BodyRadiation

BodyRadiation models radiative heat transfer between two surfaces.

This component calculates the heat flow due to thermal radiation between two surfaces, represented by node_a and node_b. The heat transfer is determined by the Stefan-Boltzmann law, where the net heat flow rate Q 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:

$$Q=Gr\cdot \sigma \cdot (node\mathrm{\_}a.T^4-node\mathrm{\_}b.T^4)$$

This component extends from Element1D

Usage

BodyRadiation(Gr, σ=5.670374419e-8)

Parameters:

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

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

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

Source

# BodyRadiation models radiative heat transfer between two surfaces.
#
# This component calculates the heat flow due to thermal radiation
# between two surfaces, represented by `node_a` and `node_b`. The heat transfer
# is determined by the Stefan-Boltzmann law, where the net heat flow rate `Q`
# 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 = Gr \cdot \sigma \cdot (node\_a.T^4 - node\_b.T^4)
# ```
component BodyRadiation
  extends 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 = Gr * σ * (node_a.T ^ 4 - node_b.T ^ 4)
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 `node_a` and `node_b`. The heat transfer
# is determined by the Stefan-Boltzmann law, where the net heat flow rate `Q`
# 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 = Gr \cdot \sigma \cdot (node\_a.T^4 - node\_b.T^4)
# ```
component BodyRadiation
  # 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
  # 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 = node_a.T - node_b.T
  node_a.Q = Q
  node_a.Q + node_b.Q = 0
  Q = Gr * σ * (node_a.T ^ 4 - node_b.T ^ 4)
metadata {}
end

Test Cases

No test cases defined.

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