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This research employs a neural network, specifically the Levenberg–Marquardt algorithm, to characterize the entropy optimization performance in the electro-magneto-hydrodynamic flow of a Casson tetra-hybrid nanofluid over a rotating disk. The problem was formulated mathematically using equations for momentum, continuity, and temperature. This study converts ordinary differential equations (ODEs) into partial differential equations (PDEs) by a self-similarity transformation. The equations are resolved via the fourth-order Runge-Kutta method in combination with a shooting technique for obtaining the required datasets. Using the Levenberg-Marquardt algorithm (LMA), these datasets are characterised as training, testing, and validation. The proposed outcomes are presented in multiple tables and graphs. This trained neural network is then utilized to predict the heat flow velocity and Nusselt number of the rotating disk. The developed model was evaluated using mean square error, error analysis, and regression analysis, thereby confirming the consistency, accuracy, and reliability of the designed technique. The best validation performance for skin friction and the Nusselt number for the Casson tetra-hybrid nanofluid flow across a rotating disk is 8752e-05 at epoch 95 and 0.00033239 at epoch 37. Training, validation, testing, and all performance metrics of the artificial neural network model are close to unity. As magnetic field strength increases, temperature profiles rise in di-hybrid, ternary-hybrid, and tetra-hybrid nanoparticle scenarios. Tetra-hybrid nanofluids are considered superior fluids when compared to di-hybrid, ternary-hybrid, and tetra-hybrid nanofluids. This optimization method holds promise for diverse applications in biotechnology, microbiology, and medicine, offering significant potential for various fields. Graphical Abstract Graphical Abstract

The purpose of this study is to investigate entropy optimization in the magneto-hydrodynamic and electro-magneto-hydrodynamic flow of a Casson hybrid nanofluid over a rotating disk with nonlinear thermal radiation. The governing dimensional partial differential equations were reduced to ordinary differential equations by using appropriate transforms and solved numerically. The effects of several physical factors on the velocity, temperature, entropy generation, Bejan number, Nusselt number, and skin friction coefficient in comparison to the nanofluid and hybrid nanofluid scenarios over a rotating disk are explored both tabularly and graphically. The constructed artificial neural network is the most appropriate for predicting the skin friction coefficient and Nusselt number over a rotating disk. As the magnetic field strength increased, the velocity profiles decreased in the nanofluid and hybrid nanofluid scenarios. When the thermal radiation increased, the amount of entropy generated for the nanofluids and hybrid nanofluids also increased. We built the artificial neural networking model using 51 sample values of the skin friction coefficient and Nusselt number as outputs. This section provides various dimensionless parameters, which are all inputs. We utilized 70% of the data for training, and 15% for validation and testing. The Levenberg–Marquardt algorithm and back-propagation were used to train the neural network. The best validation performance for skin friction and the Nusselt number for the Casson hybrid nanofluid across a rotating disk are 6652e-07 at epoch 138 and 2.7094e-05 at epoch 7. Additionally, the training, validation, testing, and performance of the ANN model were closer to unity.

This study employs numerical and statistical approaches to investigate the entropy optimization of steady Casson nanofluid flow over three different geometries subject to boundary conditions induced by convective flow. Multiple linear regression is employed to statistically examine. The present model incorporates several novel elements, such as Arrhenius activation energy, Brownian motion, the Cattaneo-Christov dual flux, thermophoresis, thermal radiation, and so on. Moreover, a comparison is presented between Newtonian and non-Newtonian fluids. By applying the proper similarity transformations, ordinary differential equations (ODEs) are obtained by converting foundational partial differential equations (PDEs). The Runge-Kutta fourth-order method is utilised to solve the obtained ODEs along with the shooting technique. The outcomes are visually depicted via tables and graphs. The velocity drops with increasing Grashof number, and the magnetic field becomes progressively more forceful as the suction parameter increases. The temperature gets reduced with the increase of the suction parameter, solute Grashof number increases with the magnetic field, thermophoresis, and radiation parameters. The entropy is observed to rise with the increase of the effective parameters (magnetic field, Brinkmann number and radiation). The MAD (mean absolute deviation), MSE (mean squared error), and RMSE (root mean square error) values are approaching zero, indicating that the derived outcomes are highly accurate. A lower MAPE (mean absolute percentage error) suggests that the model has a higher level of precision. Therefore, the outcomes of the present model are more precise and reliable. This study has various potential applications such as power plant heat exchangers, material processing industries, and solar thermal energy systems.

