Adjacent zone

¶

The adj_zone dictionary provides all necessary geometric and physical properties of an adjacent unconditioned zone (e.g., attic, basement, or corridor) required to compute the transmission heat transfer coefficient according to ISO 13789.

Adjacent Zone Input (`adj_zone`)

¶

It is possible to simulate a not conditioned adjacent zone providing the following input:

Example Structure:

{
    "name":"adj_1",
    "orientation_zone": {
        "azimuth": 0,
    },
    "area_facade_elements": np.array([20,60,30,30,50,50], dtype=object),
    "typology_elements": np.array(['OP', 'OP', 'OP', 'OP', 'GR', 'OP'], dtype=object),
    "transmittance_U_elements": np.array([0.82, 0.82, 0.82, 0.82, 0.51, 1.16], dtype=object),
    "orientation_elements": np.array(['NV', 'SV', 'EV', 'WV', 'HOR', 'HOR'], dtype=object),
    'volume': 300, 
    'building_type_class':'Residential_apartment',
    'a_use':50 
}

Field Descriptions¶

Key	Type	Description
`name`	`str`	Identifier of the adjacent zone (e.g., `"adj_1"`).
`orientation_zone.azimuth`	`float`	The azimuth angle (in degrees) of the unconditioned zone orientation. Used to determine the facing direction (0° = South, 90° = East, 180° = North, 270° = West).
`area_facade_elements`	`np.array[float]`	Array of surface areas (m²) for each façade element (walls, ground, horizontal slabs, etc.).
`typology_elements`	`np.array[str]`	Surface type codes following ISO 13789/52016 conventions: - `OP` = Opaque element (wall) - `GR` = Ground-contact surface - `HOR` = Horizontal surface (roof/floor)
`transmittance_U_elements`	`np.array[float]`	U-values (W/m²·K) corresponding to each façade element, representing their thermal transmittance.
`orientation_elements`	`np.array[str]`	Orientation of each surface according to ISO 52016 notation: - `NV` = North Vertical (north-facing wall) - `SV` = South Vertical (south-facing wall) - `EV` = East Vertical (east-facing wall) - `WV` = West Vertical (west-facing wall) - `HOR` = Horizontal (roof or floor)
`volume`	`float`	Volume (m³) of the adjacent unconditioned zone. Used to estimate ventilation exchange with the external environment.
`building_type_class`	`str`	Descriptive label for the building type (e.g., `"Residential_apartment"`, `"Office"`, `"Warehouse"`). Used for classification and potential lookup of empirical coefficients.
`a_use`	`float`	Reference area of the adjacent zone (m²). May be used for normalization or reporting.

Interpretation of Orientation Codes¶

Code	Meaning	Typical Element	Azimuth (°)
NV	North Vertical	North-facing opaque wall	180
SV	South Vertical	South-facing opaque wall	0
EV	East Vertical	East-facing opaque wall	90
WV	West Vertical	West-facing opaque wall	270
HOR	Horizontal	Roof or ground-contact surface	—
GR	Ground	Floor or basement slab	—

Example Breakdown¶

For the example above:

Element	Typology	Orientation	Area (m²)	U-Value (W/m²·K)
Wall_1	OP	NV	20	0.82
Wall_2	OP	SV	60	0.82
Wall_3	OP	EV	30	0.82
Wall_4	OP	WV	30	0.82
Floor	GR	HOR	50	0.51
Roof	OP	HOR	50	1.16

Notes¶

Arrays in the dictionary (area_facade_elements, U_elements, orientation_elements, etc.) must have the same length — one entry per building element.
The azimuth determines the active orientation for calculations (NV, SV, EV, WV, HOR).
Default ISO convention assumes 0° = South, rotating clockwise (90° = East, 180° = North, 270° = West).
Horizontal (HOR) and ground (GR) elements contribute to transmission but have no azimuth dependency.

Summary¶

The adj_zone input defines the geometry and thermal characteristics of an unconditioned adjacent space.
It serves as the foundation for ISO 13789 calculations of: - Transmission losses through opaque and ground-contact elements. - Ventilation and exchange between conditioned and unconditioned spaces. - Monthly distribution and adjustment factors for unconditioned zones.

