ThermalConductor

Lumped thermal element for heat conduction without thermal energy storage.

This component models a purely conductive thermal element. Heat flows through the conductor from the port with higher temperature to the port with lower temperature. The rate of heat flow Q is linearly proportional to the temperature difference ΔT across the element. The constant of proportionality is the thermal conductance G. The relationship is given by Fourier's law for conduction in its lumped form:

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

Element1D

Usage

ThermalConductor(G)

Parameters:

Name	Description	Units	Default value
G	Constant thermal conductance of the material	W/K

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

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

Source

# Lumped thermal element for heat conduction without thermal energy storage.
#
# This component models a purely conductive thermal element. Heat flows through the
# conductor from the port with higher temperature to the port with lower temperature.
# The rate of heat flow `Q` is linearly proportional to the temperature difference
# `ΔT` across the element. The constant of proportionality is the thermal
# conductance `G`. The relationship is given by Fourier's law for conduction in
# its lumped form:
# ```math
# Q = G \cdot \Delta T
# ```
component ThermalConductor
  extends Element1D
  # Constant thermal conductance of the material
  parameter G::ThermalConductance
relations
  Q = G*ΔT
end

Flattened Source

# Lumped thermal element for heat conduction without thermal energy storage.
#
# This component models a purely conductive thermal element. Heat flows through the
# conductor from the port with higher temperature to the port with lower temperature.
# The rate of heat flow `Q` is linearly proportional to the temperature difference
# `ΔT` across the element. The constant of proportionality is the thermal
# conductance `G`. The relationship is given by Fourier's law for conduction in
# its lumped form:
# ```math
# Q = G \cdot \Delta T
# ```
component ThermalConductor
  # 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 conductance of the material
  parameter G::ThermalConductance
relations
  ΔT = node_a.T-node_b.T
  node_a.Q = Q
  node_a.Q+node_b.Q = 0
  Q = G*ΔT
metadata {}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

• Analyses

• Tests

  • TemperatureOfTwoMassesTest