A 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 nonlinear
Jeffrey-Hamel (MHD-JHF) problem, modeling human arterial blood flow, using a hybrid
metaheuristic combining Particle Swarm Optimization (PSO) and the Perturbation Iteration
Algorithm (PIA). The model is formulated from third-order ordinary differential equations
derived from the nonlinear MHD partial differential equations of Jeffrey-Hamel flow.
Optimal artificial neural network weights are obtained by minimizing the fitness function
through the PSO-PIA algorithm. The proposed method is evaluated across four MHD-JHF
scenarios, considering different Reynolds numbers and channel angles. Numerical results
demonstrate excellent agreement with reference solutions and highlight the importance of
accurately characterizing arterial blood flow. Statistical analyses based on multiple
performance metrics confirm the method’s accuracy, efficiency, and reliability. The
framework offers potential for future extension to related problems in science and
engineering applications.