Levenberg-Marquardt technique analysis of thermal and concentration storage in cone-disk apparatus with neural network-enhancement

Abstract

An artificial intelligence-driven neural network with the Levenberg-Marquardt method (NN-LMM) has been developed to investigate the thermal and mass transfer characteristics of a liquid flowing through the conical gap in a cone-disk apparatus. The disk and cone can either remain static or rotate at changing angular speeds, with discussion for heat transfer influenced by cosmic emission. The Rosseland resemblance is employed to compute heat diffusion in this study. To monitor variations in mass removal on the exterior, thermophoresis effects are appropriated into consideration. By applying appropriate transformations, the partial differential equations (PDEs) governing this problem are converted into typical ones. A reference dataset for NN-LMM is generated, covering various influential model variations, simulating scenarios using the Lobatto III-A numerical method. The purpose of employing the Levenberg-Marquardt technique in the analysis of thermal and concentration storage in a cone-disk apparatus, enhanced by neural networks, lies in optimizing the modeling and prediction accuracy of complex fluid dynamics and heat transfer phenomena. This technique, coupled with neural network enhancement, aims to address challenges associated with traditional analytical methods by offering a robust and efficient approach to modeling intricate processes in fluid dynamics and heat transfer. The novelty of utilizing the Levenberg-Marquardt technique, along with neural network enhancement, lies in its ability to effectively capture and simulate the dynamic interactions between thermal and concentration storage in the cone-disk apparatus. By leveraging the power of neural networks to learn complex patterns and relationships from data, combined with the optimization capabilities of the Levenberg-Marquardt algorithm, this approach offers improved accuracy and predictive capabilities compared to conventional methods. It is analyzed that the mass transport field for Nt decreases as temperature ratios increase. This phenomenon occurs because the thermophoretic force becomes more pronounced at higher temperatures, causing more particles to move towards the apparatus. Further it is seen that stationary cone and a rotating disk exhibit enhanced heat transport with increasing radiation parameter values. This suggests that elevating the radiation parameter leads to more efficient heat transfer in this specific model. Highest flow intensity observed around the cone. This reference data is subjected to testing, validation, and training processes to fine-tune the approximate solution to meet the desired results. The accuracy, stability, capacity, and robustness of NN-LMM are verified through mean squared error (MSE)-based fitness curves, regression plots, error histograms and absolute error assessments. A comparative analysis demonstrates the accuracy of the proposed solver, with absolute errors in the range of 10-9 to 10-6 for all influential parameters results.