Optimizing heat transportation features of magneto-Carreau nanofluid flow through novel machine learning algorithm with the immersion of chemical process for inclined cylindrical surface

Abstract

Heat transfer in a mixed bioconvection flow of gyrotactic microorganisms and a Carreau nanofluid model across stretchable cylinder with fluctuating magnetic field effect and binary chemical reactions is investigated in this study. The study focuses on fluctuating heat source changes and non-uniform thermal conductivity patterns. This nano-bioconvection flow example is estimated using a passively controlled nanofluid pattern, which is thought to be more physically accurate than actively controlled nanofluids. With the help of the Levenberg-Marquardt backpropagation algorithm and non-linear autoregressive with exogenous inputs (LMBA-NARX), a stochastic technique, the goal of this research project is to describe the model and valuation of a differential mathematical system of the effect of bioconvection and chemical reaction on Magneto-Carreau nano fluid. This will make it possible to calculate the dynamics in a more precise, trustworthy, and proficient manner. Using the Mathematica software’s Adams approach, a reference dataset for LMBA-NARX is created for the many significant parameters of the model including curvature parameter λ, magnetic field M, mixed convection Ri, power law index n, Prandtl number Pr and Buoyancy free ration factor Nr representing different situations. In order to improve and compete the estimated outcomes with standard solutions, the outcomes of reference data are trained by including eighty percent for training and twenty percent for validation and testing methods. The stability and accuracy of LMBA-NARX is endorsed through mean square error fitness curves, regression analysis, autocorrelation of error, correlation between input and error, measured by histogram plots and evaluation of absolute errors. The exceptional measures of performance in terms of MSE are attained at level 9.5557E-13, 3.1914E-13, 4.23333E-13, 2.3363E-11, 5.2793E-15, 2.0728E-15 and 2.7701E-11 against 128, 66, 58, 73, 115, 73 and 78 epochs. The Carreau nanofluid’s velocity goes down with the increase in curvature, magnetic field, mixed convection, power law index, and buoyancy force ratio factor and the temperature of the Carreau nanofluid is inversely proportional to curvature and Prandtl number.