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Abstract Artificial Neural Networks are incredibly efficient at handling complicated and nonlinear mathematical problems, making them very useful for tackling these challenges. Artificial neural networks offer a special computational architecture that is extremely valuable in disciplines like biotechnology, biological computing, and computational fluid dynamics. The present work investigates the applicability of back-propagation artificial neural networks in conjunction with the Levenberg-Marquardt algorithm for evaluating heat transmission in hybrid nanofluids. This work focuses on the computational analysis of a MgO + GO/EG hybrid nanofluid’s steady mixed convection flow over an exponentially stretched sheet, considering multiple slip boundary conditions, thermal conductivity, heat generation, and thermal radiation. A nonlinear system of ordinary differential equations is produced from the basic associated partial differential system by performing the proper exponential similarities modifications. For generating benchmark datasets, the resulting ordinary differential equations are processed employing the bvp4c method. Considering benchmark datasets set aside for training (70%), testing (15%), and validation (15%), the Levenberg-Marquardt algorithm, which employs back-propagation in artificial neural networks, is implemented. The accuracy of the suggested strategy for handling nonlinear problems is verified utilizing mean squared error, error histograms, and regression analysis, which are all used to evaluate the methodology. Outstanding agreement is seen when ANN outputs are compared to numerical results. The flow properties, including temperature, velocity, and concentration profiles, are shown graphically and numerically. For practical purposes, it is therefore essential to analyze the flow and heat transfer in hybrid nanofluids over exponentially extending and shrinking surfaces under mixed convection and heat source scenarios. Hybrid nanofluid problems have a wide range of practical and industrial applications, such as medication delivery, manufacturing, microelectronics, nuclear plant cooling, and marine engineering.

Artificial neural networks have revolutionized machine learning by providing exceptional capabilities for modeling complicated mechanisms and solving various challenges. Backpropagation is an important training technique in the field of artificial neural networks. However, this technique must be optimized when working with complicated fluid dynamics. This study analyzes the three-dimensional radiative flow of a tangent hyperbolic fluid driven by the Cattaneo-Christov flux system across a porous stretching sheet using ANN backpropagation enhanced by Bayesian Regularization approach. Heat and mass transfer analysis includes thermal radiation, chemical reactions and Cattaneo-Christov flux model. Porosity, radiation, chemical reaction rate, and ion slip effect are among the important physical characteristics that are modified to see how they affect fluid dynamics. Using MATLAB's BVP4C solver, the velocity, temperature, and concentration profiles that result from these model equations provide the training dataset for ANNs. The dataset is divided into 80 % for training, 10 % for testing, and 10 % for validation. Performance plots, regression graphs, and error histograms are used to analyze the performance of the LMT-based ANN and demonstrate its high accuracy and efficiency. With an R2 value of 1, the ANN produced a mean squared error of around 10⁻11. Fluid mobility drops as the magnetic parameter grows, while the thermal profile exhibits an increasing trend. Similarly, decreasing fluid velocity is the outcome of raising the porosity parameter. The study's conclusions have great potential for use in sectors that need sophisticated cooling and heating equipment.

ABSTRACTIn this work, computational intelligence methodologies are used to investigate the trihybrid nanofluid, a new theoretical model with remarkable thermal transmission properties to enhance liquid thermal performance. The nanostructure Cu, Al2O3, and TiO2 were immersed in the base liquid (C2H6O2) to produce (Cu + Al2O3 + TiO2/C2H6O2) trihybrid nanofluid. In a Darcy-Forchheimer porous medium over a stretching Riga sheet, this study examines the electromagnetic ternary hybrid nanofluid flow under various slip situations. The study takes into account the complex interactions between a number of variables, including as viscous dissipation, radiation, heat sources, and chemical reactions. Similarity transformations are used to convert complex partial differential equations for flow, energy, and concentration into nonlinear ordinary differential equations. The highly nonlinear equations of the problem are solved numerically with the use of techniques from the bvp4c approach. The results of the bvp4c method produce the reference dataset required for the Levenberg-Marquardt backpropagation of neural networks (LMBNN). The neural network performance is validated using regression analysis, mean square errors, and error histogram data. The model problem’s consistency and precision are evaluated using the absolute error, which is given for each model instance at around 10−06–10−08, 10−05–10−10 and 10−06 05–10−09. In order to reduce mean square error, the nonlinear fluid dynamics system’s numerical solutions have been taken into consideration. Using the comparative configurations of MSE, error histograms, state transitions, correlation, and regression, the reliability and competence of the stochastic technique are verified.

