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This study aims to present a unique hybrid metaheuristic approach to solving the nonlinear analysis of hall currents and electric double layer (EDL) effects in multiphase wavy flow by merging the firefly algorithm (FA) and the water cycle algorithm (WCA).

Nonlinear Hall currents and EDL effects in multiphase wavy flow are originally described by partial differential equations, which are then translated into an ordinary differential equation model. The hybrid FA-WCA technique is used to take on the optimization challenge and find the best possible design weights for artificial neural networks. The fitness function is efficiently optimized by this hybrid approach, allowing the optimal design weights to be determined.

The proposed strategy is shown to be effective by taking into account multiple variables to arrive at a single answer. The numerical results obtained from the proposed method exhibit good agreement with the reference solution within finite intervals, showcasing the accuracy of the approach used in this study. Furthermore, a comparison is made between the presented results and the reference numerical solutions of the Hall Currents and electroosmotic effects in multiphase wavy flow problem.

This comparative analysis includes various performance indices, providing a statistical assessment of the precision, efficiency and reliability of the proposed approach. Moreover, to the best of the authors’ knowledge, this is a new work which has not been explored in existing literature and will add new directions to the field of fluid flows to predict most accurate results.