In this paper, a hybrid metaheuristic of Particle Swarm Optimization (PSO) and the Interior Point Algorithm (IPA) is used to analyze and find better solutions to the nonlinear magnetohydrodynamic Jeffery Hamel (MHD-JHF) problem modeling the arterial blood flow in humans. The nonlinear magnetohydrodynamic Jeffery-Hamel partial differential equations are converted into a model based on third-order ordinary differential equations. Later, a hybrid of Particle Swarm Optimization and Interior Point

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... gorithm (PSO-IPA) is used to optimize the fitness function and find the best design weights for artificial neural networks. To demonstrate the efficiency of our proposed method, MHD-JHF models with different Reynolds numbers and angles of the channel are considered to determine the four different proposed DENNMs. The proposed numerical results agree well with the reference solution for finite intervals and emphasize the importance of understanding the human arterial blood flow rate. To demonstrate the proposed technique's worth, the presented results are compared to the reference numerical solutions of MHD-JHF. Statistical analysis is given using various performance indices to demonstrate the proposed approach's precision, efficiency, and reliability of the proposed approach. In the future, the method could be extended to handle similar problems with applications in both engineering and science. INDEX TERMS Blood flow, Non-linear partial differential equations, Particle swarm optimization, Hybrid approach, Artificial neural networks, Interior point technique, Magneto-hydrodynamic, Jeffery Hamel flow, Reynolds number.