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cable_analysis

CableAnalysis dataclass 

CableAnalysis(cable: Cable, solution: ndarray)

Post-processing and validation helpers for one cable solution state.

get_thermal_resistance staticmethod 

get_thermal_resistance(rho: float, r_inner: float, r_outer: float) -> float

Calculate the thermal resistance of a concentrical layer.

Source code in cable_thermal_model/validation/cable_analysis.py 
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@staticmethod
def get_thermal_resistance(rho: float, r_inner: float, r_outer: float) -> float:
    """Calculate the thermal resistance of a concentrical layer."""
    return np.log(r_outer / r_inner) / (2 * np.pi) * rho

get_temperature_correction staticmethod 

get_temperature_correction(reference_radius: float, neighbor_radius: float, heat_flow: float, rho: float) -> float

Get the boundary-temperature correction from a neighboring grid point.

Source code in cable_thermal_model/validation/cable_analysis.py 
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@staticmethod
def get_temperature_correction(
    reference_radius: float,
    neighbor_radius: float,
    heat_flow: float,
    rho: float,
) -> float:
    """Get the boundary-temperature correction from a neighboring grid point."""
    return (reference_radius - neighbor_radius) / (3 * reference_radius + neighbor_radius) * heat_flow * rho / np.pi

get_mean_temperature_cable_layer 

get_mean_temperature_cable_layer(layer: CableLayer) -> float | None

Calculate the mean temperature for a cable layer, None if absent.

Source code in cable_thermal_model/validation/cable_analysis.py 
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def get_mean_temperature_cable_layer(self, layer: CableLayer) -> float | None:
    """Calculate the mean temperature for a cable layer, ``None`` if absent."""
    if layer not in self.cable.layers:
        return None

    layer_start, layer_end = self.cable.get_layer_indices_for_layer(layer)
    return float((self.solution[layer_start] + self.solution[layer_end]) / 2.0)

get_boundary_temperatures_for_layer 

get_boundary_temperatures_for_layer(layer: CableLayer) -> tuple[float, float]

Calculate inner and outer boundary temperatures for a cable layer.

Source code in cable_thermal_model/validation/cable_analysis.py 
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def get_boundary_temperatures_for_layer(self, layer: CableLayer) -> tuple[float, float]:
    """Calculate inner and outer boundary temperatures for a cable layer."""
    if layer not in self.cable.layers:
        raise ValueError(f"Layer {layer} is not present in the cable, cannot calculate boundary temperatures.")
    start_index, end_index = self.cable.get_layer_indices_for_layer(layer)
    outer_neighbor_index = end_index + 1 if end_index != len(self.solution) - 1 else end_index
    required_index = max(start_index, outer_neighbor_index)
    if required_index >= len(self.solution):
        raise ValueError("The solution grid is too short for the requested layer boundaries.")

    heat_flow = self.get_heat_flow_cable_layer(layer=layer)

    radii = self.cable._radii_grid
    rho = self.cable.layer_properties[layer].rho

    if start_index == 0:
        inner_temperature = self.solution[start_index]
    else:
        inner_temperature = self.solution[start_index] + self.get_temperature_correction(
            reference_radius=radii[start_index],
            neighbor_radius=radii[start_index - 1],
            heat_flow=heat_flow,
            rho=rho,
        )

    if end_index == len(self.solution) - 1:
        outer_temperature = self.solution[end_index]
    else:
        outer_temperature = self.solution[end_index] - self.get_temperature_correction(
            reference_radius=radii[end_index],
            neighbor_radius=radii[end_index + 1],
            heat_flow=heat_flow,
            rho=rho,
        )

    return inner_temperature, outer_temperature

get_heat_flow 

get_heat_flow(inner_index: int) -> float

Calculate heat flow per unit length between grid points at inner_index and inner_index + 1.

Source code in cable_thermal_model/validation/cable_analysis.py 
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def get_heat_flow(self, inner_index: int) -> float:
    """Calculate heat flow per unit length between grid points at inner_index and inner_index + 1."""
    outer_index = inner_index + 1

    if inner_index < 0 or outer_index >= len(self.cable._radii_grid):
        raise ValueError("The indices must lie within the finite difference grid of the cable.")

    if np.asarray(self.solution).ndim != 1 or outer_index >= len(self.solution):
        raise ValueError("The solution array must be one-dimensional and include values for both grid points.")

    inter_radius = self.cable._inter_radii_grid[inner_index]

    # Calculate the interstitial resistivity value between the two grid points
    inter_rho = self.cable._calculate_inter_rhos(
        radii=self.cable._radii_grid[inner_index : outer_index + 1],
        inter_radii=self.cable._inter_radii_grid[inner_index:outer_index],
        rhos=self.cable._rho_grid[inner_index : outer_index + 1],
    )[0]

    # Calculate the temperature gradient between the two grid points
    temperature_gradient = (self.solution[outer_index] - self.solution[inner_index]) / (
        self.cable._radii_grid[outer_index] - self.cable._radii_grid[inner_index]
    )

    # Calculate the heat flow using Fourier's law of heat conduction
    return -2 * np.pi * inter_radius * temperature_gradient / inter_rho

get_heat_flow_at_radius 

get_heat_flow_at_radius(r: float) -> float

Calculate approximate heat flow per unit length for a given radius.

