics coupled genetic algorithm with fuzzy interface system.

Computational fluid dynamics (CFD) simulating is a useful methodology for reduction of experiments and their associated costs. Although the CFD could predict all hydro-thermal parameters of fluid flows, the connections between such parameters with each other are impossible using this approach. Machine learning by the artificial intelligence (AI) algorithm has already shown the ability to intelligently record engineering data. However, there are no studies available to deeply investigate the implicit connections between the variables resulted from the CFD. The present investigation tries to conduct cooperation between the mechanistic CFD and the artificial algorithm. The genetic algorithm is combined with the fuzzy interface system (GAFIS). Turbulent forced convection of Al2O3/water nanofluid in a heated tube is simulated for inlet temperatures (i.e., 305, 310, 315, and 320 K). GAFIS learns nodes coordinates of the fluid, the inlet temperatures, and turbulent kinetic energy (TKE) as inputs. The fluid temperature is learned as output. The number of inputs, population size, and the component are checked for the best intelligence. Finally, at the best intelligence, a formula is developed to make a relationship between the output (i.e. nanofluid temperatures) and inputs (the coordinates of the nodes of the nanofluid, inlet temperature, and TKE). The results revealed that the GAFIS intelligence reaches the highest level when the input number, the population size, and the exponent are 5, 30, and 3, respectively. Adding the turbulent kinetic energy as the fifth input, the regression value increases from 0.95 to 0.98. This means that by considering the turbulent kinetic energy the GAFIS reaches a higher level of intelligence by distinguishing the more difference between the learned data. The CFD and GAFIS predicted the same values of the nanofluid temperature.

Investigation on performance of particle swarm optimization (PSO) algorithm based fuzzy inference system (PSOFIS) in a combination of CFD modeling for prediction of fluid flow.

Herein, a reactor of bubble column type with non-equilibrium thermal condition between air and water is mechanistically modeled and simulated by the CFD technique. Moreover, the combination of the adaptive network (AN) trainer with the fuzzy inference system (FIS) as the artificial intelligence method calling ANFIS has already shown potential in the optimization of CFD approach. Although the artificial intelligence method of particle swarm optimization (PSO) algorithm based fuzzy inference system (PSOFIS) has a good background for optimizing the other fields of research, there are not any investigations on the cooperation of this method with the CFD. The PSOFIS can reduce all the difficulties and simplify the investigation by elimination of the additional CFD simulations. In fact, after achieving the best intelligence, all the predictions can be done by the PSOFIS instead of the massive computational efforts needed for CFD modeling. The first aim of this study is to develop the PSOFIS for use in the CFD approach application. The second one is to make a comparison between the PSOFIS and ANFIS for the accurate prediction of the CFD results. In the present study, the CFD data are learned by the PSOFIS for prediction of the water velocity inside the bubble column. The values of input numbers, swarm sizes, and inertia weights are investigated for the best intelligence. Once the best intelligence is achieved, there is no need to mesh refinement in the CFD domain. The mesh density can be increased, and the newer predictions can be done in an easier way by the PSOFIS with much less computational efforts. For a strong verification, the results of the PSOFIS in the prediction of the liquid velocity are compared with those of the ANFIS. It was shown that for the same fuzzy set parameters, the PSOFIS predictions are closer to the CFD in comparison with the ANFIS. The regression number (R) of the PSOFIS (0.98) was a little more than that of the ANFIS (0.97). The PSOFIS showed a powerful potential in mesh density increment from 9477 to 774,468 and accurate predictions for the new nodes independent of the CFD modeling.

Performance and application analysis of ANFIS artificial intelligence for pressure prediction of nanofluid convective flow in a heated pipe.

