Tutorial: thermal bar

Steady-state heat conduction in a 1 m bar with the left end held at 100 °C and the right end at 0 °C. The analytical solution is a straight line — T(x) = 100·(1−x) — which makes this the perfect correctness check. All numbers below are from a real run.

1. Generate the mesh

Thermal cases have two special rules (the tools' docstrings and the setup_thermal_analysis prompt both encode them):

• use generic simplex elements (Element2D3N, triangles: true) — the convection-diffusion solver substitutes the physical element at import and its mesh checks reject quads;
• use ThermalFace2D2N boundary conditions.

mdpa_create_structured_mesh({
  "path": "/tmp/bar/mesh.mdpa",
  "kind": "rectangle", "size": [1.0, 0.1], "divisions": [20, 2],
  "element_name": "Element2D3N", "condition_name": "ThermalFace2D2N",
  "triangles": true
})
→ { "num_nodes": 63, "num_elements": 80 }

2. Scaffold the case

thermal_stationary defaults to steel-like properties (k = 15 W/m·K) and already fixes ThermalModelPart.left at 100 °C. It also sets element_replace_settings to LaplacianElement — without that, Kratos's "stationary" solver still behaves like one transient step.

create_project({
  "directory": "/tmp/bar",
  "template": "thermal_stationary",
  "name": "bar"
})

To change the hot-end temperature or conductivity, pass overrides: {"fixed_temperature": 350.0, "conductivity": 45.0}.

3. Fix the cold end

add_boundary_condition({
  "parameters_file": "/tmp/bar/ProjectParameters.json",
  "kind": "fix_temperature",
  "model_part": "ThermalModelPart.right",
  "value": 0.0
})

4. Run

run_simulation({"case_dir": "/tmp/bar", "wait_seconds": 120})
→ { "state": "succeeded" }

5. Check the profile

results_probe({"file": "/tmp/bar/vtk_output/ThermalModelPart_0_1.vtk",
               "variable": "TEMPERATURE", "point": [0.5, 0.05, 0.0]})
→ { "value": 50.0 }

results_probe({"file": "...", "variable": "TEMPERATURE", "point": [0.25, 0.05, 0.0]})
→ { "value": 75.0 }

Exactly linear: 50 °C at the midpoint, 75 °C at the quarter point — the FE solution reproduces the analytical profile to machine precision on this mesh. The integration test tests/test_run_integration.py::test_thermal_bar_linear_profile asserts the whole field against 100·(1−x).

6. Preview the field

With the optional viz extra installed (see Visualization), render the temperature field inline:

results_render({
  "file": "/tmp/bar/vtk_output/ThermalModelPart_0_1.vtk",
  "variable": "TEMPERATURE",
  "camera": "xy"
})
→ { "data_range": [0.0, 100.0] }  + the PNG shown inline

A clean left-to-right gradient from 100 °C to 0 °C. For the transient variant, results_animate({"files": "/tmp/bar/vtk_output"}) turns the whole time series into a GIF of the profile developing.

Variations

• Transient heating: template thermal_transient with end_time / time_step overrides; probe the same points across the VTK time series to watch the profile develop.
• Heat flux instead of fixed temperature: kind: "surface_heat_flux" on a boundary part (needs the ThermalFace2D2N conditions the mesh already has), or kind: "volume_heat_source" on ThermalModelPart.domain.
• Different material: overrides: {"conductivity": 400.0, "density": 8960.0, "specific_heat": 385.0} for copper.