Simulation of hybrid boiling nano fluid flow with convective boundary conditions through a porous stretching sheet through Levenberg Marquardt artificial neural networks approach

Abstract

In the domain of artificial neural networks, the Levenberg-Marquardt technique stands out for its innovative approach and convergent stability. It generates a numerical approach for the progression of a hybrid Cu–Al2CO3/water nanofluid on a porous stretched sheet (HNF-PSS), employing regression plots, state transition measures, histogram representations, and mean squared errors. This work explores the analysis of the fluid flow problem associated with HNF-PSS, introducing a novel application of an intelligent computing system that utilizes the effectiveness of neural networks trained by the Levenberg-Marquardt algorithm (NN-TLMA). The initial mathematical expression, expressed in terms of partial differential equations (PDEs) for HNF-PSS, undergoes transformation into dimensionless nonlinear ordinary differential equations (ODEs). The collection of data for the envisioned NN-TLMA involves parameters influencing the velocity of the HNF-PSS system model, generated using the Lobatto IIIa formula. The efficacy of the suggested NN-TLMA for solving the HNF-PSS is robustly verified by examinations of state transition dynamics, regression analyses, mean square error, and error histogram studies. The consistent alignment of the obtained results with corresponding solutions attests to the legitimacy of the structure, achieving a high level of accuracy within the range of 10–6 to 10–8. Insightful findings demonstrate that the thermal Biot number contributes significantly to an upsurge in fluid temperature. Furthermore, an augmentation in nanofluid concentration and thermal profile is found to increase the porosity strength of the medium. Nevertheless, an attenuation in the velocity profile is noted under these conditions. The application of this simulation work can be found in optimizing the designs of heat exchanger, in biomedical application and in renewable energy processes.