MATLAB Program for Automated Analysis of Generalized Couette Flow with Permeable Boundaries and a Quadratic Velocity Profile

This MATLAB program provides a comprehensive analysis of the generalized Couette flow between permeable parallel plates. The flow is characterized by a quadratic velocity profile at the upper boundary, defined by linear (A) and quadratic (B) coefficients, and a constant normal velocity (Vw) through the boundaries, representing wall permeability.

The code is structured in two main parts. Part 1 performs a detailed parametric study of the influence of the signs and magnitudes of coefficients A and B on the flow structure, using water at 20°C as a model fluid. Part 2 conducts a comparative analysis of the flow for six different real Newtonian fluids (water, SAE30 motor oil, and crude oil at two temperatures each), examining the effects of their varying rheological properties (dynamic viscosity and density) on the velocity, vorticity, and shear stress fields.

The core of the program is an exact analytical solution of the Navier-Stokes equations, which is used to compute all flow characteristics with high precision, avoiding numerical differentiation errors. The software automatically generates a full set of visualizations (contour plots, vector fields, line profiles) and saves the numerical results in a structured .mat file for further analysis, making it a valuable tool for researchers in fluid dynamics, tribology, and microfluidics.