Investigation of magnetized slip flow of hybrid nanofluid past nonlinearly radiative sheet with Newtonian heating: Physics informed neural network simulation

Abstract

Magnetohydrodynamic slip flows of nanofluids have many industrial applications such as cooling of electronic devices, polymer extrusion, and biomedical engineering applications. Stimulated by these applications, the present paper investigates theoretically and numerically the external boundary layer flow of an electroconductive hybrid-nanofluid on a 2-D nonlinear-radiative sheet with Newtonian heating and Naiver slip effect at the sheet boundary. The physico-mathematical model is framed using a system of partial differential equations along with physically realistic boundary conditions (slip and Newtonian heating) which are then transformed into a set of similarity differential equations using coordinate transformations developed by group theory. The transformed equations are then solved by a sophisticated technique, physics informed neural network (PINN). PINNs are the class of deep learning algorithm designed to solve differential equations. PINNs offer a data driven approach that’s considered governing physical laws directly into the learning process. We have applied limited memory Broyden–Fletcher–Goldfarb–Shanno algorithm (L-BFGS) optimizer for learning process that updates the initial weights and biases. We also have applied to an L-BFGS optimizer for learning processes that update the initial weights and biases requirements. The mean square error for each case is the order of 10^–5–10^–7. The training loss values for PINN are gradually decreasing or somewhere fluctuating with the epoch number. To justify the precision of the method, present results are compared with the existing results and an excellent correlation is found. It is found that with the increase of Nr, Nusselt number increases by 0.3125% if we add Al₂O₃ and Cu nanoparticle with H₂O. Possible applications of the findings are magnetically guided drug delivery, electronic cooling systems, microscale bioreactors, and nanoparticle transport in medical diagnostics.