Artificial neural networks computing for heat transfer flow of hybrid nanofluid in rectangular geometry

This study explores the complex dynamics of heat transfer in hybrid nanofluid flow, focusing on the unsteady squeezing motion of Graphene-Fe₃O₄/water confined between two parallel plates under the influence of a magnetic field. The lower plate is assumed to be stretchable and permeable, allowing for suction/injection, while the upper plate induces a squeezing effect by moving toward the lower plate. A system of highly nonlinear partial differential equations (PDEs) governing the velocity and temperature fields is transformed into a system of nonlinear ordinary differential equations (ODEs) using appropriate similarity transformations. These equations are solved by employing a machine learning-based framework that combines physics-informed neural networks with the atomic orbital search (PINNs-AOS) algorithm. The proposed PINNs-AOS model is validated through 50 independent runs, with convergence and accuracy assessed using statistical metrics such as fitness, absolute error, mean squared error (MSE), and Theil's inequality coefficient (TIC). These metrics consistently fall within optimal ranges: fitness (10^-5 to 10^-7), absolute error (10^-3 to 10^-5), MSE (10^-6 to 10^-8), and TIC (10^-6 to 10^-8), indicating the model's reliability and precision. Key findings reveal that enhancing the squeezing parameter (S_q) significantly enhances the velocity profile f^'(η), while raising the suction parameter (S) reduces it. An rise in the stretching parameter λ boosts fluid velocity near the wall, but causes a decline farther away due to dominant viscous forces. The temperature profile θ(η) is elevated with higher values of suction/injection and temperature ratio parameter (δ), whereas it shows a mild decline with an increase in the squeezing parameter. The PINNs-AOS approach demonstrates excellent agreement with the reference solution, confirming the method's predictive capabilities. This study confirms the accuracy of the PINNs-AOS framework that offers key insights for optimizing hybrid nanofluid flow and heat transfer in industrial applications.