Heat transfer augmentation of the nanofluids is still an attractive concept for researchers due to rising demands for designing efficient heat transfer fluids. However, the pressure loss arisen from the suspension of nanoparticles in liquid is known as a drawback for developing such novel fluids. Therefore, prediction of the nanofluid pressure, especially in internal flows, has been focused on studies. Computational fluid dynamics (CFD) is a commonly used approach for such a prediction of fluid flow. The CFD tools are perfect and precise in prediction of the fluid flow parameters. But they might be time-consuming and expensive, especially for complex models such as 3-dimension modeling and turbulent flow. In addition, the CFD could just predict the pressure, and it is disabled for finding the relationship of such variables. This study is intended to show the performance of the artificial intelligence (AI) algorithm as an auxiliary method for cooperation with the CFD. The turbulent flow of Cu/water nanofluid warming up in a pipe is considered as a sample of a physical phenomenon. The AI algorithm learns the CFD results. Then, the relation between the CFD results is discovered by the AI algorithm. For this purpose, the adaptive network-based fuzzy inference system (ANFIS) is adopted as AI tool. The intelligence condition of the ANFIS is checked by benchmarking the CFD results. The paper outcomes indicated that the ANFIS intelligence is met by employing gauss2mf in the model as the membership function and x, y, and z coordinates, the nanoparticle volume fraction, and the temperature as the inputs. The pressure predicted by the ANFIS at this condition is the same as that predicted by the CFD. The artificial intelligence of ANFIS could find the relation of the nanofluid pressure to the nanoparticle fraction and the temperature. The CFD simulation took much more time (90-110 min) than the total time of the learning and the prediction of the ANFIS (369 s). The CFD modeling was done on a workstation computer, while the ANFIS method was run on a normal desktop.

Intensification of CO2 absorption using MDEA-based nanofluid in a hollow fibre membrane contactor.

Porous hollow fibres made of polyvinylidene fluoride were employed as membrane contactor for carbon dioxide (CO2) absorption in a gas-liquid mode with methyldiethanolamine (MDEA) based nanofluid absorbent. Both theoretical and experimental works were carried out in which a mechanistic model was developed that considers the mass transfer of components in all subdomains of the contactor module. Also, the model considers convectional mass transfer in shell and tube subdomains with the chemical reaction as well as Grazing and Brownian motion of nanoparticles effects. The predicted outputs of the developed model and simulations showed that the dispersion of CNT nanoparticles to MDEA-based solvent improves CO2 capture percentage compared to the pure solvent. In addition, the efficiency of CO2 capture for MDEA-based nanofluid was increased with rising MDEA content, liquid flow rate and membrane porosity. On the other hand, the enhancement of gas velocity and the membrane tortuosity led to reduced CO2 capture efficiency in the module. Moreover, it was revealed that the CNT nanoparticles effect on CO2 removal is higher in the presence of lower MDEA concentration (5%) in the solvent. The model was validated by comparing with the experimental data, and great agreement was obtained.

Prediction of gas velocity in two-phase flow using developed fuzzy logic system with differential evolution algorithm.

In this investigation, differential evolution (DE) algorithm with the fuzzy inference system (FIS) are combined and the DE algorithm is employed in FIS training process. Considered data in this study were extracted from simulation of a 2D two-phase reactor in which gas was sparged from bottom of reactor, and the injected gas velocities were between 0.05 to 0.11 m/s. After doing a couple of training by making some changes in DE parameters and FIS parameters, the greatest percentage of FIS capacity was achieved. By applying the optimized model, the gas phase velocity in x direction inside the reactor was predicted when the injected gas velocity was 0.08 m/s.

Influence of machine learning membership functions and degree of membership function on each input parameter for simulation of reactors.

To understand impact of input and output parameters during optimization and degree of complexity, in the current study we numerically designed a bubble column reactor with a single sparger in the middle of the reactor. After that, some input and output parameters were selected in the post-processing of the numerical method, and then the machine learning observation started to investigate the level of complexity and impact of each input on output parameters. The adaptive neuro-fuzzy inference system (ANFIS) method was exploited as a machine learning approach to analyze the gas-liquid flow in the reactor. The ANFIS method was used as a machine learning approach to simulate the flow of a 3D (three-dimensional) bubble column reactor. This model was also used to analyze the influence of input and output parameters together. More specifically, by analyzing the degree of membership functions as a function of each input, the level of complexity of gas fraction was investigated as a function of computing nodes (X, Y, and Z directions). The results showed that a higher number of membership functions results in a better understanding of the process and higher model accuracy and prediction capability. X and Y computing nodes have a similar impact on the gas fraction, while Z computing points (height of reactor) have a uniform distribution of membership function across the column. Four membership functions (MFs) in each input parameter are insufficient to predict the gas fraction in the 3D bubble column reactor. However, by adding two membership functions, all features of gas fraction in the 3D reactor can be captured by the machine learning algorithm. Indeed, the degree of MFs was considered as a function of each input parameter and the effective parameter was found based on the impact of MFs on the output.

