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

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.