ThermalResistor
IconThermalResistor
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.
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 nodea.T - nodeb.T | K |
Q | Heat flow rate through the element, positive from nodea to nodeb | W |
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
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
- Examples
- Experiments
- Analyses