LIBRARY

Components.BodyRadiation

BodyRadiation models radiative heat transfer between two surfaces.

This component calculates the heat flow due to thermal radiation between two surfaces, represented by port_a and port_b. The heat transfer is determined by the Stefan-Boltzmann law, where the net heat flow rate Q_flow is proportional to the difference between the fourth powers of the absolute temperatures of the two surfaces and the net radiation conductance Gr. The parameter Gr encapsulates factors such as surface emissivities, areas, and the view factor between the surfaces. The governing equation is:

$$Q_{flow}=Gr\cdot \sigma \cdot (port\mathrm{\_}a.T^4-port\mathrm{\_}b.T^4)$$

This component extends from ThermalComponents.Interfaces.Element1D

Usage

ThermalComponents.Components.BodyRadiation(Gr, σ=5.670374419e-8)

Parameters:

Name	Description	Units	Default value
Gr	Net radiation conductance, incorporating view factors, surface areas, and emissivities.	–

Connectors

• port_a - This connector represents a thermal port with temperature and heat flow as the potential and flow variables, respectively. (HeatPort)

• port_b - This connector represents a thermal port with temperature and heat flow as the potential and flow variables, respectively. (HeatPort)

Variables

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

Behavior

$$\begin{array}{rl}\mathtt{\Delta }\mathtt{T}\left(t\right)& =-\mathtt{port}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{T}\left(t\right)+\mathtt{port}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{T}\left(t\right)\\ \mathtt{port}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{Q}\mathtt{\_}\mathtt{flow}\left(t\right)& =\mathtt{Q}\mathtt{\_}\mathtt{flow}\left(t\right)\\ \mathtt{port}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{Q}\mathtt{\_}\mathtt{flow}\left(t\right)+\mathtt{port}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{Q}\mathtt{\_}\mathtt{flow}\left(t\right)& =0\\ \mathtt{Q}\mathtt{\_}\mathtt{flow}\left(t\right)& =\mathtt{Gr}(-{\left(\mathtt{port}\mathtt{\_}\mathtt{b}\mathtt{.}\mathtt{T}\left(t\right)\right)}^4+{\left(\mathtt{port}\mathtt{\_}\mathtt{a}\mathtt{.}\mathtt{T}\left(t\right)\right)}^4)\sigma \end{array}$$

Source

"""
BodyRadiation models radiative heat transfer between two surfaces.

This component calculates the heat flow due to thermal radiation
between two surfaces, represented by `port_a` and `port_b`. The heat transfer
is determined by the Stefan-Boltzmann law, where the net heat flow rate `Q_flow`
is proportional to the difference between the fourth powers of the absolute
temperatures of the two surfaces and the net radiation conductance `Gr`.
The parameter `Gr` encapsulates factors such as surface emissivities, areas,
and the view factor between the surfaces.
The governing equation is:

math Q_{flow} = Gr \cdot \sigma \cdot (port_a.T^4 - port_b.T^4)

"""
component BodyRadiation
  extends ThermalComponents.Interfaces.Element1D
  "Net radiation conductance, incorporating view factors, surface areas, and emissivities."
  parameter Gr::Real
  "Stefan-Boltzmann constant (W·m⁻²·K⁻⁴)."
  final parameter σ::Real(units = "W/(m2.K4)") = 5.670374419e-8
relations
  Q_flow = Gr * σ * (port_a.T ^ 4 - port_b.T ^ 4)
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 1100, "rot": 0}],
    "icons": {"default": "dyad://ThermalComponents/BodyRadiation.svg"}
  }
}
end

Flattened Source

"""
BodyRadiation models radiative heat transfer between two surfaces.

This component calculates the heat flow due to thermal radiation
between two surfaces, represented by `port_a` and `port_b`. The heat transfer
is determined by the Stefan-Boltzmann law, where the net heat flow rate `Q_flow`
is proportional to the difference between the fourth powers of the absolute
temperatures of the two surfaces and the net radiation conductance `Gr`.
The parameter `Gr` encapsulates factors such as surface emissivities, areas,
and the view factor between the surfaces.
The governing equation is:

math Q_{flow} = Gr \cdot \sigma \cdot (port_a.T^4 - port_b.T^4)

"""
component BodyRadiation
  "Port 'a' for thermal connection"
  port_a = HeatPort() {
    "Dyad": {
      "placement": {"icon": {"iconName": "port_a", "x1": -50, "y1": 450, "x2": 50, "y2": 550}}
    }
  }
  "Port 'b' for thermal connection"
  port_b = HeatPort() {
    "Dyad": {
      "placement": {"icon": {"iconName": "port_b", "x1": 950, "y1": 450, "x2": 1050, "y2": 550}}
    }
  }
  "Temperature difference across the element, calculated as port_a.T - port_b.T"
  variable ΔT::Temperature
  "Heat flow rate through the element, positive from port_a to port_b"
  variable Q_flow::HeatFlowRate
  "Net radiation conductance, incorporating view factors, surface areas, and emissivities."
  parameter Gr::Real
  "Stefan-Boltzmann constant (W·m⁻²·K⁻⁴)."
  final parameter σ::Real(units = "W/(m2.K4)") = 5.670374419e-8
relations
  ΔT = port_a.T - port_b.T
  port_a.Q_flow = Q_flow
  port_a.Q_flow + port_b.Q_flow = 0
  Q_flow = Gr * σ * (port_a.T ^ 4 - port_b.T ^ 4)
metadata {
  "Dyad": {
    "labels": [{"label": "$(instance)", "x": 500, "y": 1100, "rot": 0}],
    "icons": {"default": "dyad://ThermalComponents/BodyRadiation.svg"}
  }
}
end

Test Cases

No test cases defined.

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