A hybrid RSA-IPA optimizer for designing an artificial neural network to study the Jeffery-Hamel blood flow with copper nanoparticles: Application to stenotic tapering artery

Abstract

In this study, the effects of copper nanoparticles are taken into account to create a new hybrid metaheuristic for solving the nonlinear MHD Jeffery-Hamel blood flow problem. Since copper nanoparticles are effective in lowering the hemodynamics of stenosis, the subject has scientific and biological implications. The coupled partial differential equations are converted to ordinary differential equations using suitable transformations. Considering an artificial neural network as a solution, the error function has been formed for the differential equations. A hybrid of the reptile search algorithm (RSA) and the interior point algorithm (IPA) is used to minimise the error function (≤10−05). The initial weights are first updated using the RSA algorithm (maximum 20 iterations), which is used as a tool for global search; later, IPA is used for quick local convergence. To validate the proposed technique’s accuracy, comparison studies are conducted using the fourth-order Runge-Kutta method and the hybrid PSO-IPA algorithm. Statistical analysis is provided using multiple performance indices to demonstrate the suggested approach’s precision, efficiency, and reliability. The research findings indicate that the outcomes achieved by the developed RSA-IPA technique exhibit superior performance compared to previously established methodologies, with an accuracy level of 10−04. The findings indicate that a rise in the volume fraction of cu-nanoparticles results in a decrease in the rate of blood flow. The research advances studies of blood flow in the medical sciences.

Keywords

• Jeffery-Hamel problem
• Blood flow
• Copper nanoparticles
• Reptile search algorithm
• Interior point method
• Artificial neural networks