Intelligent Levenberg-Marquardt neural network solution to flow of carbon nanotubes in a nozzle of liquid rocket engine

In this research, we utilized artificial neural networks along with the Levenberg-Marquardt algorithm (ANN-LMA) to interpret numerical computations related to the efficiency of heat transfer in a regenerative cooling channel of a rocket engine. We used a mixture of Kerosene and carbon nanotubes (CNTs) for this purpose, examining both single-wall carbon nanotubes and multi-wall carbon nanotubes. The primary equations were converted into a dimensionless form using a similarity transformation technique. To establish a reference dataset for ANN- LMA and to analyze the movement and heat transfer properties of CNTs, we employed a numerical computation method called bvp4c, which is a solver for boundary value problems in ordinary differential equations using finite difference schemes combined with the Lobatto IIIA algorithm in MATLAB mathematical software. The ANN- LMA method was trained, tested and validated using these reference datasets to approximate the solutions of the flow model under different scenarios involving various significant physical parameters. We evaluated the accuracy of the proposed ANN- LMA model by comparing its results with the reference outcomes. We validated the performance of ANN- LMA in solving the Kerosene-based flow with CNTs in a rocket engine through regression analysis, histogram studies, and the calculation of the mean square error. The comprehensive examination of parameters undertaken in this research endeavor is poised to provide invaluable support to aerospace engineers as they endeavor to craft regenerative equipment with optimal efficiency. The pragmatic implications of our study are wide-ranging, encompassing domains as diverse as aerospace technology, materials science, and artificial intelligence. This research holds the potential to catalyze progress across multiple sectors and foster the evolution of increasingly efficient and sustainable systems.