In each not thermal adjacent zone the calcualtion of heat transfer coefficent by transmission is made using the function transmission_heat_transfer_coefficient_ISO13789, thta is based to the EN ISO 13789:2017 standard.

Transmission heat transfer coefficients - EN ISO 13789

¶

def transmission_heat_transfer_coefficient_ISO13789(cls, adj_zone, n_ue=0.5, qui=0)

Inputs¶

Name	Type	Description
`adj_zone`	`dict`	Dictionary containing the geometric and physical properties of the adjacent (unconditioned) zone. Must include surface orientations, areas, U-values, and volume.
`n_ue`	`float`, default `0.5`	Air change rate (h⁻¹) between the unconditioned zone and the external environment.
`qui`	`float`, default `0`	Airflow rate (m³/h) between conditioned and unconditioned zones. Typically zero to avoid underestimating transmission.

Purpose¶

This function implements the ISO 13789:2017 method for calculating the transmission heat transfer coefficient (H_tr) between conditioned, unconditioned, and external zones of a building.

It provides a quantitative measure of heat losses through building envelope elements and ventilation exchange with unconditioned spaces and the exterior.

How it works¶

1) Identify Orientation

The function uses the azimuth of the adjacent zone (adj_zone["orientation_zone"]["azimuth"]) to map it to an orientation name (NV, SV, EV, WV) based on predefined azimuth angles:

Orientation	Azimuth (°)
NV	180
SV	0
EV	90
WV	270

2) Extract Arrays

From the adj_zone dictionary: - areas: surface areas (m²)
- U_values: transmittances (W/m²K)
- orientations: list of orientation strings for each facade element

3) Boolean Masks

Two masks are defined to separate: - mask_selected: surfaces facing the unconditioned zone
- mask_others: other external surfaces

4) Transmission Losses

Between conditioned and unconditioned zones:

\[ H_{d,zt-ztu} = \sum (A_i \cdot U_i) \text{ for selected orientation} \]

From unconditioned zone to exterior:

\[ H_{d,ztu-ext} = \sum (A_i \cdot U_i) \text{ for other orientations} \]

5) Ventilation Losses

Ventilation heat transfer coefficients are added according to ISO 13789:

\[ H_{ve,iu} = 0.33 \times q_{iu} \]

\[ H_{ve,ue} = 0.33 \times q_{ue} \]

Where:
- `ρ·cp = 0.33 Wh/(m³·K)` for air
- `q_iu`: airflow between conditioned and unconditioned zones (m³/h)  
- `q_ue = V_u × n_ue`: airflow between unconditioned zone and exterior

6) Total Heat Transfer

\[ H_{ue} = H_{d,ztu-ext} + H_{ve,ue} \\ H_{iu} = H_{d,zt-ztu} + H_{ve,iu} \]

\[ H_{ztu,tot} = H_{ue} + H_{iu} \]

7) Adjustment Factor (b₍ztu₎ₘ) The adjustment factor accounts for the ratio between losses to the exterior and total losses of the unconditioned zone:

\[ b_{ztu,m} = \frac{H_{ue}}{H_{ue} + H_{iu}} = \frac{H_{ue}}{H_{ztu,tot}} \tag{4.13} \]

\(b_{ztu,m}\in[0,1]\) measures how much the unconditioned zone is “anchored” to the outside rather than to the conditioned neighbor.

8) Distribution Factor (F₍ztc₎ₘ)

If multiple conditioned zones exist, the distribution factor allocates transmission between them:

\[ F_{ztc,ztu,m} = \frac{H_{ztc,i,ztu,m}}{\sum_j H_{ztc,j,ztu,m}} \]

Here it is set to 1.0 since only one conditioned zone is assumed.

Physics¶

The total heat transfer coefficient H_tr is computed as:

\[ H_{tr} = H_d + H_g + H_u + H_a \]

Where: - H_d: Transmission through external envelope (W/K)
- H_g: Transmission through ground (W/K)
- H_u: Transmission through unconditioned zones (W/K)
- H_a: Transmission to adjacent buildings (W/K)

In this function, we focus on the unconditioned zone contribution (H_u).

