MATLAB Code for Simulating Unsteady Plane-Poiseuille Flow with Wall Transpiration and Periodic Pressure Gradient

This dataset contains a complete, ready-to-run MATLAB script for the computational analysis of an unsteady plane-Poiseuille flow with wall transpiration (permeability) and an oscillating pressure gradient. The physical model considers viscous, incompressible flow between two parallel plates. The lower plate is stationary, while the upper plate moves with a constant velocity (Couette component) and allows for uniform fluid injection/suction (transpiration). The driving pressure gradient has both a steady and a harmonically oscillating component.

The provided script implements an analytical solution to this complex flow problem. The code architecture separates physical parameter definitions, computational functions, and visualization routines. It performs a parametric study and generates a comprehensive set of visualizations, including:

The influence of wall transpiration velocity on steady-state velocity profiles.

The spatial structure and temporal evolution of the oscillatory flow component.

Frequency response analysis (amplitude and phase) of the flow oscillation at the channel mid-gap.

3D and contour plots of the total velocity field V_x(z,y,t), illustrating the combined Couette, Poiseuille, and oscillatory effects.

Analysis of the effect of the oscillating pressure gradient amplitude.

Visualization of the complex wavenumber parameters governing the oscillatory boundary layer.

The code is meticulously commented, modularized with dedicated functions, and uses physically realistic parameters for water at 20°C. It is designed for researchers and students in fluid dynamics, applied mathematics, and engineering, serving as an educational tool for understanding unsteady viscous flows and as a benchmark for validating numerical solvers. The script is self-contained and directly reproduces all figures from the associated theoretical study.