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In the applications of polymer film production and lubrication systems, ternary hybrid nanofluids can significantly enhance product performance by improving thermal conduction. This study focuses on investigating a nanofluid consisting of alumina (Al2O3), zincite (ZnO), and magnetite (Fe3O4) dispersed in water to optimize its thermal and flow properties. By integrating magnetohydrodynamic (MHD) flow dynamics over a stretching/shrinking sheet with velocity slip and employing both analytical solutions and numerical analysis through MATLAB’s BVP4C, the research investigates critical parameters such as suction/injection, magnetic strength, and slip effects on surface properties and thermal transfer. The results show that increased nanoparticle hybridity, suction/injection, and magnetic strength enhance skin friction and the local Nusselt number in the primary solution, while the secondary solution shows reductions. Velocity accelerates with increased suction/injection and magnetic parameters, while temperature decreases with higher velocity slip, suction/injection, and magnetic strength. Stability analysis highlights the robustness of the primary solution and the complexities of secondary solutions, with ternary and binary nanofluids outperforming mono nanofluids under shrinking sheet conditions (λ = −6) and achieving thermal efficiency gains of 0.43% and 0.2%, respectively. This study’s novelty lies in determining the critical conditions for one, two, or no solutions and integrating analytical and numerical methods for comprehensive insights. The contribution of this work extends to optimizing heat transfer in advanced industrial applications using ternary hybrid nanofluids.

The industrial significance of stability analysis for dual solutions and heat transfer sets the stage for this research. Focusing on Maxwell ternary nanofluid flow, the study aims to enhance thermal conductivity and stability by delving into viscous dissipation and velocity slip effects on a stretching/shrinking sheet. Employing a mathematical model, refined with nondimensional transformations and MATLAB’s BVP4C solver, the research identifies dual solutions and examines the influence of key parameters on fluid dynamics and heat transfer. Results showcase a progressive improvement in convective heat transfer and skin friction from mono nanofluid (NF) to binary hybrid nanofluid (HNF), culminating with ternary hybrid nanofluid (THNF). These improvements are significantly associated with the suction/injection parameter (S), whereas the slip (σ) and elastic (K) parameters enhance thermal transfer but negatively affect skin friction efficiency at elevated levels. The robustness of the upper branch solutions underscores the reliability of these findings. Remarkably, at λ=−1.25 with a nanoparticle volume fraction of 0.04, ternary nanofluids achieve a 2.9% thermal efficiency leap over HNF, which itself surpasses NF by 0.46%. These findings hold potential for significant advancements in sectors such as electronics, manufacturing, energy, biomedical, environmental engineering, aerospace, and automotive, aiming at elevating thermal efficiency.

This study explores using hybrid nanofluids to improve water quality by enhancing heat transfer and substance decomposition. Nanofluids effectively remove pollutants, optimise heat transfer, control pollution sources, and regulate fluid dynamics, which can lead to efficient pollution management in water systems. Thus, the present research examines the flow of an unsteady hybrid Al2O3–Cu/water nanofluid near the stagnation region in a porous medium, considering the discharge concentration and convective boundary conditions. Governing equations in ordinary differential equations are obtained using similarity transformations. The BVP4C solver in MATLAB is employed to expose dual solutions. The volume fraction of copper φa2, the suction/injection parameter (S), and the unsteadiness parameter (A), collectively contribute to the delay of the boundary layer separation. Increasing the values of φa2,A, and S enhances convective heat transfer. When the sheet shrunk between the range of −16.2 and −13, hybrid nanofluid has higher convective thermal transfer than nanofluid. Moreover, an increment in φa2 and S raises the skin friction coefficients and mass diffusion rates. Stability analysis reveals that the first solution is stable while the second one is unstable.

The forced convection thin-film hybrid nanofluid flow over a stretching sheet with heat transfer is investigated in the present study. The effect of the suction and injection is considered. The concerned hybrid nanoparticles are copper and alumina which are dissolved in blood base fluid. Suitable similarity variables are applied to convert the nonlinear governing partial differential equations subject to appropriate boundary conditions into a set of ordinary differential equations. The MATLAB solver bvp4c is utilized to solve the similarity transformed governing equations numerically. There exists a great agreement when the present computed findings are compared with the published results for a limiting condition. Dual solutions are obtained for the velocity and temperature profiles. Conflict behavior is observed for the effect of the unsteadiness parameter and mass transfer parameter on both solutions of the velocity and temperature distributions. The increment of the mass transfer parameter has enhanced the velocity profile in the injection case, while an opposite trend is detected in the suction situation.

The characteristics of Stefan blowing effects in a magneto-hydrodynamic flow of a Casson fluid past a stretching sheet are investigated. The effects of radiation, heat source/sink, Newtonian heating, Arrhenius activation energy and binary chemical reaction are considered for heat and mass transfer analysis. The homotopy analysis method (HAM) was utilised to solve the transformed non-dimensionalized equations analytically. The impact of various physical parameters affecting the flow are investigated. Further, the relationship of various parameters on the skin friction and rate of heat and mass transfer was explored using correlation and probable error. A sensitivity analysis was carried out based on the Response Surface Methodology to analyse the effect of Stefan blowing parameter, magnetic parameter and stretching/shrinking parameter on the reduced Nusselt number and reduced Sherwood number. A constant positive sensitivity for the reduced Nusselt number towards the Stefan blowing parameter for all levels of magnetic parameter and stretching/shrinking parameter was found. Further, the reduced Sherwood number indicated a negative sensitivity towards the Stefan blowing parameter.