If radius lies between two grid points r[i] and r[i+1], heat flow between these two points is returned. If radius equals a grid point r[i], heat flow between r[i-1] and r[i] is returned.

Source code in cable_thermal_model/validation/cable_analysis.py 
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def get_heat_flow_at_radius(self, r: float) -> float:
    """Calculate approximate heat flow per unit length for a given radius.

    If radius lies between two grid points r[i] and r[i+1], heat flow between these two points is returned.
    If radius equals a grid point r[i], heat flow between r[i-1] and r[i] is returned.
    """
    if r <= self.cable._radii_grid[0] or r > self.cable._radii_grid[-1]:
        raise ValueError("The radius must lie within the finite-difference grid of the cable.")

    i = np.searchsorted(self.cable._radii_grid, r) - 1

    return self.get_heat_flow(inner_index=int(i))

get_heat_flow_cable_layer 

get_heat_flow_cable_layer(layer: CableLayer) -> float

Calculate the heat flow per meter for a non-heat-generating cable layer.

Source code in cable_thermal_model/validation/cable_analysis.py 
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def get_heat_flow_cable_layer(self, layer: CableLayer) -> float:
    """Calculate the heat flow per meter for a non-heat-generating cable layer."""
    start_index, end_index = self.cable.get_layer_indices_for_layer(layer)
    if end_index <= start_index:
        raise ValueError("The outer index should be larger than the inner index.")
    if layer == CableLayer.Conductor:
        raise ValueError("The conductor layer generates heat, cannot calculate heat flow.")

    heat_flow_start = self.get_heat_flow(inner_index=start_index)
    heat_flow_end = self.get_heat_flow(inner_index=end_index - 1)

    if not np.isclose(heat_flow_start, heat_flow_end, rtol=1e-5):
        raise ValueError(
            "The heat flow should be the same across both grid points of the layer, but got "
            f"{heat_flow_start} and {heat_flow_end} for layer {layer}."
        )

    return heat_flow_start

get_heat_loss_cable_layer 

get_heat_loss_cable_layer(layer: CableLayer) -> float

Calculate the net heat loss (W/m) for one layer in the cable.

Source code in cable_thermal_model/validation/cable_analysis.py 
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def get_heat_loss_cable_layer(self, layer: CableLayer) -> float:
    """Calculate the net heat loss (W/m) for one layer in the cable."""
    layers = self.cable.layers
    if layer not in layers:
        return 0.0

    layer_index = layers.index(layer)
    heat_in = 0.0 if layer_index == 0 else self.get_heat_flow_cable_layer(layer=layers[layer_index - 1])

    heat_out = self.get_heat_flow_cable_layer(layer=layers[layer_index + 1])
    return heat_out - heat_in

get_thermal_resistance_cable_layer 

get_thermal_resistance_cable_layer(layer: CableLayer) -> float

Calculate the thermal resistance for a cable layer, 0 if absent.

Source code in cable_thermal_model/validation/cable_analysis.py 
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def get_thermal_resistance_cable_layer(self, layer: CableLayer) -> float:
    """Calculate the thermal resistance for a cable layer, 0 if absent."""
    if layer not in self.cable.layers:
        return 0.0

    layer_properties = self.cable.layer_properties[layer]
    return self.get_thermal_resistance(
        rho=layer_properties.rho,
        r_inner=layer_properties.inner_radius,
        r_outer=layer_properties.outer_radius,
    )

get_thermal_resistance_external_medium 

get_thermal_resistance_external_medium(ambient_temperature: float) -> float

Calculate thermal resistance between cable sheath surface and ambient.

Source code in cable_thermal_model/validation/cable_analysis.py 
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def get_thermal_resistance_external_medium(self, ambient_temperature: float) -> float:
    """Calculate thermal resistance between cable sheath surface and ambient."""
    _, surface_temperature = self.get_boundary_temperatures_for_layer(layer=CableLayer.Sheath)
    heat_flow = self.get_heat_flow_cable_layer(layer=CableLayer.Sheath)
    return (surface_temperature - ambient_temperature) / heat_flow