Nonlinear dynamics of laminar flow in porous channels: Effects of wall dilation and inertial–viscous interplay

This research introduces a computationally efficient and highly accurate modification to the operational matrix method (OMM) for solving nonlinear boundary value problems commonly encountered in thermal-fluid engineering. The model addresses steady-state, two-dimensional, incompressible laminar magnetohydrodynamic (MHD) boundary layer flow of a nanofluid over a continuously stretching surface, taking into account effects such as Brownian motion, thermophoresis, chemical reaction rates, and species diffusion, characterized by the Lewis number. The modified OMM eliminates the need to solve large nonlinear systems by utilizing a direct forward coefficient evaluation approach, significantly reducing computational cost while maintaining accuracy. Simulation results reveal that increasing the Brownian motion parameter N b enhances thermal boundary layer thickness but reduces nanoparticle concentration, while higher thermophoresis. N t and chemical reaction rate λ lead to pronounced changes in both temperature and concentration fields. The method achieved an L2-truncation error on the order of 1 0 − 14 , outperforming traditional numerical solvers such as BVP4C, RKF45, and VIM. The key novelty lies in the method’s capability to satisfy nonlinear boundary conditions exactly without iterative correction, linearization, or discretization. This advancement makes it highly suitable for heat and mass transfer applications in advanced energy systems, cooling of electronic equipment, and nanofluid-based heat exchangers.