MATLAB code for automated construction of exact solutions for non-uniform unidirectional flows of a viscous incompressible fluid between permeable plates

This dataset contains a complete MATLAB implementation for the analytical and numerical study of steady viscous incompressible flow between two permeable parallel plates with linearly non-uniform boundary conditions. The code computes the exact analytical solution for the velocity field and derives key hydrodynamic quantities: vorticity, shear stress, pressure distribution, local Reynolds number, and volumetric flow rate. The package generates publication-ready visualizations, including 3D surfaces, contour plots, vector fields, streamlines, and cross-sectional profiles. The solution accounts for wall permeability through the convective term in the Navier–Stokes equation and correctly reduces to the generalized Couette flow in the limit of zero permeability. All results are fully reproducible with the provided code and default parameters.