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.本仓库提供一段MATLAB脚本，用于自动化计算并可视化无限长水平渗透壁面通道内粘性不可压缩流体的非齐次库埃特-泊肃叶（Couette–Poiseuille）流动精确解析解。 该脚本实现了一种全新的解析解，可同时涵盖三类核心物理效应：(1) 运动上壁面的线性非均匀边界条件；(2) 沿通道方向的恒定压力梯度；(3) 两侧渗透壁面的均匀抽吸/注入速度。程序可计算完整的二维速度场Vx(y,z)，并推导切应力、涡量、局部雷诺数等相关流体力学特性。 核心特性： 1. 精确解：可作为验证计算流体动力学（Computational Fluid Dynamics, CFD）数值代码的基准模型。 2. 对比分析：可针对指定温度下的三种常见流体（水、原油、机油）计算流动结果。 3. 综合可视化：可生成八幅可视化图像，涵盖速度剖面、二维流场、等值线、矢量图以及输运参数αh。 4. 自包含性：脚本内已定义全部参数，无需额外外部依赖。 本工具专为流体力学、微流控学与润滑理论领域的研究人员与学生设计，可为带有渗透壁面的复杂流动提供可靠的解析参考依据。