Levenberg–Marquardt back-propagation algorithm for a developing unsteady hybrid nanofluid mixed convective flow across a revolving sphere: irreversibility analysis

Abstract

Enhanced thermal conductivity and shielding applications in electronic devices, solar collectors and concentrators have motivated researchers to deal with the study of nanofluid modelling in the presence of rotating sphere. In this study, a detailed investigation has been conducted on a rotating sphere using the Tiwari–Das model in the presence of radiation, magnetic and buoyancy effects to carry out thermal analysis and irreversibility analysis using various external parameters. The energy conversion effects have been captured using irreversibility analysis based on second law of thermodynamics. The dimensionless nonlinear ordinary differential equations were solved numerically using MATLAB bvp4c code, and back-propagation analysis was performed with the aid of ANN (artificial neural network). The outcomes reveal a surge in velocity along the x-direction with the unsteadiness parameter \((A)\), showing that the mono-nanofluid surpasses the hybrid nanofluid in velocity. Conversely, the z-direction velocity displays a reverse trend. There is an enhancement in the entropy of the system with augmenting radiation \((R)\) and magnetic parameter \((M)\). The skin friction coefficient decreased by 2.93–4.51% on increasing the unsteadiness parameter \((A)\). Nusselt number increased with increasing rotational parameter \(\left(\lambda \right).\) Entropy of the system \(\left(NG\right)\) and Bejan number \((Be)\) increased with increasing \(R\) values. The maximum absolute error was of the order of \({10}^{-11}.\) The maximum mean squared error for Nusselt number was 3.0251E-11, which was attained in 441 epochs.