Effect of millimetric perforations on CO 2 diffusion and thermal transmittance of multi-layered breathing walls

Abstract

The effect of 2 mm millimetric perforations on the performance of multi-layered breathing exterior wall systems was investigated in relation to both thermal transmittance and carbon dioxide (CO₂) diffusion. The study aimed to determine whether such perforations on glass fiber coated gypsum board (GFCGB) layers could enhance gas permeability without significantly compromising thermal insulation. Three wall configurations were prepared: a reference wall with unperforated GFCGB, and two alternatives with perforations of 2 mm spaced at 5 and 1 cm intervals. These were tested in a custom-built cold box setup designed to simulate indoor and outdoor conditions and allow simultaneous measurement of steady-state U values and effective CO₂ diffusion coefficients (D_EFF). Results showed that the introduction of perforations increased D_EFF value by 14% and 54% for the 5 and 1 cm intervals, respectively, compared to the unperforated reference. The measured U values of all testes systems, obtained by the cold-box tests under the steady-state laboratory boundary conditions, are within the range of 0.32–0.36 W/m²·K. The findings suggest that improved gas diffusion may be achieved through carefully designed perforation patterns without substantial thermal penalty. This study represents the first application of the D_EFF parameter to multi-layered wall systems composed of industrially available materials, marking a shift from material-scale evaluations to envelope-scale performance assessment. The perforated wall system proposed here offers a low-tech, scalable approach for breathable building envelopes, particularly relevant in settings where mechanical ventilation may be limited or absent. Overall, the study shows that air permeability, when quantified and optimized, can be treated as a functional property of building envelopes, contributing to healthier and more sustainable architectural solutions.

Keywords

breathing walls millimetric pore carbon dioxide diffusion coefficient U-value building envelope self-ventilation

Introduction

The escalating demand for building cooling and ventilation in hot climates continues to intensify the energy and carbon burden of maintaining acceptable indoor conditions. This has renewed interest in envelope-integrated passive strategies that can support air exchange and tempering without relying exclusively on mechanical ventilation. Within this context, breathing wall systems have been proposed as multi-layered porous envelope systems that permit controlled transport through the wall body and can, under suitable conditions, recover heat while limiting conductive losses.

For example, a recent study has shown that millimeter-scale channels can be designed such that incoming air is tempered with low-grade heat and conductive losses remain small (Craig and Grinham, 2017). In warm regions, breathing walls combined with night-time ventilation can further enhance heat dissipation and cooling performance (Alongi et al., 2017, 2020a, 2020b, 2021). Collectively, this body of literature supports the potential of porous envelope systems to reduce operational energy associated with ventilation and cooling, while highlighting that performance is strongly dependent on material properties, geometry, and boundary conditions (A. Alongi et al., 2017; Craig and Grinham, 2017).

The existing literature can be broadly grouped into three themes. First, experimental and design-oriented research has primarily focused on thermal behavior and heat-exchange performance of porous envelope concepts, often emphasizing how pore/channel geometries influence heat recovery and conduction (A. Alongi et al., 2017; Alongi et al., 2021a; Craig and Grinham, 2017). Second, complementary modeling and parametric studies have explored the sensitivity of energy performance to permeability, airflow rate, and conductivity, generally confirming that well-designed porous envelopes can improve thermal performance when airflow pathways and material properties are carefully tuned (Li et al., 2021; Wang et al., 2018; Zhang et al., 2019, 2021). The third has begun to frame gas transport through permeable building elements in terms of diffusion-related measurable parameters, including a methodology for quantifying an effective CO₂ diffusion coefficient (D_EFF, cm²·s⁻¹) for porous building materials (Karanfil and Tavukçuoğlu, 2023). However, diffusion-driven CO₂ transport has not been consistently quantified for envelope systems alongside thermal transmittance measurements, even though design decisions in practice are typically made at the envelope system scale.

This points to a specific gap relevant to breathing envelope design: while thermal performance of breathing walls is widely reported, the effect of introducing additional, controlled millimetric pores into the lining layers of a multi-layer breathable wall assembly has not been evaluated in a paired manner in terms of both its system-level CO₂ permeability and its measured thermal transmittance (U-value). In addition, because multi-layered systems typically contain a highly resistive insulation core, it remains unclear whether perforation-enabled increases in gas permeability through linings translate into a detectable change in U-value under standard steady-state laboratory conditions.

