Internal heat source example

This example creates and simulates a plate with a heat source in the middle and different boundary conditions on each side.

# sphinx_gallery_tags = ["network", "solving", "build", "stationary", "geometric"]
# sphinx_gallery_thumbnail_path = "_static/examples/internal_heat_source.svg"

import os
import numpy as np

from pyrc import (
    Node,
    InternalHeatSource,
    SolidBoundaryConditionCell,
    Viewer,
    connect_cells_with_resistors,
    RCNetwork,
    LinePlot,
)
from pyrc.core.materials import Copper

Create the plate as grid of cells

grid_resolution = 15
plate_thickness = 0.003
material = Copper()
grid = Node.create_grid(
    grid_size=(grid_resolution, grid_resolution, 1),
    delta=(1, 1, plate_thickness),
    material=material,
    temperature=20,
)
capacitors: list[Node] = grid.flatten().tolist()

Add heat source in a circle at the center

radius = 2.5
center_x, center_y = (grid.shape[0] - 1) / 2, (grid.shape[1] - 1) / 2
x, y = np.ogrid[: grid.shape[0], : grid.shape[1]]
mask = (x - center_x) ** 2 + (y - center_y) ** 2 <= radius**2
cells_in_circle = grid[mask, 0]

for cell in cells_in_circle:
    cell.add_internal_heat_source(
        InternalHeatSource(
            node=cell,
            specific_power_in_w_per_meter_squared=1000,
            area_direction=np.array((0, 0, 1)),
        )
    )

Create boundary conditions and place them adjacent to cell grid

bc_x_negative = SolidBoundaryConditionCell(temperature=-10, position=(0, 0, 0), delta=(0.1, 1, plate_thickness))
capacitors[0].place_adjacent(bc_x_negative, "-x")
bc_x_positive = SolidBoundaryConditionCell(temperature=-5, position=(0, 0, 0), delta=(0.1, 1, plate_thickness))
capacitors[-1].place_adjacent(bc_x_positive, "x")
bc_y_negative = SolidBoundaryConditionCell(temperature=-2, position=(0, 0, 0), delta=(1, 0.1, plate_thickness))
capacitors[0].place_adjacent(bc_y_negative, "-y")
bc_y_positive = SolidBoundaryConditionCell(temperature=3, position=(0, 0, 0), delta=(1, 0.1, plate_thickness))
capacitors[-1].place_adjacent(bc_y_positive, "y")

boundaries = [bc_x_negative, bc_x_positive, bc_y_negative, bc_y_positive]

View the network with VPython (add debugger breakpoint to view)

The coordinate system arrows are disabled because they are very big for this network. Comment out these lines if you just want to run the code. But during network build up it is nice to see if you placed everything correct.

viewer = Viewer(draw_coordinate_system=False)
viewer.add_new_from_list(capacitors)
viewer.add_new_from_list(boundaries)

Connect everything with resistors between all Cells

resistors = connect_cells_with_resistors([*capacitors, *boundaries])

Create RCNetwork

network = RCNetwork(load_from_pickle=False, load_solution=False)
network.rc_objects.set_lists(capacitors=capacitors, resistors=resistors, boundaries=boundaries)

Solve network.

We solve the network stationary (analytical).

network.solve_stationary()

Parse the result to show it in ParaView

Open the case in ParaView using the 00_simulation.pvd file

network.rc_solution.write_paraview_data(
    folder=os.path.normpath(r"/path/to/result/folder"),
    use_degrees_celsius=False,  # temperature is already in °C
)

The result looks like this (or at least quite similar; the picture might be from an earlier version):

🏷 Tags: network, solving, build, stationary, geometric