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 ($\mathrm{\Delta }T$) 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:

$$\mathrm{\Delta }T=R\cdot Q$$

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

Element1D

Usage

ThermalResistor(R)

Parameters:

Name	Description	Units	Default value
R	Constant thermal resistance of the material	K/W

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

Name	Description	Units
ΔT	Temperature difference across the element, calculated as node_a.T - node_b.T	K
Q	Heat flow rate through the element, positive from node_a to node_b	W

Behavior

$$\begin{array}{rl}\mathtt{\Delta }\mathtt{T}\left(t\right)& =-\mathtt{node}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{T}\left(t\right)+\mathtt{node}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{T}\left(t\right)\\ \mathtt{node}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{Q}\left(t\right)& =Q\left(t\right)\\ \mathtt{node}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{Q}\left(t\right)+\mathtt{node}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{Q}\left(t\right)& =0\\ \mathtt{\Delta }\mathtt{T}\left(t\right)& =RQ\left(t\right)\end{array}$$

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
end

Flattened 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
  # 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 {}
end

Test Cases

No test cases defined.

Related

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