It is important to note that this interpretation of building envelope permeability contrasts with the conventional “airtightness-first” priority, in which uncontrolled transport is minimized as a primary design objective. For instance, one of the proposals is a concept of an optimized container house wall that has gas layers (e.g. argon) within its multi-layered configuration, where airtightness is a functional prerequisite. In that configuration, the steel shell acts as a gas layer holder, and leakage prevention is obligatory for the targeted thermal performance (Omle et al., 2024). In this kind of conventional practice shaped by this “airtightness-first” logic, indoor air quality is not considered an envelope design parameter. Instead, it is implicitly assumed that acceptable IAQ can only be achieved through mechanical ventilation and bulk air exchange. Moreover, this airtightness priority downgrades the building envelope to a passive barrier and positions IAQ as a secondary outcome to be “fixed” by mechanical systems rather than designed using the building skin. Therefore, this study discovers the under-researched potential of building envelopes as passive self-ventilation elements.

Beyond CO₂, “breathability” is also commonly interpreted through water-vapor permeability, which can influence indoor humidity balance. In principle, highly water vapor permeable and porous materials can absorb moisture when indoor relative humidity rises and can release it when the air becomes drier, thereby damping humidity peaks and fluctuations (Kaczorek and Basińska, 2024; Larcher et al., 2025; Posani et al., 2025). Although quantification of moisture transport or indoor humidity outcomes are not within the scope of this study, the above-mentioned potential benefits are an additional motivation for delving into breathable envelope research.

Instead of relying solely on mechanical systems to provide good IAQ and humidity control, systems that increase energy demand and operational complexity (especially during events like the COVID-19 pandemic where fresh air intake requirements surged) the building envelope itself emerges as an active participant in air management. The measurable D_EFF parameter makes it possible to scientifically assess and fine-tune the contribution of porous materials to indoor air quality. As a result, breathing walls and breathable building skins no longer represent fringe or experimental concepts but are becoming central to reimagining sustainable architecture practices.

Against this background, the present study experimentally investigates how controlled 2 mm perforations introduced into the two GFCGB lining layers of a multi-layered breathing exterior wall system influence both CO₂ diffusion performance and thermal transmittance. The work evaluates an airtight reference and progressively “breathable” configurations created via defined perforation patterns, and quantifies system-level D_EFF (cm²·s⁻¹) using a sealed cold box CO₂ concentration decay method, while measuring U-values for the same wall mockups simultaneously. By reporting paired D_EFF and U-value outcomes for comparable multi-layered wall mockups, the study provides design-relevant experimental evidence on the diffusion–thermal trade-off associated with perforation-enhanced breathability. The findings are interpreted within the limitations of the laboratory setup (diffusion-based CO₂ transmission under controlled temperature and concentration gradients, without imposed pressure-driven airflow) and are intended to support future envelope optimization through room-scale IAQ modeling efforts.

Breathing wall system design rationale

In ventilation systems relying on advection and convection, created by pressure differences between indoor and outdoor environments (supported either mechanically or by naturally), indoor air is exhausted mass-wise, while outdoor air is brought in. Simply, existing ventilation and breathing wall technologies primarily rely on air transmission between indoor and outdoor environments via advection and convection. Mass transfer in fluids occurs in four ways: diffusion, advection (horizontal transport), convection (vertical transport), and phase change (Incropera et al., 2007). To sustainably improve indoor air quality, understanding and utilizing these ways of mass transfer, especially diffusion and advection, is crucial. In a non-stationary mixture of gases A and B, the absolute flux of gas A (e.g. CO₂ in air mixtures) is calculated by considering two primary factors, diffusion and advection (Incropera et al., 2007). To be clearer, theoretically, when advection is zero, meaning pressure differences drive no horizontal mass movement of air, the gas mixture (e.g. air) is stationary, and mass transfer of gas A (e.g. CO₂ in air mixture) occurs entirely through diffusion. Mass and heat transfer are coupled phenomena, but critically, improving air quality does not necessarily require bulk mass exchange or full air replacement. For instance, 78% of atmospheric air is composed of nitrogen gas (Seinfeld and Pandis, 2016), which remains physiologically unprocessed and is merely conditioned by heating or cooling systems. Therefore, it is sufficient for specific pollutant gases (e.g. CO₂ or VOCs) to diffuse outward through the porous wall body without removing the entire air volume. This selective gas removal via diffusion can occur without energy loss associated with advection. Pore structures with high airflow resistivity and high tortuosity have the potential to minimize advection but allow gas diffusion. Breathing walls with such porous layers are predicted to allow gas diffusion but maintain the U-value within the limits.