Computational Modeling of Transport in Porous Media Using an Adaptive Network-Based Fuzzy Inference System.

This investigation is conducted to study the integration of the artificial intelligence (AI) method with computational fluid dynamics (CFD). The case study is hydrodynamic and heat-transfer analyses of water flow in a metal foam tube under a constant wall heat flux (i.e., 55 kW/m2). The adaptive network-based fuzzy inference system (ANFIS) is an AI method. A 3D CFD model is established in ANSYS-FLUENT software. The velocity of the fluid in the x-direction (Ux) is considered as an output of the ANFIS. The x, y, and z coordinates of the node's location are added to the ANFIS step-by-step to achieve the best intelligence. The number and type of membership functions (MFs) are changed in each step. The training process is done by the CFD results on the tube cross-sections at different lengths (i.e., z = 0.1, 0.2, 0.3, 0.4, 0.6, 0.7, 0.8, and 0.9), while all data (including z = 0.5) are selected for the testing process. The results showed that the ANFIS reaches the best intelligence with all three inputs, five MFs, and "gbellmf"-type MF. At this condition, the regression number is close to 1.

High-performance hybrid modeling chemical reactors using differential evolution based fuzzy inference system.

Bubbly flow behavior simulation in two-phase chemical reactors such bubble column type reactors is widely employed for chemical industry purposes. The computational fluid dynamics (CFD) approach has been employed by engineers and researchers for modeling these types of chemical reactors. In spite of the CFD robustness for simulating transport phenomena and chemical reactions in these reactors, this approach has been known as expensive for modeling such turbulent complex flows. Artificial intelligence (AI) algorithm of the adaptive network-based fuzzy inference system (ANFIS) are largely understood and utilized for the CFD approach optimization. In this hybrid approach, the CFD findings are learned by AI algorithms like ANFIS to save computational time and expenses. Once the pattern of the CFD results have been captured by the AI model, this hybrid model can be then used for process simulation and optimization. As such, there is no need for further simulations of new conditions. The objective of this paper is to obviate the need for expensive CFD computations for two-phase flows in chemical reactors via coupling CFD data to an AI algorithm, i.e., differential evolution based fuzzy inference system (DEFIS). To do so, air velocity as the output and the values of the x, and y coordinates, water velocity, and time step as the inputs are inputted the AI model for learning the flow pattern. The effects of cross over as the DE parameter and also the number of inputs on the best intelligence are investigated. Indeed, DEFIS correlates the air velocity to the nodes coordinates, time, and liquid velocity and then after the CFD modeling could be replaced with the simple correlation. For the first time, a comparison is made between the ANFIS and the DEFIS performances in terms of the prediction capability of the gas (air) velocity. The results released that both ANFIS and DEFIS could accurately predict the CFD pattern. The prediction times of both methods were obtained to be equal. However, the learning time of the DEFIS was fourfold of ANFIS.

Liquid temperature prediction in bubbly flow using ant colony optimization algorithm in the fuzzy inference system as a trainer.

