HeatSystemTest

Models a thermal system with a fixed temperature source heating a heat capacitor via a conductor; serves as a test component.

This component simulates the transient thermal behavior of a heat capacitor (mass) connected to an ideal fixed temperature source (source) through a thermal conductor (conductor). It is designed as a test component for the HeatCapacitor, FixedTemperature, and ThermalConductor base models. The heat capacitor is characterized by its thermal capacitance C and an initial temperature T0. The fixed temperature source maintains a constant temperature T. Heat transfer between the source and the capacitor is facilitated by the thermal conductor, which has a thermal conductance G. The temperature of the heat capacitor, denoted mass.T, changes over time according to the first-order differential equation:

$$C\cdot \frac{d(mass.T)}{dt}=Q_{flow}$$

where Q_{flow} represents the heat flow rate into the capacitor. This heat flow is determined by the temperature difference across the conductor and its conductance:

$$Q_{flow}=G\cdot (T_{source}-mass.T)$$

In this component, T_{source} is the temperature T from the source subcomponent. Consequently, mass.T will asymptotically approach T as the simulation progresses.

Usage

HeatSystemTest(T=10.0, T0=-10.0, C=10.0, G=10.0)

Parameters:

Name	Description	Units	Default value
T	Temperature of the fixed temperature source	–	10
T0	Initial temperature of the heat capacitor	–	-10
C	Thermal capacitance of the heat capacitor	–	10
G	Thermal conductance of the conductor	–	10

Behavior

$$\left[\begin{array}{c}\mathrm{connect}(sourc{e}_{+}node,conducto{r}_{+}nod{e}_a)\\ \mathrm{connect}(conducto{r}_{+}nod{e}_b,mas{s}_{+}node)\\ \mathtt{mass}\mathtt{.}\mathtt{T}\left(t\right)=\mathtt{mass}\mathtt{.}\mathtt{node}\mathtt{.}\mathtt{T}\left(t\right)\\ \frac{\mathrm{d}\mathtt{mass}\mathtt{.}\mathtt{T}\left(t\right)}{\mathrm{d}t}=\mathtt{mass}\mathtt{.}\mathtt{dT}\left(t\right)\\ \mathtt{mass}\mathtt{.}\mathtt{dT}\left(t\right)=\frac{\mathtt{mass}\mathtt{.}\mathtt{node}\mathtt{.}\mathtt{Q}\left(t\right)}{\mathtt{mass}\mathtt{.}\mathtt{C}}\\ \mathtt{source}\mathtt{.}\mathtt{node}\mathtt{.}\mathtt{T}\left(t\right)=\mathtt{source}\mathtt{.}\mathtt{T}\\ \mathtt{conductor}\mathtt{.}\mathtt{\Delta }\mathtt{T}\left(t\right)=-\mathtt{conductor}\mathtt{.}\mathtt{node}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{T}\left(t\right)+\mathtt{conductor}\mathtt{.}\mathtt{node}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{T}\left(t\right)\\ \mathtt{conductor}\mathtt{.}\mathtt{node}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{Q}\left(t\right)=\mathtt{conductor}\mathtt{.}\mathtt{Q}\left(t\right)\\ \mathtt{conductor}\mathtt{.}\mathtt{node}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{Q}\left(t\right)+\mathtt{conductor}\mathtt{.}\mathtt{node}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{Q}\left(t\right)=0\\ \mathtt{conductor}\mathtt{.}\mathtt{Q}\left(t\right)=\mathtt{conductor}\mathtt{.}\mathtt{G}\mathtt{conductor}\mathtt{.}\mathtt{\Delta }\mathtt{T}\left(t\right)\end{array}\right]$$