Accordingly, the study proposes a multi-layered and breathing insulated exterior wall system that provides passive ventilation and improves IAQ. This proposed cold facade system consists of five main layers, from the inside to outside, respectively, as shown in Figure 1:

12.5 mm Glass Fiber Coated Gypsum Board (GFCGB)

100 mm glass wool (two layers of 50 mm-thick glass wool insulation panel)

12.5 mm GFCGB

50 mm ventilation cavity

Rain screen with inlets and outlets

Figure 1.

The concept of the multi-layered wall composition examined by this study functions as a breathable, insulated, and ventilated wall, while the perforation design of Layer 1 and Layer 3 changes to encourage CO₂ diffusion through the wall section in a controlled manner. (1) 12.5 mm Glass Fiber Coated Gypsum Board (GFCGB), (2) 100 mm (50 mm × 2) glass wool, (3) 12.5 mm GFCGB, (4) 50 mm air cavity, (5) rainscreen with air inlets and outlets.

The first three layers comprise the “permeable” part of the breathing wall system (Figure 1) which allows the indoor air pollutants to diffuse outdoors while allowing the fresh air from outside to diffuse inward without creating an unpleasant airflow for the users. This study focuses exclusively on and assesses this “permeable” section of the system, in terms of CO₂ permeability and thermal transmittance (Figure 1). The wall composition, which integrates millimetric perforations of up to 2 mm in diameter on the surface layers to enable passive gas diffusion while minimizing advective flow, has been officially patented (TURKPATENT, 2024).

As a common practice, the rain screen protects the wall system from external factors such as precipitation, wind, and sunlight. There are vents on the rain screen layer that will provide fresh air inlet and outlet, making the breathing wall a cold facade. The ventilation cavity between the rain screen and the breathing thermal insulation prevents the physical contact between these two layers and thus eliminates the risk of capillary suction in the horizontal direction from the rain curtain surface to the inner wall layers. With the air circulation provided by the clean air inlet and outlet, possible condensation problems in the ventilation cavity are prevented. Thus, if the rain curtain gets wet, the rest of the wall is protected from water and humidity. The effect of these rain screen and ventilation cavity layers of the breathing wall systems to the gas permeability and thermal performance of the wall system are not in the scope of this study.

Material and method

Here, the proposed breathing wall system is assumed to be a double-frame exterior dry wall system that forms the enclosing part of the building envelope. The wall frame can be made of metal or timber. This proposed system is a non-load-bearing façade system that can be attached to the main structure of the building. The structural system of the building (e.g. reinforced concrete or steel frame) or the wall frame elements are therefore not a part of the tested mockups and are outside the scope of this study.

The experiments focus only on “permeable” part of the proposed breathing wall system to clarify how millimetric drilled pores on GFCGB affect thermal transmittance and CO₂ permeability of an insulated dry wall system with GFCGB lining on both sides. GFCGB was selected as the lining material of the permeable wall mockups because it is already globally available, already exhibits high vapor permeability, and is inherently lightweight and porous (Sulong et al., 2019).

During sample preparation it became evident that manufacturing constraints limit how small the holes can be: drill bits thinner than 2 mm snapped frequently, whereas 2 mm bits remained intact throughout the series. On this practical ground, 2 mm was identified as the smallest diameter to consider for the experiments.

Accordingly, the study therefore adopted three lining variants for subsequent cold box tests:

GFCGB with no perforation (baseline).

GFCGB with 2 mm pores at 5 cm intervals (low perforation frequency).

GFCGB with 2 mm pores at 1 cm intervals (high perforation frequency).

