Element1D

Element1D is partial one-dimensional thermal element for models without energy storage.

This partial component provides the basic connectors and variables to create one-dimensional heat transfer models that do not store energy. It defines two thermal connection ports, node_a and node_b. The temperature difference across the element is $\mathrm{\Delta }T$, and the heat flow rate through the element from node_a to node_b is $Q$.

The key equations governing its behavior are:

Temperature difference:

$$\mathrm{\Delta }T=node\mathrm{\_}a.T-node\mathrm{\_}b.T$$

Heat flow assignment at ports (assuming $Q$ flows from node_a to node_b):

$$node\mathrm{\_}a.Q=Q$$$$node\mathrm{\_}b.Q=-Q$$

The relationship for node_b.Q is derived from the model's energy balance equation $mathnode\mathrm{\_}a.Q+node\mathrm{\_}b.Q=0$, which signifies that no energy is stored within the element.

Usage

Element1D()

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

Source

# Element1D is partial one-dimensional thermal element for models without energy storage.
#
# This partial component provides the basic connectors and variables to create
# one-dimensional heat transfer models that do not store energy. It defines two
# thermal connection ports, `node_a` and `node_b`. The temperature difference
# across the element is $\Delta T$, and the heat flow rate through the
# element from `node_a` to `node_b` is $Q$.
#
# The key equations governing its behavior are:
#
# Temperature difference:
# ```math
# \Delta T = node\_a.T - node\_b.T
# ```
#
# Heat flow assignment at ports (assuming $Q$ flows from `node_a` to `node_b`):
# ```math
# node\_a.Q = Q
# ```
# ```math
# node\_b.Q = -Q
# ```
#
# The relationship for `node_b.Q` is derived from the model's energy balance equation
# $math node\_a.Q + node\_b.Q = 0$, which signifies that no energy is stored
# within the element.
partial component Element1D
  # 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
relations
  ΔT = node_a.T-node_b.T
  node_a.Q = Q
  node_a.Q+node_b.Q = 0
end

Flattened Source

# Element1D is partial one-dimensional thermal element for models without energy storage.
#
# This partial component provides the basic connectors and variables to create
# one-dimensional heat transfer models that do not store energy. It defines two
# thermal connection ports, `node_a` and `node_b`. The temperature difference
# across the element is $\Delta T$, and the heat flow rate through the
# element from `node_a` to `node_b` is $Q$.
#
# The key equations governing its behavior are:
#
# Temperature difference:
# ```math
# \Delta T = node\_a.T - node\_b.T
# ```
#
# Heat flow assignment at ports (assuming $Q$ flows from `node_a` to `node_b`):
# ```math
# node\_a.Q = Q
# ```
# ```math
# node\_b.Q = -Q
# ```
#
# The relationship for `node_b.Q` is derived from the model's energy balance equation
# $math node\_a.Q + node\_b.Q = 0$, which signifies that no energy is stored
# within the element.
partial component Element1D
  # 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
relations
  ΔT = node_a.T-node_b.T
  node_a.Q = Q
  node_a.Q+node_b.Q = 0
metadata {}
end

Test Cases

No test cases defined.

Related

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