Intelligent backpropagated neural networks application on Couette-Poiseuille flow of variable viscosity in a composite porous channel filled with an anisotropic porous layer

This study examines Couette-Poiseuille flow of variable viscosity within a channel that is partially filled with a porous medium. To enhance its practical relevance, we assume that the porous medium is anisotropic with permeability varying in all directions, making it a positive semidefinite matrix in the momentum equation. We assume the Navier-Stokes equations govern the flow in the free flow region, while the Brinkman-Forchheimer-extended Darcy's equation governs the flow inside the porous medium. The coupled system contains a nonlinear term from the Brinkman-Forchheimer equation. We propose an approximate solution using an iterative method valid for a wide range of porous media parameter values. For both high and low values of the Darcy number, the asymptotic solutions derived from the regular perturbation method and matched asymptotic expansion show good agreement with the numerical results. However, these methods are not effective in the intermediate range. To address this, we employ the artificial Levenberg-Marquardt method with a back-propagated neural network (ALMM-BNN) paradigm to predict the solution in the intermediate range. While it may not provide the exact solutions, it successfully captures the overall trend and demonstrates good qualitative agreement with the numerical results. This highlights the potential of the ALMM-BNN paradigm as a robust predictive tool in challenging parameter ranges where numerical solutions are either difficult to obtain or computationally expensive. The current model provides valuable insights into the shear stress distribution of arterial blood flow, taking into account the variable viscosity of the blood in the presence of inertial effects. It also offers a framework for creating glycocalyx scaffolding and other microfluidic systems that can mimic the biological glycocalyx.