Cube Thermal Steady-State Demo

A self-contained demo repository for a mock 3D cube thermal steady-state simulator, bundled with:

• a Streamlit app
• a notebook
• pytest coverage for the simulator
• a lightweight VTU exporter for ParaView

Simulator Dynamics

This simulator models steady-state heat conduction in a 3D rectangular cube using a finite difference method on a structured grid. The governing equation is the heat conduction equation in steady-state:

∇·(k ∇T) + q = 0

where:

• T is the temperature field (K)
• k is the thermal conductivity (W/m·K), assumed constant
• q is the volumetric heat source (W/m³), representing internal heat generation per unit volume

The equation is discretized using finite differences, resulting in a system of linear equations solved iteratively until convergence.

Boundary Conditions

The cube has convective heat transfer on all faces to the ambient environment at temperature T_amb, except the x=0 face which has convection to an external heat source at temperature T_source.

• x=0 face: Convection to external source: -k ∂T/∂x = h (T_source - T)
• x=Lx face: Convection to ambient: -k ∂T/∂x = h (T - T_amb)
• y=0 and y=Ly faces: Convection to ambient: -k ∂T/∂y = h (T - T_amb)
• z=0 and z=Lz faces: Convection to ambient: -k ∂T/∂z = h (T - T_amb)

where h is the convective heat transfer coefficient (W/m²·K).

Input Parameters

The simulator takes the following input parameters for each simulation sample:

• thermal_conductivity (W/m·K): Thermal conductivity of the cube material. Typical range: 5.0 - 25.0. Determines how easily heat conducts through the material.
• volumetric_heat_source (W/m³): Internal heat generation rate per unit volume. Typical range: 5.0e3 - 4.0e4. Represents sources like electrical heating or chemical reactions.
• T_source (K): Temperature of the external heat source at the x=0 face. Typical range: 300.0 - 1000.0. Drives heat into the cube via convection.
• convective_h (W/m²·K): Convective heat transfer coefficient on all boundaries. Typical range: 2.0 - 20.0. Higher values mean better heat transfer.
• initial_temperature (K): Initial temperature guess for the iterative solver. Typical range: 285.15 - 315.15. Affects convergence speed but not the final solution.

Mesh and Solver Parameters

These are configuration parameters set once per simulator instance:

• nx, ny, nz: Number of nodes in x, y, z directions (integer, ≥2). Typical: 4-16. Higher values increase accuracy but computational cost.
• length_x, length_y, length_z (m): Cube dimensions. Default: 1.0, 0.75, 0.5. Physical size of the domain.
• ambient_temperature (K): Ambient/reference temperature. Default: 293.15 (20°C). Used in boundary conditions.
• max_iterations: Maximum number of solver iterations. Default: 4000. Prevents infinite loops.
• tolerance: Convergence tolerance on maximum nodal temperature change. Default: 1e-6. Smaller values mean more accurate solutions.
• initialisation: Initial temperature field guess ("ambient" or "linear_hot_to_cold"). Default: "ambient". Affects convergence speed.

Repo structure

cube-thermal-demo-repo/
├── app/
│   └── streamlit_app.py
├── notebooks/
│   └── cube_thermal_demo.ipynb
├── src/
│   └── digilab_simulators/
│       ├── __init__.py
│       ├── vtu.py
│       └── simulators/
│           ├── __init__.py
│           ├── base.py
│           └── fea_box.py
├── tests/
│   └── test_cube_thermal_simulator.py
├── pyproject.toml
└── README.md

Quick start

poetry install

Run tests:

pytest

Run the Streamlit app:

streamlit run app/streamlit_app.py

Open the notebook:

jupyter notebook notebooks/cube_thermal_demo.ipynb

Notes

This is a compact mock solver intended for demo workflows, surrogate modelling, and visualisation pipelines. It is not intended for engineering sign-off or certified thermal analysis.