BodyRadiation

Lumped thermal element for radiation heat transfer

Element1D

Usage

BodyRadiation(Gr, σ=5.670374419*10^(-8))

Parameters:

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

Behavior

\[ \begin{align} \mathtt{{\Delta}T}\left( t \right) &= - \mathtt{node\_b.T}\left( t \right) + \mathtt{node\_a.T}\left( t \right) \\ \mathtt{node\_a.Q}\left( t \right) &= Q\left( t \right) \\ \mathtt{node\_a.Q}\left( t \right) + \mathtt{node\_b.Q}\left( t \right) &= 0 \\ Q\left( t \right) &= \mathtt{Gr} \left( - \left( \mathtt{node\_b.T}\left( t \right) \right)^{4} + \left( \mathtt{node\_a.T}\left( t \right) \right)^{4} \right) \sigma \end{align} \]

Source

# Lumped thermal element for radiation heat transfer
component BodyRadiation
  extends Element1D
  # Net radiation conductance between two surfaces
  parameter Gr::Real
  # Stefan–Boltzmann constant
  final parameter σ::Real = 5.670374419*10^(-8)
relations
  Q = Gr*σ*(node_a.T^4-node_b.T^4)
end

# Lumped thermal element for radiation heat transfer
component BodyRadiation
  node_a = Node() [{
    "Dyad": {
      "placement": {"icon": {"iconName": "node_a", "x1": -100, "y1": 400, "x2": 100, "y2": 600}}
    }
  }]
  node_b = Node() [{
    "Dyad": {
      "placement": {"icon": {"iconName": "node_b", "x1": 900, "y1": 400, "x2": 1100, "y2": 600}}
    }
  }]
  variable ΔT::Temperature
  variable Q::HeatFlowRate
  # Net radiation conductance between two surfaces
  parameter Gr::Real
  # Stefan–Boltzmann constant
  final parameter σ::Real = 5.670374419*10^(-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

Related

• Examples
• Experiments
• Analyses