Heat Conduction Simulation Plugin

Overview

This plugin for Sim4Life provides heat conduction simulation capabilities using the finite difference method. It solves the steady-state heat equation in three dimensions, allowing engineers and researchers to model thermal conductivity problems across various materials and geometries.

Mathematical Model

The plugin solves the steady-state heat conduction equation:

$$\nabla \cdot (k \nabla T) + Q = 0$$

Where:

• $T$ is the temperature field
• $k$ is the thermal conductivity (which can vary spatially)
• $Q$ is the volumetric heat source
• $\nabla \cdot$ is the divergence operator
• $\nabla$ is the gradient operator

Features

• 3D steady-state heat conduction simulations
• Support for heterogeneous materials with different thermal conductivities
• Boundary condition type:
  • Dirichlet (fixed temperature)
• Customizable heat sources
• Integration with the Sim4Life modeling environment
• Results visualization and post-processing

Usage

1. Create a new simulation by selecting "Heat Conduction" from the simulation types
2. Define material properties by adding materials to your model
3. Set up boundary conditions on model surfaces
4. Configure heat sources if needed
5. Adjust grid settings for your desired resolution
6. Run the simulation
7. Visualize and analyze temperature distribution results

Example Applications

• Thermal analysis of electronic devices
• Biomedical thermal modeling (e.g., tissue heating during procedures)
• Building thermal performance simulations
• Heat sink design optimization
• Industrial process thermal analysis

Technical Implementation

This plugin is implemented as a modular component with:

• Model classes for simulation settings
• Controller classes for UI integration
• Solver backend for numerical computation
• Input/output handlers for data processing

Requirements

• Sim4Life core application
• Python 3.11 or higher
• Compatible mesh generation tools

Installation

The plugin can be installed directly through pip:

pip install s4l-heat-conduction-plugin

For development installations:

git clone <repository-url>
cd heat-conduction
pip install -e .