A qualitative analysis of the artificial neural network model and numerical solution for the nanofluid flow through an exponentially stretched surface - Ullah, Asad; Yao, Hongxing; Waseem,; Saboor, Abdus; Awwad, Fuad A.; Ismail, Emad A. A. (Frontiers in Physics, 2024)
This article aims to analyze the two-dimensional (2D) nanofluid (Ag/C 2 H 6 O 2 ) flow past an exponentially stretched sheet. The magnetic field impact, heat 1 source/sink, and convection in the thermal profile are taken into account.The complexity of the problem is reduced by introducing a dimensionless group of functions. The reduced model is transformed into a system of first-order Ordinary Differential Equations (ODEs). This system is further analyzed with the Artificial Neural Network (ANN), which is trained with the Levenberg-Marquardt algorithm. The whole data set is sub divided into three parts; training (70%), validation (15%) and testing (15%). The impact of nonlinear heat source/sink parameter, magnetic parameter, volume fraction of nanoparticles, and Prandtl number is displayed through graphs. The heat source, volume fraction, and the Prandtl number cause to increase in the thermal profile with its larger values. The magnetic parameter causes to decline in both the thermal and momentum boundary layers with its higher values. The analysis shows that the thermal energy profile is enhanced with the larger values of the volume fraction of silver nanopartilces and heat source. For each case study, the residual error (RE), regression line, and validation of the results are presented. The performance of the proposed methodology is numerically tabulated for the nanoparticles volume fraction in Table 3, where the minimum absolute error (AE) is 5.3373e -11 at ϕ = 0.05. Based on this, we recommend ϕ = 0.05 for better performance.The AEs for ANN and bvp4c are computed for the state variables in Table 4 and 5 for the magnetic parameter M = 5, 10 and 15. These tables show that overall performance of ANN and further validate the present study.We have also validated the results of ANN through mean squared error graphically, where the accuracy of the proposed methodology is proved.