MATLAB Code for Exact Analytical Solution of Nonhomogeneous Couette–Poiseuille Flow with Permeable Boundaries

This repository contains a MATLAB script for the automated computation and visualization of exact analytical solutions for the nonhomogeneous Couette–Poiseuille flow of a viscous incompressible fluid in an infinite horizontal channel with permeable boundaries.
The code implements a novel solution that simultaneously accounts for three key physical effects: (1) a linearly non-uniform boundary condition on the moving upper wall, (2) a constant pressure gradient along the channel, and (3) a uniform suction/injection velocity through both permeable walls. The program calculates the full 2D velocity field Vx(y,z) and derives associated hydrodynamic characteristics such as shear stress, vorticity, and local Reynolds number.
Key features:
Exact Solution: Provides a benchmark for validating numerical CFD codes.
Comparative Analysis: Computes results for three common fluids (water, crude oil, motor oil) at specified temperatures.
Comprehensive Visualization: Generates eight figures illustrating velocity profiles, 2D fields, isolines, vector plots, and the transport parameter αh .
Self-contained: All parameters are defined within the script; no external dependencies are required.
This tool is designed for researchers and students in fluid mechanics, microfluidics, and lubrication theory who require a reliable, analytical reference for complex flows with permeable boundaries.