Design of bio-inspired computing technique for nanofluidics based on nonlinear Jeffery–Hamel flow equations

Abstract

In this study, stochastic numerical treatment is presented for boundary value problems (BVPs) arising in nanofluidics for nonlinear Jeffery–Hamel flow (NJ-HF) equations using feed-forward artificial neural networks (ANNs) optimized with bio-inspired computing based on genetic algorithms (GAs) integrated with the active-set method (ASM). NJ-HF equations associated with both convergent and divergent channels, involving nanoparticles, are derived from the transformation of Navier–Stokes partial differential equations to nonlinear BVPs of third-order ordinary differential equations. The mathematical model of the transformed BVPs is developed with the help of ANNs in an unsupervised manner and the design parameters of these networks are trained with GAs, ASM, and GA–ASM. The design scheme is evaluated for NJ-HF by taking water as a base fluid containing three different types of nanomaterials: copper (Cu), alumina (Al2O3), and titania (TiO2) under various scenarios based on the angle of the channels and Reynolds numbers. Accuracy and convergence of the designed scheme are validated through comparison with standard numerical results using the Adams method.