MATLAB Code for Exact Analytical Solution of Nonhomogeneous Couette–Poiseuille Flow with Permeable Boundaries
Description
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.
Files
Steps to reproduce
To reproduce the results presented in this dataset, follow these steps: Open MATLAB: Launch MATLAB R2023b or a compatible version. Load the script: Open the file CouettePoiseuille_PermeableBoundaries.m in the MATLAB Editor. Run the script: Execute the entire script by clicking the "Run" button (or pressing F5). Observe the output: The program will automatically: Calculate velocity fields for three test fluids (water, crude oil, motor oil) under various pressure gradients and suction/injection velocities. Generate eight figures visualizing key flow characteristics: velocity profiles, 2D velocity fields, shear stress, vorticity, velocity magnitude, isolines, and transport parameter. Print comparative results (mean velocity, flow rate, Reynolds number, alpha*h) to the Command Window. Save all generated plots as high-resolution PNG files (figure1_velocity_profiles.png, etc.) in the current working directory. No additional software, libraries, or external data are required. All parameters and fluid properties are defined within the script itself.
Institutions
- Samara State Technical University
- Ural'skij federal'nyj universitet imeni pervogo Prezidenta Rossii B N El'cina