In the current research paper a novel hybrid model combining first-principle and artificial intelligence (AI) was developed for simulation of a chemical reactor. We study a 2-dimensional reactor with heating sources inside it by using computational fluid dynamics (CFD). The type of considered reactor is bubble column reactor (BCR) in which a two-phase system is created. Results from CFD were analyzed in two different stages. The first stage, which is the learning stage, takes advantage of the swarm intelligence of the ant colony. The second stage results from the first stage, and in this stage, the predictions are according to the previous stage. This stage is related to the fuzzy logic system, and the ant colony optimization learning framework is build-up this part of the model. Ants movements or swarm intelligence of ants lead to the optimization of physical, chemical, or any kind of processes in nature. From point to point optimization, we can access a kind of group optimization, meaning that a group of data is studied and optimized. In the current study, the swarm intelligence of ants was used to learn the data from CFD in different parts of the BCR. The learning was also used to map the input and output data and find out the complex connection between the parameters. The results from mapping the input and output data show the full learning framework. By using the AI framework, the learning process was transferred into the fuzzy logic process through membership function specifications; therefore, the fuzzy logic system could predict a group of data. The results from the swarm intelligence of ants and fuzzy logic suitably adapt to CFD results. Also, the ant colony optimization fuzzy inference system (ACOFIS) model is employed to predict the temperature distribution in the reactor based on the CFD results. The results indicated that instead of solving Navier-Stokes equations and complex solving procedures, the swarm intelligence could be used to predict a process. For better comparisons and assessment of the ACOFIS model, this model is compared with the genetic algorithm fuzzy inference system (GAFIS) and Particle swarm optimization fuzzy inference system (PSOFIS) method with regards to model accuracy, pattern recognition, and prediction capability. All models are at a similar level of accuracy and prediction ability, and the prediction time for all models is less than one second. The results show that the model's accuracy with low computational learning time can be achieved with the high number of CIR (0.5) when the number of inputs ≥ 4. However, this finding is vice versa, when the number of inputs < 4. In this case, the CIR number should be 0.2 to achieve the best accuracy of the model. This finding could also highlight the importance of sensitivity analysis of tuning parameters to achieve an accurate model with a cost-effective computational run.

Evaluation of product of two sigmoidal membership functions (psigmf) as an ANFIS membership function for prediction of nanofluid temperature.

A nanofluid containing water and nanoparticles made of copper (Cu) inside a cavity with square shape is simulated utilizing the computational fluid dynamics (CFD) approach. The nanoparticles made up 15% of the nanofluid. By performing the simulation, the CFD output is characterized by the coordinates in the x, y, nanofluid temperature, and velocity in the y-direction that these outputs are obtained for different physical time iterations. Moreover, the CFD outputs are examined by one of the artificial techniques, i.e. adaptive network-based fuzzy inference system (ANFIS). For this purpose, the data was clustered via grid partition clustering, and the type of membership functions (MFs) was chosen product of two sigmoidal membership functions (psigmf). After reaching 99.9% of intelligence in ANFIS, the nanofluid temperature is predicted for the entire data, which are included in the learning processes. The results showed that the method of ANFIS can predict the thermal properties in different physical times at different computing points without having a training background at those times. Additionally, this study shows that with three membership functions at each input, the model's accuracy is higher than four functions.

Computational modeling of drug separation from aqueous solutions using octanol organic solution in membranes.

Continuous membrane separation of pharmaceuticals from an aqueous feed was studied theoretically by development of high-performance mechanistic model. The model was developed based on mass and momentum transfer to predict separation and removal of ibuprofen (IP) and its metabolite compound, i.e. 4-isobutylacetophenone (4-IBAP) from aqueous solution. The modeling study was carried out for a membrane contactor considering mass transport of solute from feed to organic solvent (octanol solution). The solute experiences different mass transfer resistances during the removal in membrane system which were all taken into account in the modeling. The model's equations were solved using computational fluid dynamic technique, and the simulations were carried out to understand the effect of process parameters, flow pattern, and membrane properties on the removal of both solutes. The simulation results indicated that IP and 4-IBAP can be effectively removed from aqueous feed by adjusting the process parameters and flow pattern. More removal was obtained when the feed flows in the shell side of membrane system due to improving mass transfer. Also, feed flow rate was indicated to be the most affecting process parameter, and the highest solute removal was obtained at the lowest feed flow rate.

gbell Learning function along with Fuzzy Mechanism in Prediction of Two-Phase Flow.

