L-BFGS optimizer based PINNs framework for magnetized Eyring-Powell flow in vertical channel: Applications to pin-fin heat sink design

The remarkable aspect of this study is that it explains heat transport and fluid behavior over a non-horizontal channel using the Eyring-Powell fluid model. Another key highlight is the solution of the physical model’s partial differential equations (PDEs) through Physics-Informed Neural Networks (PINNs), which makes this work a unique contribution in the field. This study explores the thermal and fluid transport behavior of time dependent Eyring-Powell flow within a non-horizontal channel in presence of magnetized environment. Additionally, the temporally varying magnetic field introduces significant magnetohydrodynamic (MHD) influences, modifying the flow dynamics and heat transfer characteristics in a non-trivial manner. The system of PDEs based on physical assumptions are normalized through proper similarity transformations. Further, PDEs are solved through limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimizer based PINNs. It computes and enhances the efficiency of training and accuracy of the network. This combination allows for mesh-free solutions of PDEs. This is an innovative approach which provides a powerful tool for understanding and optimizing non-Newtonian fluid dynamics in engineering and industrial applications. PINNs scheme made sure that boundary conditions are stable for physically involved profiles. Contours for magnitude of velocity, dimensionless temperature and concentration are also shown in the result section. It is noted that Velocity increases for higher Grashof number and decreases for Eyring fluid parameter, Magnetic parameter and Reynold number. Velocity increases for higher Grashof number and decreases for Eyring fluid parameter, Magnetic parameter and Reynold number. Temperature gets increasing for Brinkman number, Heat source or sink parameter and decreases for Magnetic number. Concentration decreases for chemical reactions and increasing for heat sink source parameter and Grashof number.