An effective recruitment evaluation plays an important role in the success of companies, industries and institutions. In order to obtain insight on the relationship between factors contributing to systematic recruitment, the artificial neural network and logic mining approach can be adopted as a data extraction model. In this work, an energy based k satisfiability reverse analysis incorporating a Hopfield neural network is proposed to extract the relationship between the factors in an electronic (E) recruitment data set. The attributes of E recruitment data set are represented in the form of k satisfiability logical representation. We proposed the logical representation to 2-satisfiability and 3-satisfiability representation, which are regarded as a systematic logical representation. The E recruitment data set is obtained from an insurance agency in Malaysia, with the aim of extracting the relationship of dominant attributes that contribute to positive recruitment among the potential candidates. Thus, our approach is evaluated according to correctness, robustness and accuracy of the induced logic obtained, corresponding to the E recruitment data. According to the experimental simulations with different number of neurons, the findings indicated the effectiveness and robustness of energy based k satisfiability reverse analysis with Hopfield neural network in extracting the dominant attributes toward positive recruitment in the insurance agency in Malaysia.

The present theoretical work endeavors to solve the Sutterby nanofluid flow and heat transfer problem over a permeable moving sheet, together with the presence of thermal radiation and magnetohydrodynamics (MHD). The fluid flow and heat transfer features near the stagnation region are considered. A new form of similarity transformations is introduced through scaling group analysis to simplify the governing boundary layer equations, which then eases the computational process in the MATLAB bvp4c function. The variation in the values of the governing parameters yields two different numerical solutions. One of the solutions is stable and physically reliable, while the other solution is unstable and is associated with flow separation. An increased effect of the thermal radiation improves the rate of convective heat transfer past the permeable shrinking sheet.

The dynamic behaviours of an artificial neural network (ANN) system are strongly dependent on its network structure. Thus, the output of ANNs has long suffered from a lack of interpretability and variation. This has severely limited the practical usability of the logical rule in the ANN. The work presents an integrated representation of k-satisfiability (kSAT) in a mutation hopfield neural network (MHNN). Neuron states of the hopfield neural network converge to minimum energy, but the solution produced is confined to the limited number of solution spaces. The MHNN is incorporated with the global search capability of the estimation of distribution algorithms (EDAs), which typically explore various solution spaces. The main purpose is to estimate other possible neuron states that lead to global minimum energy through available output measurements. Furthermore, it is shown that the MHNN can retrieve various neuron states with the lowest minimum energy. Subsequent simulations performed on the MHNN reveal that the approach yields a result that surpasses the conventional hybrid HNN. Furthermore, this study provides a new paradigm in the field of neural networks by overcoming the overfitting issue.

This paper studies the combined effects of viscous dissipation, first and second-order slip and variable transport properties on phase-change hydromagnetic bio-nanofluid convection flow from a stretching sheet. Nanoscale materials possess a much larger surface to volume ratio than bulk materials, significantly modifying their thermodynamic and thermal properties and substantially lowering the melting point. Gyrotactic non-magnetic micro-organisms are present in the nanofluid. The transport properties are assumed to be dependent on concentration and temperature. Via appropriate similarity variables, the governing equation with boundary conditions are converted to nonlinear ordinary differential equations and are solved using the BVP4C subroutine in the symbolic software MATLAB. The non-dimensional boundary value features a melting (phase change) parameter, temperature-dependent thermal conductive parameter, first as well as second-order slip parameters, mass diffusivity parameter, Schmidt number, microorganism diffusivity parameter, bioconvection Schmidt number, magnetic body force parameter, Brownian motion and thermophoresis parameters. Extensive computations are visualized for the influence of these parameters. The present simulation is of relevance in the fabrication of bio-nanomaterials for bio-inspired fuel cells.

A mathematical model is presented for three-dimensional unsteady boundary layer slip flow of Newtonian nanofluids containing gyrotactic microorganisms over a stretching cylinder. Both hydrodynamic and thermal slips are included. By applying suitable similarity transformations, the governing equations are transformed into a set of nonlinear ordinary differential equations with appropriate boundary conditions. The transformed nonlinear ordinary differential boundary value problem is then solved using the Runge-Kutta-Fehlberg fourth-fifth order numerical method in Maple 18 symbolic software. The effects of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fractions and microorganism motile density functions have been illustrated graphically. Comparisons of the present paper with the existing published results indicate good agreement and supports the validity and the accuracy of our numerical computations. Increasing bioconvection Schmidt number is observed to depress motile micro-organism density function. Increasing thermal slip parameter leads to a decrease in temperature. Thermal slip also exerts a strong influence on nano-particle concentration. The flow is accelerated with positive unsteadiness parameter (accelerating cylinder) and temperature and micro-organism density function are also increased. However nano-particle concentration is reduced with positive unsteadiness parameter. Increasing hydrodynamic slip is observed to boost temperatures and micro-organism density whereas it decelerates the flow and reduces nano-particle concentrations. The study is relevant to nano-biopolymer manufacturing processes.