In modern times, the chatbot is implemented to store data collected through a question and answer system, which can be applied in the Python program. The data to be used in this program is the Cornell Movie Dialog Corpus which is a dataset containing a corpus which contains a large collection of metadata-rich fictional conversations extracted from film scripts. The application of chatbot in the Python program can use various models, the one specifically used in this program is the LSTM. The output results from the chatbot program with the application of the LSTM model are in the form of accuracy, as well as a data set that matches the information that the user enters in the chatbot dialog box input. The choice of models that can be applied is based on data that can affect program performance, with the aim of the program which can determine the high or low level of accuracy that will be generated from the results obtained through a program, which can be a major factor in determining the selected model. Based on the application of the LSTM model into the chatbot, it can be concluded that with all program test results consisting of a variety of different parameter pairs, it is stated that Parameter Pair 1 (size_layer 512, num_layers 2, embedded_size 256, learning_rate 0.001, batch_size 32, epoch 20) from File 3 is the LSTM Chatbot with the avg accuracy value of 0.994869 which uses the LSTM model is the best parameter pair.

The proficiency of hybrid nanoparticles in increasing heat transfer has impressed many researchers to analyze the working of those fluids further. The current work studies the impact of entropy generation on electromagnetohydrodynamic (EMHD) hybrid nanofluid (copper-aluminum oxide) flow over a rotating disk in the presence of the porous medium, Darcy-Forchheimer, heat generation, viscous dissipation, and thermal radiation. By applying the self-similarity variables, the partial differential equations are converted int o ordinary differential equations. Aft er that, the dimensionless equations are numerically solved using the Runge-Kutta (R-K) technique, and the comparison is made between the numerical technique (R-K method) and the Homotopy Perturbation Method (HPM), where HPM yields a more effective and dependable conclusion. To highlight their physical significance, unique characteristic graphs are shown for the profiles of velocity, temperature, entropy generation, and Bejan number, along with a suitable explanation. The hybrid nanofluid velocity decreases with larger values of the magnetic parameter, but the velocity profile increases with the higher electric field. The findings are novel and innovative, with several modern industrial applications, and the results are in excellent concurrence with the relevant literature. Applications of the current research are refrigeration, electronics, heat exchangers, and lubricants.

The present study investigates the effects of Soret and Dufour on MHD non-Darcy convective flow of a viscous incompressible radiating micropolar fluid past an inclined permeable plate with non-uniform heat source or sink and chemical reaction. The flow field with partial differential equations are converted to a system of nonlinear coupled ordinary differential equations by similarity transformations and solved employing shooting method. Swiftness in the momentum of the fluid is observed as the Darcian and fluid parameter ascends. Speed of the fluid in angular rotation ascends as the material parameter or sheet inclination or magnetic parameter increases. Molecular diffusion rate is more as the microparticles undergo chemical reactions. While the thermal distribution rate reduces because of the reactions. Rest of the results are interpreted graphically. A good agreement is observed with the previous publications. The presence of chemical reaction makes the problem industrially applicable taking the case of heterogeneous reactions.

