In this article, we considered a 3D symmetric flow of a ternary hybrid nanofluid flow (THNF) past a nonlinear stretching surface. The effect of the thermal radiation is considered. The THNF nanofluid SiO${}_2$+Cu+MoS${}_2$/H${}_2$O is considered in this work, where the shapes of the particles are assumed as blade, flatlet, and cylindrical. The problem is formulated into a mathematical model. The modeled equations are then reduced into a simpler form with the help of suitable transformations. The modeled problem is then tackled with a new machine learning approach known as a hybrid cuckoo search-based artificial neural network (HCS-ANN). The results are presented in the form of figures and tables for various parameters. The impact of the volume fraction coefficients ${\varphi }_1$, ${\varphi }_2$, and ${\varphi }_3$, and the radiation parameter is displayed through graphs and tables. The higher numbers of the radiation parameter $\left(Rd\right)$ and the cylinder-shaped nanoparticles, ${\varphi }_3$, enhance the thermal profile. In each case, the residual error, error histogram, and fitness function for the optimization problem are presented. The results of the HCS-ANN are validated through mean square error and statistical graphs in the last section, where the accuracy of our implemented technique is proved.

Fins and radial fins are essential elements in engineering applications, serving as critical components to optimize heat transfer and improve thermal management in a wide range of sectors. The thermal distribution within a radial porous fin was investigated in this study under steady-state conditions, with an emphasis on the impact of different factors. The introduction of an inclined magnetic field was investigated to assess the effects of convection and internal heat generation on the thermal behavior of the fin. The dimensionless form of the governing temperature equation was utilized to facilitate analysis. Numerical solutions were obtained through the implementation of the Hybrid Cuckoo Search Algorithm-based Artificial Neural Network (HCS-ANN). The Hartmann number (M) and the Convection-Conduction parameter (Nc) were utilized in the evaluation of heat transfer efficiency. Enhanced efficiency, as evidenced by decreased temperature and enhanced heat removal, was correlated with higher values of these parameters. Residual errors for both M and Nc were contained within a specified range of $ 10^{-6} $ to $ 10^{-14} $, thereby offering a quantitative assessment of the model's accuracy. As a crucial instrument for assessing the performance and dependability of predictive models, the residual analysis highlighted the impact of fractional orders on temperature fluctuations. As the Hartmann number increased, the rate of heat transfer accelerated, demonstrating the magnetic field's inhibitory effect on convection heat transport, according to the study. The complex relationship among Nc, fractional order (BETA), and temperature was underscored, which motivated additional research to improve our comprehension of the intricate physical mechanisms involved. This study enhanced the overall understanding of thermal dynamics in radial porous fins, providing significant implications for a wide array of applications, including aerospace systems and heat exchangers.

In this paper, a hybrid cuckoo search technique is combined with a single-layer neural network (BHCS-ANN) to approximate the solution to a differential equation describing the curvature shape of the cornea of the human eye. The proposed problem is transformed into an optimization problem such that the $L_2–$error remains minimal. A single hidden layer is chosen to reduce the sink of the local minimum values. The weights in the neural network are trained with a hybrid cuckoo search algorithm to refine them so that we obtain a better approximate solution for the given problem. To show the efficacy of our method, we considered six different corneal models. For validation, the solution with Adam’s method is taken as a reference solution. The results are presented in the form of figures and tables. The obtained results are compared with the fractional order Darwinian particle swarm optimization (FO-DPSO). We determined that results obtained with BHCS-ANN outperformed the ones acquired with other numerical routines. Our findings suggest that BHCS-ANN is a better methodology for solving real-world problems.