Two-Temperature Model for Porous Media Heat Transfer

A Python program for solving two-dimensional heat transfer problems in porous media using the two-temperature model (solid and liquid phases) with incompressible fluid flow.

The solver uses explicit finite difference method to discretize and solve the coupled heat transfer equations for both solid and fluid phases. The program features:

- Graphical user interface built with Tkinter
- Real-time visualization of temperature fields using matplotlib
- Interactive contour plots with time slider for temporal evolution
- Multiple velocity profile options (Constant, Parabolic, Cosine, Brinkman)
- Built-in porous media presets with adjustable parameters
- Support for various boundary conditions
- Temperature profiles visualization along channel length and height

The program allows users to:
1. Input geometric parameters (L, H) and grid resolution (Nx, Ny)
2. Set physical properties for both fluid and solid phases
3. Define boundary and initial conditions
4. Run transient heat transfer simulations
5. Visualize results through interactive contour plots and temperature profiles
6. Save simulation results in NPZ format for further analysis

The solver accounts for:
- Heat conduction in both phases
- Interfacial heat transfer between phases
- Convective heat transfer in fluid phase
- Volumetric heat sources in both phases
- Velocity profile effects on heat transfer