ThermalResistor

Represents a pure thermal resistance relating temperature difference to heat flow rate.

This component models a lumped thermal resistance where heat is transported without being stored. The relationship between the temperature difference ($\Delta T$) across the component and the heat flow rate ($Q$) through it is defined by its constant thermal resistance ($R$). The fundamental behavior is captured by Fourier's law of heat conduction in its lumped form:

\[\Delta T = R \cdot Q\]

This component is acausal and inherits from Element1D, implying it has two thermal ports through which heat can flow.

This component extends from Element1D

Usage

ThermalComponents.ThermalResistor(R)

Parameters:

Connectors

• node_a - This connector represents a thermal node with temperature and heat flow as the potential and flow variables, respectively. (Node)
• node_b - This connector represents a thermal node with temperature and heat flow as the potential and flow variables, respectively. (Node)

Variables

Behavior

\[ \begin{align} \mathtt{{\Delta}T}\left( t \right) &= - \mathtt{node\_b.T}\left( t \right) + \mathtt{node\_a.T}\left( t \right) \\ \mathtt{node\_a.Q}\left( t \right) &= Q\left( t \right) \\ \mathtt{node\_a.Q}\left( t \right) + \mathtt{node\_b.Q}\left( t \right) &= 0 \\ \mathtt{{\Delta}T}\left( t \right) &= R Q\left( t \right) \end{align} \]

Source

# Represents a pure thermal resistance relating temperature difference to heat flow rate.
#
# This component models a lumped thermal resistance where heat is transported without being stored.
# The relationship between the temperature difference ($\Delta T$) across the
# component and the heat flow rate ($Q$) through it is defined by its constant
# thermal resistance ($R$). The fundamental behavior is captured by Fourier's law of heat conduction
# in its lumped form:
# ```math
# \Delta T = R \cdot Q
# ```
# This component is acausal and inherits from `Element1D`, implying it has two
# thermal ports through which heat can flow.
component ThermalResistor
  extends Element1D
  # Constant thermal resistance of the material
  parameter R::ThermalResistance
relations
  ΔT = R * Q
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 1100, "rot": 0}],
    "icons": {"default": "dyad://ThermalComponents/ThermalResistor.svg"}
  }
}
end

# Represents a pure thermal resistance relating temperature difference to heat flow rate.
#
# This component models a lumped thermal resistance where heat is transported without being stored.
# The relationship between the temperature difference ($\Delta T$) across the
# component and the heat flow rate ($Q$) through it is defined by its constant
# thermal resistance ($R$). The fundamental behavior is captured by Fourier's law of heat conduction
# in its lumped form:
# ```math
# \Delta T = R \cdot Q
# ```
# This component is acausal and inherits from `Element1D`, implying it has two
# thermal ports through which heat can flow.
component ThermalResistor
  # Port 'a' for thermal connection
  node_a = Node() [{
    "Dyad": {
      "placement": {"icon": {"iconName": "node_a", "x1": -100, "y1": 400, "x2": 100, "y2": 600}}
    }
  }]
  # Port 'b' for thermal connection
  node_b = Node() [{
    "Dyad": {
      "placement": {"icon": {"iconName": "node_b", "x1": 900, "y1": 400, "x2": 1100, "y2": 600}}
    }
  }]
  # Temperature difference across the element, calculated as node_a.T - node_b.T
  variable ΔT::Temperature
  # Heat flow rate through the element, positive from node_a to node_b
  variable Q::HeatFlowRate
  # Constant thermal resistance of the material
  parameter R::ThermalResistance
relations
  ΔT = node_a.T - node_b.T
  node_a.Q = Q
  node_a.Q + node_b.Q = 0
  ΔT = R * Q
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 1100, "rot": 0}],
    "icons": {"default": "dyad://ThermalComponents/ThermalResistor.svg"}
  }
}
end

Test Cases

No test cases defined.

Related

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