Perturbation Iteration Algorithm-Based Semi-Analytical Blood Flow Model for the Jeffrey Hamel

Abstract

  This study presents an enhanced approach for solving the magneto- hydrodynamic nonlinearJeffrey-Hamel (MHD-JHF) problem, modeling human arterial blood flow, using a hybridmetaheuristic combining Particle Swarm Optimization (PSO) and the Perturbation IterationAlgorithm (PIA). The model is formulated from third-order ordinary differential equationsderived from the nonlinear MHD partial differential equations of Jeffrey-Hamel flow.Optimal artificial neural network weights are obtained by minimizing the fitness functionthrough the PSO-PIA algorithm. The proposed method is evaluated across four MHD-JHFscenarios, considering different Reynolds numbers and channel angles. Numerical resultsdemonstrate excellent agreement with reference solutions and highlight the importance ofaccurately characterizing arterial blood flow. Statistical analyses based on multipleperformance metrics confirm the method’s accuracy, efficiency, and reliability. Theframework offers potential for future extension to related problems in science andengineering applications.