Investigating the radiative heat transfer analysis of magnetized Cross fluid flow capturing variable properties around paraboloid surface using artificial intelligence stochastic approach

This piece of research intends to model the mathematical expressions for heat and mass transfer in the boundary layer flow of a non-Newtonian fluid over a radiative paraboloid surface. The non-Newtonian fluid model, specifically the Cross Nanofluidic Model (DNFM), exhibits shear thickening and thinning behavior. The governing equations are obtained from the CNFM and are manipulated from Partial Differential Equations (PDEs) to Ordinary Differential Equations (ODEs) using transformation similarity variables. The Levenberg-Marquardt Method (LMM), which is a powerful Artificially Intelligent (AI) numerical solver tool for solving mathematical problems in non-linear form, is employed to solve these ODEs. LMM is a widely used optimization technique available in MATLAB's optimization toolbox. The study analyzes the effects of various parameters on the fluid velocity f′η, thermal energy transport (temperature profile) θη and mass transportation (concentration profile) ϕη characteristics. The results show that the viscosity coefficient θr and Hartmann number Ha decrease the velocity field f′η, while thermal radiation Rd and thermal conductivity κ coefficients increase the temperature. Activation energy Ea and mass diffusion coefficient τ2 enhance concentration ϕη, whereas the reaction rate coefficient Kr reduces it. The impact of the Weissenberg number We on skin friction Cf is also explored. Finally, comparisons with already conducted are made to validate the findings in numerical and graphical forms. AI-NNs are utilized for training, validation and testing, for which the pictorial response is generated for Performance Analysis (PR-AN), Training State Function (TR-ST-FN), Regression Analysis (RE-AN), Fitness State of Function (FT-ST-FN) and Error Histograms (ER-HM). Further the Solution Plots (SN-PT) and Absolute Error Plots (AB-ER-PT) depict the variation of velocity field f′η, temperature field θη and concentration field ϕη and the absolute difference between the numerical solution and the reference solution along the parameters involved, respectively.