Source

# Models a thermal system with a fixed temperature source heating a heat capacitor via a conductor; serves as a test component.
#
# This component simulates the transient thermal behavior of a heat capacitor (`mass`)
# connected to an ideal fixed temperature source (`source`) through a thermal conductor (`conductor`).
# It is designed as a test component for the `HeatCapacitor`, `FixedTemperature`, and `ThermalConductor` base models.
# The heat capacitor is characterized by its thermal capacitance `C` and an initial temperature `T0`.
# The fixed temperature source maintains a constant temperature `T`. Heat transfer between the
# source and the capacitor is facilitated by the thermal conductor, which has a thermal conductance `G`.
# The temperature of the heat capacitor, denoted `mass.T`, changes over time according to the
# first-order differential equation:
# ```math
# C \cdot \frac{d(mass.T)}{dt} = Q_{flow}
# ```
# where `Q_{flow}` represents the heat flow rate into the capacitor. This heat flow is
# determined by the temperature difference across the conductor and its conductance:
# ```math
# Q_{flow} = G \cdot (T_{source} - mass.T)
# ```
# In this component, `T_{source}` is the temperature `T` from the `source` subcomponent.
# Consequently, `mass.T` will asymptotically approach `T` as the simulation progresses.
component HeatSystemTest
  # Heat capacitor subcomponent representing the thermal mass
  mass = HeatCapacitor(C=C, T0=T0)
  # Fixed temperature source subcomponent
  source = FixedTemperature(T=T)
  # Thermal conductor subcomponent facilitating heat flow
  conductor = ThermalConductor(G=G)
  # Temperature of the fixed temperature source
  parameter T::Real = 10.0
  # Initial temperature of the heat capacitor
  parameter T0::Real = -10.0
  # Thermal capacitance of the heat capacitor
  parameter C::Real = 10.0
  # Thermal conductance of the conductor
  parameter G::Real = 10.0
relations
  connect(source.node, conductor.node_a)
  connect(conductor.node_b, mass.node)
metadata {
  "Dyad": {
    "tests": {
      "case1": {
        "stop": 10,
        "atol": {"mass.T": 0.001, "mass.dT": 0.001},
        "expect": {"final": {"mass.T": 9.999, "mass.dT": 0}}
      }
    }
  }
}
end

Flattened Source

# Models a thermal system with a fixed temperature source heating a heat capacitor via a conductor; serves as a test component.
#
# This component simulates the transient thermal behavior of a heat capacitor (`mass`)
# connected to an ideal fixed temperature source (`source`) through a thermal conductor (`conductor`).
# It is designed as a test component for the `HeatCapacitor`, `FixedTemperature`, and `ThermalConductor` base models.
# The heat capacitor is characterized by its thermal capacitance `C` and an initial temperature `T0`.
# The fixed temperature source maintains a constant temperature `T`. Heat transfer between the
# source and the capacitor is facilitated by the thermal conductor, which has a thermal conductance `G`.
# The temperature of the heat capacitor, denoted `mass.T`, changes over time according to the
# first-order differential equation:
# ```math
# C \cdot \frac{d(mass.T)}{dt} = Q_{flow}
# ```
# where `Q_{flow}` represents the heat flow rate into the capacitor. This heat flow is
# determined by the temperature difference across the conductor and its conductance:
# ```math
# Q_{flow} = G \cdot (T_{source} - mass.T)
# ```
# In this component, `T_{source}` is the temperature `T` from the `source` subcomponent.
# Consequently, `mass.T` will asymptotically approach `T` as the simulation progresses.
component HeatSystemTest
  # Heat capacitor subcomponent representing the thermal mass
  mass = HeatCapacitor(C=C, T0=T0)
  # Fixed temperature source subcomponent
  source = FixedTemperature(T=T)
  # Thermal conductor subcomponent facilitating heat flow
  conductor = ThermalConductor(G=G)
  # Temperature of the fixed temperature source
  parameter T::Real = 10.0
  # Initial temperature of the heat capacitor
  parameter T0::Real = -10.0
  # Thermal capacitance of the heat capacitor
  parameter C::Real = 10.0
  # Thermal conductance of the conductor
  parameter G::Real = 10.0
relations
  connect(source.node, conductor.node_a)
  connect(conductor.node_b, mass.node)
metadata {
  "Dyad": {
    "tests": {
      "case1": {
        "stop": 10,
        "atol": {"mass.T": 0.001, "mass.dT": 0.001},
        "expect": {"final": {"mass.T": 9.999, "mass.dT": 0}}
      }
    }
  }
}
end

Test Cases

Test Case case1

Related

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• Analyses