MATLAB Code: Analytical Solution of Unsteady Flow Between Permeable Plates with Transpiration

This dataset contains a MATLAB script that computes and visualizes the analytical solution for unsteady viscous flow between two parallel permeable plates with wall transpiration (normal blowing/suction). The code implements a complete analytical solution based on separation of variables and Fourier series expansion, describing the time evolution of velocity profiles from initial state to steady conditions.

The implementation includes:

Computation of both longitudinal (U) and shear (u1) velocity components

Time-dependent development of velocity profiles

2D velocity field reconstruction in the cross-sectional plane

Spatial-temporal diagrams of flow development

Analysis of Fourier mode contributions and decay rates

Parameter studies on transpiration effects and pressure gradients

Comparison with classical no-transpiration solutions

The code is self-contained and well-documented, providing immediate visualization of five comprehensive figures that illustrate different aspects of the flow physics. Physical parameters such as plate spacing, fluid viscosity, transpiration velocity, pressure gradient, and wall velocities can be easily modified to study various flow regimes.