Abstract This study explores the impacts of heat transportation on hybrid (Ag + MgO) nanofluid flow in a porous cavity using artificial neural networks (Bayesian regularization approach (BRT-ANN) neural networks technique). The cavity considered in this analysis is a semicircular shape with a heated and a cooled wall. The dynamics of flow and energy transmission in the cavity are influenced by various features such as the effect of magnetize field, porosity and volume fraction of nanoparticles. To explore the outcomes of these features on hybrid nanofluid thermal and flow transport, a BRT-ANN model is developed. The ANN model is trained using a dataset generated through numerical scheme. The trained ANN model is then used to predict the heat and flow transport characteristics for various input parameters. The accuracy of the ANN simulation is confirmed through comparison of the predicted results with the results obtained through numerical simulations. By maintaining the corrugated wall uniformly heated, we inspected the levels of isotherms, streamlines and heat transfer distribution. A graphical illustration highlights the characteristics of the Hartmann and Rayleigh numbers, permeability component in porous material, drag force and rate of energy transport. According to the percentage analysis, nanofluids (Ag + MgO/H2O) are prominent to enhance the thermal distribution of traditional fluids. The study demonstrates the potential of ANNs in predicting the impacts of various factors on hybrid nanofluid flow and heat transport, which can be useful in designing and optimizing heat transfer systems.

Abstract The flow at a time-independent separable stagnation point on a Riga plate under thermal radiation and electro-magnetohydrodynamic settings is examined in this research. Two distinct base fluids-H2O and C2H6O2 and TiO2 nanostructures develop the nanocomposites. The flow problem incorporates the equations of motion and energy along with a unique model for viscosity and thermal conductivity. Similarity components are then used to reduce these model problem calculations. The Runge Kutta (RK-4) function yields the simulation result, which is displayed in graphical and tabular form. For both involved base fluid theories, the nanofluids flow and thermal profiles relating to the relevant aspects are computed and analyzed. According to the findings of this research, the C2H6O2 model heat exchange rate is significantly higher than the H2O model. As the volume percentage of nanoparticles rises, the velocity field degrades while the temperature distribution improves. Moreover, for greater acceleration parameters, TiO2/ C2H6O2has the highest thermal coefficient whereas TiO2/ H2O has the highest skin friction coefficient. The key observation is that C2H6O2 base nanofluid has a little higher performance than H2O nanofluid.

Current work explores the intricacies of magnetohydrodynamic and mix convectional boundary-layer flow concerning couple stress Casson nanofluid (CSCNF) dynamics via a 3D stretchable surface. The addition of active and passive control mechanisms for nanoscales creates an innovative dimension to the exploration. Remarkably, the analysis incorporates the influence of non-Fourier and non-Fickian heat and mass flux, alongside the effects of thermophoresis and Brownian diffusion, to systematically investigate the heat and mass transportation phenomena. The governing equations (PDEs) describing the MHD-3DCSCNF model are converted into a set of ordinary differential equations to facilitate the ANN analysis. Employing the bvp4c technique, a dataset is systematically generated for the back propagation artificial neural network with Levenberg–Marquardt Algorithm (BANN-LMA) through four distinct scenarios. Via accurate testing, validation, and training, the BANN-LMA produces estimated results for the MHD-3DCSCNF problem. The performance validation of BANN-LMA is executed through several metrics, involving the mean squared error, error histogram and regression analysis. The training process, characterized by minimizing the MSE through a gradient descent methodology with optimized weights, exhibits a compelling correlation R = 1, between the target and network output. Furthermore, the consistent convergence observed highlights the method robustness and reliability.

Abstract This study looks at the natural convections of Cu + Al2O3/H2O nanofluid into a permeable chamber. The magnetic field is also executed on the flow field and the analysis has been approached numerically by the control volume method. The study of hybrid nanofluid heat in terms of the transfer flux was supplemented with a wide range of parameters of hybrid nanofluid fractions, Rayleigh numbers Hartmann numbers and porosity factor. It's also determined that the flow and thermal distribution are heavily affected by the concentration of the nanoparticles. The concentration of nanoparticles increases the transport of convective energy inside the enclosure. The primary findings demonstrate that a rise in both the Rayleigh number and Darcy number leads to an improvement in convective heat transfer within the enclosure. However, the porosity has a negligible effect. Additionally, the rotation in a clockwise direction has a beneficial impact on the dispersion of heat transfer throughout the cavity. Furthermore, it is concluded that hybrid nanofluids are more reliable than conventional fluids in improving thermal properties.

