Node of building element

¶

The following two functions calculates the number of nodes to be used in opaque and transparent elements in the 5-node thermal network model.

def Number_of_nodes_element(cls, building_object) -> numb_nodes_facade_elements

Parameters¶

Name	Type	Description
`building_object`	`dict`	Building model containing a list of surfaces under `building_surface`. Each element defines its physical type.

Required Fields in `building_object["building_surface"]`¶

Field	Description
`type`	Element type string: • `"opaque"` or `"OP"` → Opaque element • `"transparent"` or `"W"` → Transparent element (window) • `"adiabatic"` → Internal/insulated partition with no heat flow.

Purpose¶

Determines the number of thermal nodes for each building element, according to its type (opaque, transparent, or adiabatic).
This step is part of the nodal network definition in EN ISO 52016-1:2017, used for energy balance and dynamic thermal simulations.

How it works¶

Initialize all elements as 5-node systems
```
el_list = len(building_object["building_surface"])
Pln = np.full(el_list, 5)
```
ISO 52016 default: each opaque surface is modeled with 5 thermal nodes.

Adjust per element type

Transparent ("transparent") → 2 nodes (external/internal surfaces only).
Adiabatic ("adiabatic") → 0 nodes (no heat transfer).

for i, surf in enumerate(building_object["building_surface"]):
    if surf["type"] == "transparent":
        Pln[i] = 2
    elif surf["type"] == "adiabatic":
        Pln[i] = 0

Compute cumulative node index (PlnSum)
```
for Eli in range(1, el_list):
    PlnSum[Eli] = PlnSum[Eli-1] + Pln[Eli-1]
```
Each element’s node sequence starts where the previous one ends.
Compute the last node index (Rn)
```
Rn = PlnSum[-1] + Pln[-1] + 1
```
Adds one final node for matrix dimensioning in the solver.

Return wrapper

return numb_nodes_facade_elements(Rn, Pln, PlnSum)

Note

The type of the surface has been mapped in the calculation using the following code:

OP: Opaque element
W: Transparent element
GR: Ground-contact element
AD: Adiabatic element
ADJ: Adjacent element

...
for i, surf in enumerate(building_object["building_surface"]):
    if surf["type"] == "opaque":
        if surf["sky_view_factor"] == 0:
            typology_elements[i] = "GR"
        else:
            typology_elements[i] = "OP"
    elif surf["type"] == "adiabatic":
        typology_elements[i] = "AD"
    elif surf["type"] == "transparent":
        typology_elements[i] = "W"
    elif surf["type"] == "adjacent":
        typology_elements[i] = "ADJ"
    surf["ISO52016_type_string"] = typology_elements[i]

Output¶

Variable	Type	Description
`Rn`	`int`	Index of the last node in the complete nodal vector. Used for vector and matrix sizing.
`Pln`	`np.ndarray[int]`	Array of the number of nodes per element: 5 for opaque, 2 for transparent, 0 for adiabatic.
`PlnSum`	`np.ndarray[int]`	Sequential cumulative node indices for mapping all elements.
`numb_nodes_facade_elements`	`object`	Wrapper containing `(Rn, Pln, PlnSum)`.

Example¶

building_object = {
    "building_surface": [
        {"type": "opaque"},
        {"type": "transparent"},
        {"type": "opaque"},
        {"type": "adiabatic"}
    ]
}

nodes = Number_of_nodes_element(building_object)
print("Rn:", nodes.Rn)
print("Pln:", nodes.Pln)
print("PlnSum:", nodes.PlnSum)

Example Output:

Rn: 13
Pln: [5 2 5 0]
PlnSum: [0 5 7 12]

Notes¶

Opaque and adiabatic surfaces are both considered non-transparent; adiabatic ones simply have no conductive nodes.
The nodal indexing ensures continuous node numbering across all envelope elements — crucial for constructing the global heat transfer matrix.
ISO 52016 recommends 5 nodes for opaque elements (multi-layer walls/roofs) and 2 nodes for transparent elements (windows).
The function prepares data for the later calculation of heat capacity, conductance, and solar absorption matrices.

Calculation of conduttance

¶

def Conduttance_node_of_element(cls, building_object, lambda_gr=2.0) -> conduttance_elements

Parameters¶

Name	Type	Default	Description
`building_object`	`dict`	—	Building structure containing the envelope elements in `building_surface`.
`lambda_gr`	`float`	`2.0`	Ground thermal conductivity (W/m·K), used for ground-contact elements (`GR`).

Required Fields in `building_object["building_surface"]`¶

Each surface element must include:

Field	Description
`ISO52016_type_string`	ISO 52016 element type string: • `OP` = Opaque element • `W` = Transparent (window) • `GR` = Ground-contact • `AD` or `ADJ` = Adjacent wall
`u_value`	Overall thermal transmittance (W/m²·K).
`convective_heat_transfer_coefficient_internal`	Internal convective heat transfer coefficient (W/m²·K).
`radiative_heat_transfer_coefficient_internal`	Internal radiative heat transfer coefficient (W/m²·K).
`area`	Element surface area (m²).
(optional) `convective_heat_transfer_coefficient_external`	If not defined, default = 20 W/m²·K (ISO 13789).
(optional) `radiative_heat_transfer_coefficient_external`	If not defined, default = 4.14 W/m²·K (ISO 13789).

