MATLAB Code for Inhomogeneous Couette–Poiseuille Flow with Rayleigh Friction and Permeable Boundaries

This dataset contains a MATLAB script for simulating a non-uniform Couette-Poiseuille flow with Rayleigh friction. The code models a steady, pressure-driven viscous flow between two parallel plates with prescribed boundary conditions for axial and transverse velocities and shear gradients. The influence of Rayleigh friction is incorporated as a linear damping term in the momentum equation.

The script provides a numerical study of velocity profiles, shear distribution, three-dimensional velocity fields, and energy dissipation (both viscous and Rayleigh) across a range of friction parameters. Special attention is given to numerical stability through the use of robust hyperbolic function implementations, preventing overflow for large parameter values.

Key features include:

Computation of axial velocity U(z), shear gradient a(z), transverse velocity V(z), and total velocity Vx(y,z) profiles.

Three-dimensional visualization of the velocity field Vx(y,z).

Analysis of viscous and Rayleigh dissipation profiles and their relative contributions.

Investigation of boundary layer thickness as a function of the Rayleigh friction parameter.

Generation of publication-quality figures (PNG and PDF) with consistent formatting.

The code is designed for fluid dynamics research and education, illustrating the combined effects of pressure gradient, wall motion, and distributed friction on channel flow. All physical parameters (channel height, viscosity, density, boundary conditions) are customizable, making the script adaptable to various flow configurations.