Abstract Hybrid nanofluids are extremely important in field of engineering and technology due to their higher heat transportation performance resulting in increased heat transfer rates. In the presence of thermal heat flux, the effect of a slanted MHD with velocity slip condition on a CNTs hybrid nanocomposite across a gradually extending surface is investigated. In present analysis, Maxwell nanofluid is embedded with SWCNT and MWCNT (single and multiple wall carbon nanotubes) nanoparticles. The nanomaterials transformation framework is obtained by employing Xue modified theoretical model. Various factors like dissipation, thermal radiations and Ohmic heat influences are adequately implemented in heat formulation. The physical features of thermodynamical mechanism of irreversibility are explored. The thermodynamics second law is used to produce the entropy optimization formulation. In addition, entropy is utilized to assess the energy aspects of a heat exchanger. Utilizing appropriate parameters, the model nonlinear PDEs are transformed to ODEs. The HAM technique is used to compute the solution of nonlinear ODEs. For both types of CNTs, the variations of entropy rate, Bejan number, velocity and temperature field versus key technical parameters is analyzed. The Nu and C f computational result for both CNTs are examined in tabulated and chart form. Velocity is inversely proportional to magnetic and solid volume nanoparticle parameters. The Br and Rd accelerates NG and Be for both nanocomposites. Additionally, a comparison of the HAM result and the numerical result is validated.

The current investigation employs a numerical simulation to demonstrate the impact of hall current on unsteady free convective flow caused by hybrid-nanofluid over a revolving sphere approaching the stagnation point. The prominent characteristics of Lorentz force as a result of magnetic field coupling with hybrid nanofluid is also explored. The process of energy and mass transmission is inspected with nonlinear thermal radiations, non-uniform energy supply, dissipation and nonlinear chemical reaction. In current flow model, a unique class of nanofluid known as the hybrid nanofluid is being used, which contain GO (graphene oxide) and MoS2 (molybdenum disulfide) with water. The angular speed of both the sphere and free stream changes frequently with time. Employing adequate dimensionless variables, the partial-differential patterns strongly non-linear that represent the situational analysis are morphed into non-linear ordinary differential patterns. The analytical outcomes of ordinary differential pattern have been developed via OHAM technique. Utilizing tables and graphs, various aspects of such controllable physical characteristics have been highlighted and explored in depth. For varying values of M,φ,δ,Sc and Kn,the variations in Cfx, Cfz,Nu and Sh in MoS2-GO/H2O are the greatest as contrasted to MoS2/H2O. The results are also compared to those reported existing literature and they are noticed to be in very close agreement.

For the reliable results of regression analysis, influence diagnostic methods play an important role. The performance of various proposed residuals for the gamma-Pareto regression model (G-PRM) is presented in this study. These proposed residuals are partitioned into standardized and adjusted residual forms. For the detection of influential observations, difference of fits (DFFITS) was used in both standardized and adjusted residuals. To detect influential points, these residuals are compared through Monte Carlo Simulation also real data (Ardennes data) are analysed to show the benefits of the proposed methods. The likelihood residuals performed better for small dispersion than others. Additionally, all forms of adjusted residuals are the same, not much more efficient than the standardized form. All standardized residuals behave in the same way for wider dispersion, and they are superior to the likelihood residuals for the detection of influential points. [ABSTRACT FROM AUTHOR]

The subject of discussion in this analysis is the time independent flow of electrically conducting nanofluid with entropy generation over a radially flexible disk. Considerations for magnetic fields, nonuniform heat generation, Darcy-Forchheimer porous space, dissipation, Ohmic heating and chemical reactions with activation energy are incorporated into the flow distribution. For a number of engineering and biomedical objectives, a mathematical model is introduced with the goal of accelerating the rate of energy transmission and improving the performance and efficiency of heat energy transportation. Titanium dioxide nanomaterial is consisting of two base fluid, water and ethylene glycol (EG), to synthesize the nanofluid (water/TiO2 and ethylene EG/TiO2). Additionally, the second thermodynamic law has been used to model entropy generation. This model takes into account the irreversibility of heat, fluid friction and joule dissipation processes. The problem has been modeled as a set of partial differential equations. That are streamlined into a system of ODEs by using similarity substitutions. The retrieved differential equations are then assessed utilizing computational approach HAM. For consistency and validity, the results are examined using numerical methodology (shooting method). Also, investigations are conducted into the effects of the radiation, magnetic factors, Brinkman number, volume fraction of nanoparticles on the entropy and Bejan number. Moreover, visually and computationally, the impacts of design variables on the movement, temperature and concentration profile, drag force, heat and mass flux rate are explored. The findings exhibit great comparability when examined to those of the articles that were previously published. The planned analysis demonstrates the significance of this nanofluids in industrial, pharmaceutical, chemical and nuclear plants as well as solar and other technologies.