Purpose¶

Calculates the thermal conductance between the internal nodes (pli and pli-1) of each construction element in accordance with EN ISO 52016-1 (Section 6.5.7).
It defines the inter-nodal conductances (W/m²·K) that represent the heat transfer capability through each layer of opaque, transparent, or ground-contact elements in the 5-node thermal network model.

How it works¶

Initialize constants and arrays
- Ground resistance:
\[ R_{gr} = \frac{0.5}{\lambda_{gr}} \;(\text{m}^2K/W) \]
- Build lists of:
  - element types (el_type),
  - U-values,
  - internal heat-transfer coefficients (h_ci, h_ri),
  - external coefficients (h_ce, h_re).
Assign external coefficients
- Default convective = 20 W/m²·K, radiative = 4.14 W/m²·K.
- For adjacent elements (AD), both coefficients are set to 0 → no external exchange.
Compute construction resistance

\[R_{c,eli} = \frac{1}{U_{eli}} - \frac{1}{(h_{ci}+h_{ri})} - \frac{1}{(h_{ce}+h_{re})}\]

This represents the core conduction resistance of the element (m²·K/W).
Distribute conductances among layers

For each element i, the nodal conductances h_pli_eli[layer, i] are defined as:

Layer 1 (node pair 1–2)

Type Formula

OP, ADJ \( h = 6/R_c \)

W \( h = 1/R_c \)

GR \( h = 2/R_{gr} \)

Layer 2 (node pair 2–3)

Type Formula

OP, ADJ \( h = 3/R_c \)

GR \( h = 1/(R_c/4 + R_{gr}/2) \)

Layer 3 (node pair 3–4)

Type Formula

OP, ADJ \( h = 3/R_c \)

GR \( h = 2/R_c \)

Layer 4 (node pair 4–5)

Type Formula

OP, ADJ \( h = 6/R_c \)

GR \( h = 4/R_c \)
Return The final 4×N matrix is wrapped in conduttance_elements(h_pli_eli=h_pli_eli).

Note

The type of the surface has been mapped in the calculation using the following code:

OP: Opaque element
W: Transparent element
GR: Ground-contact element
AD: Adiabatic element
ADJ: Adjacent element

...
for i, surf in enumerate(building_object["building_surface"]):
    if surf["type"] == "opaque":
        if surf["sky_view_factor"] == 0:
            typology_elements[i] = "GR"
        else:
            typology_elements[i] = "OP"
    elif surf["type"] == "adiabatic":
        typology_elements[i] = "AD"
    elif surf["type"] == "transparent":
        typology_elements[i] = "W"
    elif surf["type"] == "adjacent":
        typology_elements[i] = "ADJ"
    surf["ISO52016_type_string"] = typology_elements[i]

Outputs¶

Type	Description
`conduttance_elements`	Wrapper object containing the matrix `h_pli_eli` (4×N) where N = number of envelope elements. Each row corresponds to a node pair (`pli`, `pli−1`) and each column to an element. Units: W/m²·K.

Example¶

h = Conduttance_node_of_element(building_object=bui, lambda_gr=2.0)
H = h.h_pli_eli
print(H.shape)  # (4, N)
print(H[:, 0])  # conductance values for element #0

Notes¶

For adjacent surfaces (AD), external heat-transfer coefficients are zero (no external exchange).
Ground-contact elements use simplified analytical correlations (ISO 13370).
R_c is set to ∞ for “AD” elements → conductance = 0.
Default coefficients (20 W/m²·K, 4.14 W/m²·K) are consistent with ISO 13789 recommendations.
The 4 layers correspond to the 5-node surface temperature network used in ISO 52016.

References¶

EN ISO 52016-1:2017 – Energy performance of buildings — Calculation of energy needs for heating and cooling, Section 6.5.7.
EN ISO 13789:2017 – Thermal performance of buildings — Transmission and ventilation heat transfer coefficients — Calculation method.
EN ISO 13370:2017 – Heat transfer via the ground — Calculation methods (for ground-related resistances).

Type	Formula
`OP`, `ADJ`	\( h = 6/R_c \)
`W`	\( h = 1/R_c \)
`GR`	\( h = 2/R_{gr} \)

Type	Formula
`OP`, `ADJ`	\( h = 3/R_c \)
`GR`	\( h = 1/(R_c/4 + R_{gr}/2) \)

Node of building element

Parameters¶

Required Fields in building_object["building_surface"]¶

Purpose¶

How it works¶

Output¶

Example¶

Notes¶

Calculation of conduttance

Parameters¶

Required Fields in building_object["building_surface"]¶

Purpose¶

How it works¶

Outputs¶

Example¶

Notes¶

References¶

Required Fields in `building_object["building_surface"]`¶

Required Fields in `building_object["building_surface"]`¶