The integration of the computational fluid dynamics (CFD) and the adaptive network-based fuzzy inference system, known as ANFIS, is investigated for simulating the hydrodynamic in a bubble column reactor. The Eulerian-Eulerian two-phase model is employed as the CFD approach. For the ANFIS technique, a sensitivity analysis is done by varying the number of inputs and the number of membership functions (MFs). The x and z coordinates of the fluid location, the air velocity, and the pressure are considered as the inputs of the ANFIS, while the air vorticity is the output. The results revealed that the ANFIS with all four inputs and the MFs of five achieved the highest intelligence with the regression number close to 1. More specifically, gbell function in the learning framework is used to train all local computing nodes from solving Navier-Stokes equations. In the decision or prediction part, the fuzzy mechanism is used for the prediction of extra nodes that solve, which Navier-Stokes equations did not solve. The results show that the gbell function enables us to fully train all numerical points and also store data set in the frame of mathematical equations. Besides, this function responds well with the number of inputs and MFs for accurate prediction of reactor hydrodynamics. Additionally, a high number of MFs and input parameters influence the accuracy of the method during prediction. In the current study, gbell MF was studied to investigate its accuracy in the prediction of the two-phase flow. Also, different numbers of MFs were considered to investigate the level of accuracy and capability of prediction. ANFIS clustering methods, grid partition and fuzzy C-mean (FCM) clustering, are compared to see the ability of the method in prediction. To compare the accuracy of the ANFIS method with FCM clustering, the data were compared to the gaussmf function. The results showed that the method has high accuracy and that it could predict the flow pattern.

Influence of number of membership functions on prediction of membrane systems using adaptive network based fuzzy inference system (ANFIS).

In membrane separation technologies, membrane modules are used to separate chemical components. In membrane technology, understanding the behavior of fluids inside membrane module is challenging, and numerical methods are possible by using computational fluid dynamics (CFD). On the other hand, the optimization of membrane technology via CFD needs time and computational costs. Artificial Intelligence (AI) and CFD together can model a chemical process, including membrane technology and phase separation. This process can learn the process by learning the neural networks, and point by point learning of CFD mesh elements (computing nodes), and the fuzzy logic system can predict this process. In the current study, the adaptive neuro-fuzzy inference system (ANFIS) model and different parameters of ANFIS for learning a process based on membrane technology was used. The purpose behind using this model is to see how different tuning parameters of the ANFIS model can be used for increasing the exactness of the AI model and prediction of the membrane technology. These parameters were changed in this study, and the accuracy of the prediction was investigated. The results indicated that with low number of inputs, poor regression was obtained, less than 0.32 (R-value), but by increasing the number of inputs, the AI algorithm led to an increase in the prediction capability of the model. When the number of inputs increased to 4, the R-value was increased to 0.99, showing the high accuracy of model as well as its high capability in prediction of membrane process. The AI results were in good agreement with the CFD results. AI results were achieved in a limited time and with low computational costs. In terms of the categorization of CFD data-set, the AI framework plays a critical role in storing data in short memory, and the recovery mechanism can be very easy for users. Furthermore, the results were compared with Particle Swarm Optimization (PSOFIS), and Genetic Algorithm (GAFIS). The time for prediction and learning were compared to study the capability of the methods in prediction and their accuracy.

Simulation of liquid flow with a combination artificial intelligence flow field and Adams-Bashforth method.

