Deep learning multilayer stochastic intelligent computing for the analysis of irregular heat source of Carreau nanofluid within the vicinity of an exponentially expanding cylinder

In pattern recognition, data analysis, and decision-making, it is obvious that there are currently artificial intelligence (AI) techniques being applied and are already impacting the research in various fields of study. This research investigates the numerical evaluation of the irregular heat source by capitalizing the knacks of AI based technique multilayer predictive analysis combined with Levenberg Marquardt Algorithm abbreviated as MLPA-LMA on Carreau Nano-fluid flowing through Exponential Expanding Cylinder. The Two-dimensional axisymmetric incompressible Carreau Nanofluid Flow Model (CNFFM) over a nonlinear stretched cylinder of radius R is assumed. To apply the proposed technique, the dataset with varying values of Weissenberg parameter (We), Embedded constant parameters ($A_1,A_2,A_3$ & $A_4$), Stretching index (m), Small perturbation number ($\epsilon$) and Prandtl number (Pr) for the CNFFM is created. The strengths of the AI based MLPA-LMA are then applied in evaluating the dataset of CNFFM to calculate the estimated solutions. The achieved and impactful values of convergence are between the ranges of E-12 to E-16 all through the eight scenarios on CNFFM. The rationale of implementing the proposed MLPA-LMA methodology is substantiated by showing all eight graphical scenarios with mean square error (MSE), error histogram, time series, regression chart and other error-efficiency diagrams, such as error autocorrelation and input error cross correlation plots. The results obtained using the AI based MLPA-LMA technique corroborate the authenticity of the proposed technique for fairly and accurately solving the CNFFM.