Artificial neural network with Levenberg-Marquardt training algorithm for heat transfer analysis of Ag-TiO2/water hybrid nanofluid flow between two parallel rotating disks

Abstract

The authors have investigated the axisymmetric and three-dimensional, steady, incompressible, and bioconvective flow of AgTiO 2 /water hybrid nanofluid between two infinite and parallel rotating disks. Practical uses of flows between two rotating disks include brake systems in vehicles, engines, disks in computers, atomizers, rotating air cleaners, gas turbines, and evaporators. This study was conducted within a Darcy-Forchheimer porous medium and considered the impact of a magnetic field, heat source, and thermal radiation. The governing mathematical equations are transformed into coupled and nonlinear ordinary differential equations through similarity transformations. Subsequently, these equations are numerically solved using MATLAB's built-in function "bvp4c". A multilayer perceptron based artificial neural network (ANN) model has been formulated to predict the Nusselt number (heat transfer rate) on both the lower and upper surfaces of the disk. The model utilizes the Levenberg-Marquardt training algorithm, renowned for its exceptional learning capability, as the training method for the ANN. Moreover, the authors generated a dataset consisting of 84 data points for each case using numerical methods to construct the proposed Multilayer Perceptron Artificial Neural Network. The computed mean squared error values for the developed ANN model, targeting Nusselt number predictions, were found to be 2x10 -6 , 5x10 -6 , 9x10 -6 , and 3x10 - 6. Additionally, the regression ( R 2 ) values, serving as an additional performance parameter, were determined as 0.999317, 0.997672, 0.999963, and 0.999840, respectively. A comprehensive assessment of these outcomes, strongly affirms that the ANN model has been crafted with a high degree of accuracy for predicting Nusselt numbers.