Direct numerical simulation (DNS) of particle hydrodynamics in the multiphase industrial process enables us to fully learn the process and optimize it on the industrial scale. However, using high-resolution computational calculations for particle movement and the interaction between the solid phase and other phases in fine timestep is limited to excellent computational resources. Solving the Eulerian flow field as a source of solid particle movement can be very time-consuming. However, by the revolution of the fast and accurate learning process, the Eulerian domain can be computed by smart modeling in a very short computational time. In this work, using the machine learning method, the flow field in the square shape cavity is trained, and then the Eulerian framework is replaced with a machine learning method to generate the artificial intelligence (AI) flow field. Then the Lagrangian framework is coupled with this AI flow field, and we simulate particle motion through the fully AI framework. The Adams-Bashforth finite element method is used as a conventional CFD method (Eulerian framework) to simulate the flow field in the cavity. After simulating fluid flow, the ANFIS method is used as an AI model to train the Eulerian data-set and represents AI fluid flow (framework). The Lagrangian framework is coupled with the AI method, and the particle freely migrates through this artificial framework. The results reveal that there is a great agreement between Euler-Lagrangian and AI- Lagrangian in the cavity. We also found that there is an excellent agreement between AI overview with the Adams-Bashforth approach, and the new combination of machine learning and CFD method can accelerate the calculation of the flow field in the square-shaped cavity. AI model can mimic the vortex structure in the cavity, where there is a zero-velocity structure in the center of the domain and maximum velocity near the moving walls.

Pattern recognition of the fluid flow in a 3D domain by combination of Lattice Boltzmann and ANFIS methods.

Many numerical methods have been used to simulate the fluid flow pattern in different industrial devices. However, they are limited with modeling of complex geometries, numerical stability and expensive computational time for computing, and large hard drive. The evolution of artificial intelligence (AI) methods in learning large datasets with massive inputs and outputs of CFD results enables us to present completely artificial CFD results without existing numerical method problems. As AI methods can not feel barriers in numerical methods, they can be used as an assistance tool beside numerical methods to predict the process in complex geometries and unstable numerical regions within the short computational time. In this study, we use an adaptive neuro-fuzzy inference system (ANFIS) in the prediction of fluid flow pattern recognition in the 3D cavity. This prediction overview can reduce the computational time for visualization of fluid in the 3D domain. The method of ANFIS is used to predict the flow in the cavity and illustrates some artificial cavities for a different time. This method is also compared with the genetic algorithm fuzzy inference system (GAFIS) method for the assessment of numerical accuracy and prediction capability. The result shows that the ANFIS method is very successful in the estimation of flow compared with the GAFIS method. However, the GAFIS can provide faster training and prediction platform compared with the ANFIS method.

ANFIS grid partition framework with difference between two sigmoidal membership functions structure for validation of nanofluid flow.

In this study, a square cavity is modeled using Computational Fluid Dynamics (CFD) as well as artificial intelligence (AI) approach. In the square cavity, copper (Cu) nanoparticle is the nanofluid and the flow velocity characteristics in the x-direction and y-direction, and the fluid temperature inside the cavity at different times are considered as CFD outputs. CFD outputs have been assessed using one of the artificial intelligence algorithms, such as a combination of neural network and fuzzy logic (ANFIS). As in the ANFIS method, we have a non-dimension procedure in the learning step, and there is no issue in combining other characteristics of the flow and thermal distribution beside the x and y coordinates, we combine two coordinate parameters and one flow parameter. This ability of method can be considered as a meshless learning step that there is no instability of the numerical method or limitation of boundary conditions. The data were classified using the grid partition method and the MF (membership function) type was dsigmf (difference between two sigmoidal membership functions). By achieving the appropriate intelligence in the ANFIS method, output prediction was performed at the points of cavity which were not included in the learning process and were compared to the existing data (the results of the CFD method) and were validated by them. This new combination of CFD and the ANFIS method enables us to learn flow and temperature distribution throughout the domain thoroughly, and eventually predict the flow characteristics in short computational time. The results from AI in the ANFIS method were compared to the ant colony and fuzzy logic methods. The data from CFD results were inserted into the ant colony system for the training process, and we predicted the data in the fuzzy logic system. Then, we compare the data with the ANFIS method. The results indicate that the ANFIS method has a high potentiality compared to the ant colony method because the amount of R in the ANIFS system is higher than R in the ant colony method. In the ANFIS method, R is equal to 0.99, and in the ant colony method, R is equal to 0.91. This shows that the ant colony needs more time for both the prediction and training of the system. Also, comparing the pattern recognition in the two systems, we can obviously see that by using the ANFIS method, the predictions completely match the target points. But the other method cannot match the flow pattern and velocity distribution with the CFD method.