The objective of the current article is to probe entropy generation in EMHD thermal transports of hybrid nanofluid which has indeed been enhanced by better thermal transfer to handle growing heat density of tiny and other technological operations. Non-Newtonian fluids like Casson and Williamson are encrypted for this present physical model and also in the blood, gold ( Au ) and silver ( Ag ) are hybridized to form an extremely diluted, homogeneous combination. The non-linear PDE system of equations are synthesized into an ordinary differential system via appropriate self-similarity variables, which are then computed by utilizing the homotopy perturbation technique. Visual representations are used to demonstrate the effects of various factors. With a few exceptions, the model’s study results are pretty close to those found in the literature. For various profiles, with the influence of active parameters, the results are displayed graphically. This shows that when the parameters of magnetic, Casson and Williamson fluids are inclined, the radial and azimuthal velocity profiles decrease, sharply it attains contradiction phenomena to the increasing electric field inputs. Entropy production increases for magnetic fields and the Bejan number exhibits declination. The predictions are pertinent to the delivery of targeted nanoparticle drugs in hematology.

This work concentrates on the study of the unsteady hydromagnetic heat and mass transfer of a Newtonian fluid in a permeable stretching surface with viscous dissipation and chemical reaction. Thermal radiation, velocity slip, concentrate slip are also considered. The unsteady in the flow, velocity, temperature and concentration distribution is past by the time dependence of stretching velocity surface temperature and surface concentration. Appropriate similarity transformations are used to convert the governing partial differential equations into a system of coupled non-linear differential equations. The resulting coupled non-linear differential equations are solved numerically by using the fourth order Runge-Kutta method along with shooting technique. The impact of various pertinent parameters on velocity, temperature, concentration, skin friction coefficient, Nusselt number and the Sherwood number are presented graphically and in tabular form. Our computations disclose that fluid temperature has inverse relationship with the radiation parameter.

The radiation effects on unsteady flow of a viscous incompressible fluid past an exponentially accelerated infinite isothermal vertical plate with uniform mass diffusion is considered in the presence of magnetic field and heat source. The governing partial differential equations are converted into a non-dimensional form and solved numerically by applying a Crank-Nicholson type of implicit finite difference method with a tri-diagonal matrix manipulation and an iterative procedure. The profiles of unsteady velocity, temperature and concentration are shown graphically for different values of thermo physical parameters. Also, the simulated values of the skin-friction coefficient, Nusselt number and Sherwood number are presented. This model finds applications in solar energy collection systems, geophysics and astrophysics, aero space and also in the design of high temperature chemical process systems.

This study’s primary objective is to investigate the Jeffery–Hamel model and entropy generation on the Magnetohydrodynamic (MHD) flow of second-grade hybrid nanofluid across stretchable converging and diverging channels. Silver (Ag) and ferroferric oxide (Fe 3 O 4 ) are nanoparticles, using blood as the base fluid. The controlling nonlinear coupled Partial Differential Equations (PDEs) are transformed into Ordinary Differential Equations (ODEs) with similarity transformations and then solved using the Homotopy Perturbation Method (HPM) and shooting technique (Runge–Kutta fourth order) in the MAPLE software. The Homotopy Perturbation Method (HPM) is compared to the Numerical Method (NM), and the results are more accurate and reliable. The effects of velocity, temperature, entropy production, and the Bejan number on physical parameters like a magnetic field, Reynolds number, magnetic field, porosity, and the Brinkman number are discussed through graphs and tables. The heat transfer and skin friction coefficients are also studied and portrayed as graphs. The velocity profile increases for second-grade hybrid nanofluid across stretchable converging and diverging channels as the magnetic field parameter increase. The velocity profile decreases as Deborah’s number increases for the converging channel. As Deborah’s number increases, the velocity profile increases for the diverging channels. The magnetic field and volume fraction increase as the skin friction and Nusselt number increase for second-grade hybrid nanofluid across stretchable converging and diverging channels. This theoretical model, which incorporates MHD with blood flow, is essential for biomedical applications, magnetic resonance imaging (MRI), particularly radiofrequency ablation (RFA), tumour treatment, and cancer therapy. Graphical abstract