Machine learning-based algorithm to analyze the impact of magnetic dipole on thermal performance of Carreau-Yasuda nanofluid flow based on Darcy-Forchheimer theory

Since trend of nanotechnology is developing progressively in past decades, so resultantly studies on innovative heat transmission fluid called nanofluids have become increasingly popular. The invention of this enhanced heat transfer nanofluid results in a great revolution in modern engineering as well as science. The researchers and scientists have shown a great interest in research on nanofluid due to its wide assortment of solicitations in numerous sectors along with environmental friendliness properties of nanofluid. In this investigation we examine a non-Newtonian ferrofluid that exhibits magnetic effects. A useful technique for converting non-linear systems of partial differential equations into non-linear O.D.Es is similarity transformation. The bvp4c method is used to obtain the numerical results. A detailed graphic representation of the temperature, velocity along with concentration profiles is provided. It is investigated that an escalation in the estimations of Brownian movement parameter, the concentration gradient decreases and the thermal profile shows increasing behavior. Furthermore, Artificial Intelligence (AI) Neural Networks (NNs) of the non-traditional Levenberg Marquardt Backpropagation Algorithm (LMBA) are used to solve equations numerically. A variety of performance metrics, such as Mean Squared Error, Training State of Function, Fitness State of Function, Regression Analysis Plots, and Error Histograms, are used to assess the model's correctness under various conditions and determine how well the projected NNs of AI work using LMBA. A detailed analysis is also carried out to look at the effects of the important variables on the velocity, temperature, and concentration profiles.