Abstract To enhance the surface properties of solids the mechanism of thin films is frequently used. Penetration, degradation, stiffness, illumination, diffusion, absorption, and electric performance are all characteristics of a bulk substance medium that a thin film can improve. In nanotechnology, thin film processing can be extremely useful. Therefore, the time-dependent nonlinearly convective stream of thin film nanoliquid over an inclined stretchable sheet with magnetic effect is investigated in current work. The features of mass and heat transport processes are explained using important factors like thermophoresis and Brownian movement. Nonlinear partial differential equations are obtained to model the time-dependent liquid film flow over an inclined surface, which are then turned into couple ordinary differential equations utilizing appropriate alterations. The results of the computation of the model problem are collected using an analytical approach Homotopy Analysis Method and presented the final finding numerically and graphically. During the flow assessment, the impact of individual flow factors such as magnetic, Brownian, and thermophoresis parameters on regular profiles (temperature, velocity, and concentration) are analyzed and found to be quite remarkable. Furthermore, the consequence of M and Nt factors on the velocity, concentration and thermal distribution leads to diminishing conduct. On the other hand, the thermal profile of the liquid film rises in response to the thermophoresis factor. The % wise variation in the skin friction, Nusselt number and Sherwood number versus physical parameters has been obtained and discussed.

Abstract This work investigates numerically the solution of Darcy–Forchheimer flow for hybrid nanofluid by employing the slip conditions. Basically, the fluid flow is produced by a swirling disk and is exposed to thermal stratification along with non-linear thermal radiation for controlling the heat transfer of the flow system. In this investigation, the nanoparticles of titanium dioxide and aluminum oxide have been suspended in water as base fluid. Moreover, the Darcy–Forchheimer expression is used to characterize the porous spaces with variable porosity and permeability. The resulting expressions of motion, energy and mass transfer in dimensionless form have been solved by HAM (Homotopy analysis method). In addition, the influence of different emerging factors upon flow system has been disputed both theoretically in graphical form and numerically in the tabular form. During this effort, it has been recognized that velocities profiles augment with growing values of mixed convection parameter while thermal characteristics enhance with augmenting values of radiation parameters. According to the findings, heat is transmitted more quickly in hybrid nanofluid than in traditional nanofluid. Furthermore, it is estimated that the velocities of fluid $$f^{\prime}\left( \xi \right),g\left( \xi \right)$$ f ′ ξ , g ξ are decayed for high values of $$\phi_{1} ,\phi_{2} ,\,Fr$$ ϕ 1 , ϕ 2 , F r and $$k_{1}$$ k 1 factors.

Abstract In this investigation, heat transportation together with irreversibility analysis for the flow of couple stress hybrid nanofluid past over a stretching surface is considered. The innovative characteristics and aims of this work are to note that the transportation heat couple stress model involves EMHD, viscous dissipation, Joule heating, and heat absorption, and omission. The hybrid nanofluid is prepared due to the suspension of the solid nanoparticles of the SWCNTs and MWCNTs in pure human blood. This mathematical model is an appropriate model for biological advantages including testing of human blood for drug deliveries to various parts of the human body. Particularly, the Prandtl number used for the blood is 21 and very large as compared to the other base fluids. Necessary modifications are used to translate the defining partial differential equations and boundary conditions into a layout that can be computed. To obtain mathematical approximations for the resulting scheme of nonlinear differential equations, the innovative homotopy analysis method (HAM) is used. The explanation for velocity, energy, and entropy are exposed and the flow against various influential factors ( $$E,\;M,\;k,\;Q,\;S\;{\text{and}}\;Ec$$ E , M , k , Q , S and E c ) is discussed graphically. The numerical values are calculated and summarized for dimensionless $$C_{{fx}} \;{\text{and}}\;Nu_{x} .$$ C fx and N u x . In addition, the current study is compared for various values of $$\Pr$$ Pr to that published literature and an impressive agreement in terms of finding is reported. It has also been noticed that the $$M$$ M and $$E$$ E factors retard the hybrid nanofluid flow, while the temperature of fluid becomes upsurges by the rise in these factors. 11.95% enhancement in the heat transfer rate has been attained using the hybrid nanofluids.

