Analyzing unsteady flow of shear-thinning nanofluids over a cylinder with exponential stretching and shrinking: An artificial neural network approach

Abstract

Current study aims to implement a novel intelligent numerical computing framework by applying a computational artificial neural network designated with Bayesian regularization network (BRN) to underscore a comparative analysis for the impact of unsteady shear-thinning behavior of the flow of nanofluid through an exponentially stretching or shrinking cylinder. Transformed governing model of ordinary differential equations in cylindrical coordinates based on Buongiorno model is analyzed. The reference dataset for Buongiorno model is obtained by using Adam numerical solver against six scenarios with the variation of parameters namely, stretching/shrinking parameter, Weissenberg number, Reynold number, Brownian motion parameter, Prandtl number, and Lewis number. The acquired datasets are feed into a supervised computational framework utilizing BRN to approximate solutions for the unsteady shear-thinning behavior of flow system. The robustness of the stochastic process based on the BRN is validated through extensive simulation including convergence plots using the mean square errors, the performance of adaptive control parameters in the optimization algorithm, error distribution histograms and regression analysis. The optimal validation performance is observed in relation to epoch number index at epoch 621, 239, 548, 427, 580, 826 and 717 respective to all the scenarios. Further, observed mean squared errors (MSE) between target and output data of approximately 1.1383 × 10⁻¹¹, 4.4409 × 10⁻¹¹, 4.3824 × 10⁻¹², 3.7145 × 10⁻¹², 3.4385 × 10⁻¹³, 1.0341 × 10⁻¹¹and 3.1188 × 10⁻¹¹, recorded at times of 2 s, 1 s, 2 s, 2 s, 3 s, and 2 s respectively. These quantitative measures demonstrate minimal error margin which ensure the reliable alignment with numerical data.