Output¶

Variable	Type	Description
`H_ztu_tot`	`float`	Total transmission heat transfer coefficient between the conditioned zone and the adjacent unconditioned zone (W/K).
`b_ztu_m`	`float`	Monthly adjustment factor for the unconditioned adjacent zone (dimensionless).
`F_ztc_ztu_m`	`float`	Distribution factor of the transmission coefficient between conditioned and unconditioned zones (dimensionless).

Example¶

def transmission_heat_transfer_coefficient_ISO13789(BUI, adj_zone_name, n_ue=0.5, qui=0):
    adj = get_adj_zone(BUI, adj_zone_name)
    A = np.asarray(adj["area_facade_elements"], dtype=float)
    U = np.asarray(adj["transmittance_U_elements"], dtype=float)
    ORI = np.asarray(adj["orientation_elements"])
    # Define which orientations correspond to zt-ztu interface (project specific rule):
    mask_interface = is_interface_to_conditioned_zone(ORI, adj, BUI)   # boolean mask
    Hd_zt_ztu  = float(np.sum(A[mask_interface] * U[mask_interface]))   # Eq. (4.10)
    Hd_ztu_ext = float(np.sum(A[~mask_interface] * U[~mask_interface])) # Eq. (4.11)

    # Ventilation terms (Eq. 4.12)
    Vu = float(adj["volume"])
    que = Vu * n_ue
    Hve_ue = 0.33 * que
    Hve_iu = 0.33 * float(qui)

    Hue = Hd_ztu_ext + Hve_ue
    Hiu = Hd_zt_ztu + Hve_iu
    Hztu_tot = Hue + Hiu                                 # Eq. (4.12d)
    b_ztu_m  = Hue / Hztu_tot if Hztu_tot > 0 else 1.0   # Eq. (4.13)
    return float(Hztu_tot), float(b_ztu_m)

H_ztu_tot [W·K⁻¹] — total coupling of the unconditioned zone.
b_ztu_m [-] — monthly factor (in the current code computed once from static inputs).
F_ztc_ztu_m [-] — distribution factor (in the current code computed once from static inputs).

Example Output:

H_ztu_tot = 78.45  # W/K
b_ztu_m = 0.63
F_ztc_ztu_m = 1.0

Practical extraction with your `BUI` structure¶

For a given unconditioned zone adj_i:
- Build sets:
  - \(\mathcal{E}_{zt{\text -}ztu}\): elements in adj_i whose orientation_elements match the interface direction to the conditioned zone (your code uses equality tests by NV/SV/EV/WV/HOR).
  - \(\mathcal{E}_{ztu{\text -}ext}\): elements in adj_i not on the interface.
- Use adj_i.volume → \(V_u\).
- Pick n_ue from df_n_ue by air-tightness class or keep default 0.5 h⁻¹.

Edge Cases¶

If A/U vectors contain dtype=object (as in your snippet), cast explicitly to float.
If Hztu_tot = 0 (degenerate geometry), define b_ztu_m = 1.0 by convention (fully outdoor-anchored).

Notes¶

H_ztu_tot increases with larger areas, higher U-values, or greater ventilation exchange.
Default n_ue = 0.5 corresponds to “well-sealed joints, no ventilation openings” (ISO 13789 Table 7).
The function currently handles one conditioned zone; for multiple zones, extend the F_ztc_ztu_m calculation.

Adjacent zone

Adjacent Zone Input (adj_zone)

Field Descriptions¶

Interpretation of Orientation Codes¶

Example Breakdown¶

Notes¶

Summary¶

Transmission heat transfer coefficients - EN ISO 13789

Inputs¶

Purpose¶

How it works¶

Physics¶

Output¶

Example¶

Practical extraction with your BUI structure¶

Edge Cases¶

Notes¶

Adjacent Zone Input (`adj_zone`)

Practical extraction with your `BUI` structure¶