Abstract In this new world of fluid technologies, hybrid nanofluid has become a productive subject of research among scientists for its potential thermal features and abilities, which provides an excellent result as compared to nanofluids in growing the rate of heat transport. Our purpose here is to introduce the substantial influences of magnetic field on 2D, time-dependent and stagnation point inviscid flow of couple stress hybrid nanofluid around a rotating sphere with base fluid is pure blood, $${\text{TiO}}_{2} \,\,{\text{and}}\,\,{\text{Ag}}$$ TiO 2 and Ag as the nanoparticles. To translate the governing system of partial differential equations and the boundary conditions relevant for computation, some suitable transformations are implemented. To obtain the analytical estimations for the corresponding system of differential expression, the innovative Optimal Homotopy Analysis Method is used. The characteristics of hybrid nanofluid flow patterns, including temperature, velocity and concentration profiles are simulated and analyzed in detail due to the variation in the evolving variables. Detailed research is also performed to investigate the influences of relevant constraints on the rates, momentum and heat transport for both $${\text{TiO}}_{2} + {\text{Ag}} + Blood$$ TiO 2 + Ag + B l o o d and $${\text{TiO}}_{2} + Blood$$ TiO 2 + B l o o d . One of the many outcomes of this analysis, it is observed that increasing the magnetic factor will decelerate the hybrid nanofluid flow velocity and improve the temperature profile. It may also be demonstrated that by increasing the Brownian motion factor, significant improvement can be made in the concentration field of hybrid nanofluid. The increase in the nanoparticle volume fraction from 0.01 to 0.02 in the case of the hybrid nanofluid enhances the thermal conductivity from 5.8 to 11.947% and for the same value of the nanoparticle volume fraction in the case of nanofluid enhance the thermal conductivity from 2.576 to 5.197%.

Traditional recurrent neural networks (RNNs) encounter difficulty in capturing long-term temporal dependencies. However, lightweight recurrent models for speech enhancement are important to improve noisy speech, while being computationally efficient and able to capture long-term temporal dependencies efficiently. This study proposes a lightweight hourglass-shaped model for speech enhancement (SE) and automatic speech recognition (ASR). Simple recurrent units (SRU) with skip connections are implemented where attention gates are added to the skip connections, highlighting the important features and spectral regions. The model operates without relying on future information that is well-suited for real-time processing. Combined acoustic features and two training objectives are estimated. Experimental evaluations using the short time speech intelligibility (STOI), perceptual evaluation of speech quality (PESQ), and word error rates (WERs) indicate better intelligibility, perceptual quality, and word recognition rates. The composite measures further confirm the performance of residual noise and speech distortion. With the TIMIT database, the proposed model improves the STOI and PESQ by 16.21% and 0.69 (31.1%) whereas with the LibriSpeech database, the model improves STOI by 16.41% and PESQ by 0.71 (32.9%) over the noisy speech. Further, our model outperforms other deep neural networks (DNNs) in seen and unseen conditions. The ASR performance is measured using the Kaldi toolkit and achieves 15.13% WERs in noisy backgrounds. [ABSTRACT FROM AUTHOR]

A modern development in the field of fluid dynamics emphasizes on nanofluids which maintain remarkable thermal conductivity properties and intensify the transport features of heat in fluids. The present communication provides an innovative idea of MHD (magneto-hydrodynamics) unsteady, incompressible nanoliquid flow due to the stretching rotating disk with the effect of Joule heating and dissipation. The engine oil is used as a carrier fluid for an immersed rotating disk. A special type of nanoliquid, which consists of cylindrical shape nano materials CNTs (Carbon Nanotubes), is being taken into an account. The CNTs are assembled of both single and multi-walled carbon nanotubes. Some other factors such as the effect of joule heating and viscus dispassion are also used in this investigation. The foremost set of PDEs (Partial Differential Equations) of our model is reformed to the dimensionless form via invoking suitable variables. The resultant set of equations is sketched out through RK-4 method. Furthermore, the velocity profile and energy distribution versus dimensionless flow factors have been sketched and discussed. Also, the outcomes of important engineering curiosity like Nusselt number and skin friction are depicted and interpreted by taking various model factors. Radial and transverse velocity fields, declines via M (magnetic factor), while the temperature field enhances. Furthermore, the larger estimation of ϕ and ω leads to enhance the velocity field while higher estimation of S reducing the velocity and temperature fields. The current work has an extensive verity use such as nano-mechanics and electro-magnetic micro pumps.