README.md

Heat Conduction Examples

This directory contains Node.js examples demonstrating how to use the FEAScript library to solve steady-state heat conduction problems.

Examples

1. Heat Conduction in a 1D Wall (heatConduction1DWall.js)

This example demonstrates a heat flow case through a building wall.

For detailed information on the model setup, refer to the corresponding tutorial in the FEAScript website.

2. Heat Conduction in a 2D Fin (Standard Mesh) (heatConduction2DFin.js)

Basic implementation using an internally generated structured mesh.

3. Heat Conduction in a 2D Fin (Gmsh Mesh) (heatConduction2DFinGmsh.js)

Implementation using an unstructured mesh generated by Gmsh (the mesh file, rect_quad_unstruct.msh, is also located in the current directory).

For detailed information on the model setup, refer to the corresponding tutorial in the FEAScript website.

4. Heat Conduction in a 2D Rhomboid Fin (Gmsh Mesh) (heatConduction2DRhomFinGmsh.js)

Implementation using a Gmsh-generated mesh for a rhomboid domain (the mesh file, rhom_quad.msh, is also located in the current directory).

For detailed information on the model setup, refer to the corresponding tutorial in the FEAScript website.

5. Heat Conduction in a 1D Bi-Material Wall with Spatially Varying k(x) (heatConduction1DVaryingK.js)

Demonstrates passing thermalConductivity as a function of position k(x). The wall consists of two layers with different conductivities separated at mid-length. This example exercises the coefficientFunctions API with the standard linear solver.

6. Heat Conduction in a 2D Fin with Spatially Varying k(x,y) and Q(x,y) (heatConduction2DVaryingKQ.js)

Demonstrates both thermalConductivity(x, y) and heatSource(x, y) as functions of position on a 2D structured mesh. The domain is split into a high-conductivity metal half and a low-conductivity ceramic half, with a localised volumetric heat source in the upper strip.

Spatially Varying Coefficients

Both thermalConductivity and heatSource can be provided either as constants (scalars) or as functions of the physical coordinates. They are evaluated at each Gauss point during the isoparametric mapping loop, so any piecewise or smooth spatial variation is fully supported.

model.setModelConfig("heatConductionScript", {
  coefficientFunctions: {
    // Scalar (uniform)
    thermalConductivity: 10,
    // Function of x only (1D or 2D)
    // thermalConductivity: (x) => x < 0.5 ? 10 : 1,
    // Function of x and y (2D)
    // thermalConductivity: (x, y) => x < 2.0 ? 10 : 1,
    // Uniform heat source
    // heatSource: 500,
    // Localised heat source (active only in upper strip)
    heatSource: (x, y) => (y > 1.5 ? 500 : 0),
  },
});

When coefficientFunctions is omitted or a coefficient is not provided, the defaults thermalConductivity = 1 and heatSource = 0 are used. Both the standard matrix assembler and the frontal solver assembler support this feature.

Running the Node.js Examples

1. Create package.json with ES module support:

echo '{"type":"module"}' > package.json

2. Install dependencies:

npm install feascript

3. Run an example:

node heatConduction2DFin.js

(or node heatConduction2DFinGmsh.js / node heatConduction2DRhomFinGmsh.js)