This study aims to boost thermal convection through careful selection and adjustment of nanomaterial volumes, focusing on the unsteady magnetohydrodynamic flow past a moving wedge with viscous dissipation and Ohmic heating in a ternary nanofluid of alumina (Al2O3), copper oxide (CuO), and copper (Cu) in water. Employing mathematical modeling and numerical analysis via MATLAB's BVP4C, it explores how discharge concentration influences flow characteristics and identifies critical conditions for single or dual solutions. Key parameters such as motion and wedge parameters, Eckert number, magnetic strength, and nanoparticle volume ratios were scrutinized for their impact on fluid dynamics and heat transfer. Results show enhanced convective thermal transfer with increased nanoparticle hybridity and volume fraction, alongside suction/injection parameter (S), unsteadiness parameter (A), Eckert number (Ec), and magnetic parameter (M), albeit decreasing with wedge angle adjustments. Stability analysis revealed the stability of the initial solution vs the instability of the secondary. Introducing a novel time variable, τ=cAt(1−ct), this research demonstrates that at λ=−4.7(a leftward wedge) with a 0.04 nanoparticle volume fraction, ternary and hybrid nanofluids significantly outperform mono nanofluid, achieving thermal efficiency gains of 25.6% and 7.5%, respectively. This foundation underscores the potential of optimized nanofluid mixtures for advanced heat transfer applications.

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.

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.