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BodyRadiation.md

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=Grσ(node_a.T4node_b.T4)

Element1D

Usage

BodyRadiation(Gr, σ=5.670374419e-8)

Parameters:

NameDescriptionUnitsDefault value
GrNet 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

NameDescriptionUnits
ΔTTemperature difference across the element, calculated as node_a.T - node_b.TK
QHeat flow rate through the element, positive from node_a to node_bW

Behavior

ΔT(t)=node_b.T(t)+node_a.T(t)node_a.Q(t)=Q(t)node_a.Q(t)+node_b.Q(t)=0Q(t)=Gr((node_b.T(t))4+(node_a.T(t))4)σ

Source

dyad
# 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
dyad
# 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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