The mockups of the three permeable configurations were produced and then tested using a custom-built experimental setup designed to measure thermal transmittance (U-value, W/m²·K) and the effective CO₂ diffusion coefficient (D_EFF, cm²/s). Detailed material properties of each wall layer and measurement protocols are described in the following subsections.

In addition to the permeable wall mockups, an expanded polystyrene (EPS; a commonly used non-breathing building insulation material) layer is also tested for CO₂ permeability, as a representative airtight layer.

Components of the wall mockups

Each component of the wall mockups was selected deliberately from material families that are globally manufactured, widely standardized, and commonly used in lightweight building envelopes, and that also represent clearly contrasting “breathing” behaviors based on water vapor permeability (μ-value). This selection was guided by an assumption of “materials that are highly permeable to water vapor are also likely to exhibit higher CO₂ permeability,” because both transport processes are strongly influenced by pore structure, connectivity, and overall diffusion resistance within the solid matrix. The material characteristics of the layers comprising the wall mockups studied in this study are listed in Table 1. Preliminary laboratory measurements showed that GFCGB has a bulk density of 0.92 g cm⁻³ (±0.01), an effective porosity of 52% (±4%), and a vapor diffusion resistance (μ-value) of 9.6 (±0.6) confirming that the material is highly porous, highly water vapor permeable and suitable for further permeability enhancement with drilled millimetric pores.

Table 1.

The material characteristics of the layers forming the mockups of multi-layered wall sections.

Material	Density	Effective porosity	Water vapor diffusion resistance (μ-value)	Thermal conductivity (λ)	Thickness
Material	g/cm³	% by volume	Unitless	W/m·K	mm
Glass fiber coated gypsum board	0.92 ± 0.01^a	54 ± 4^a	9.6 ± 0.6^b	0.255^c	12.37 ± 0.36^a
			9.6 ± 0.6^b		12.5^c
			8.37^c		12.5^c
Glass wool insulation panel	0.018^d	N/A	1^c	0.035^c	50^c
EPS	0.030^e	N/A	40–100^e	0.038^e	20–80^e
EPS	0.030^e	N/A	54.3 ± 3.0^f	0.038^e	20–80^e

Tested by this study by gravimetric method (ASTM C134-95, 2016).

Tested by this study by wet cup method (ASTM E96/E96M − 22, 2022).

Taken from the product data sheet of the GFCGB (British Gypsum, 2025; İzocam, n.d).

Unpublished data based on the personal communication with the production company representative.

Taken from the product data sheet of the EPS (Knauf, 2025).

Empirical data from literature (TavukçuoúÏlu et al., 2013).

The original EPS lid of the EPS box (used in the cold box apparatus) was included in the cold box tests as a practical “nearly impermeable” reference layer that represents an envelope component where gas transport is intentionally suppressed. Unlike glass fiber or gypsum based products that have an interconnected pore structure, EPS is a closed cell polymer foam which has sealed voids within closed pores (Sulong et al., 2019). This microstructural characteristic is reflected in its comparatively high μ-value as presented in Table 1. Therefore, EPS provides a benchmark to verify that the cold box apparatus (employing an EPS box) does not introduce unintended leakage and quantify how much the “breathing” options increase diffusion rate relative to a conventional, diffusion-resisting insulation layer.

The brief verbal and schematic definition of each wall system is given in Figure 2. The photos of the actual EPS lid and the wall mockups of the three tested wall systems are presented in Figure 3. The perforated GFCGB samples are prepared by drilling 2 mm holes at 5 and 1 cm intervals by using a hand drill and each perforation is checked to identify if it is blocked or not (Figure 4). These mockups of the wall types are designed as the interchangeable lids of the EPS cold box apparatus

Figure 2.

The EPS lid and three types of permeable wall mockups tested by the cold box experimental setup.

Figure 3.

The EPS Box lid (upper left), Wall 00 mock-up (upper right), Wall 01 mock-up (lower left) and Wall 02 mock-up (lower right).

Figure 4.

The perforated GFCGB samples are prepared by drilling 2 mm holes with related intervals by using a hand drill (left) and each perforation is checked by holding the board to light (right) if it is blocked or not. The sample presented in the middle belongs to Wall 02, the one with the interior lining with perforation at 1 cm intervals.

Cold box experimental setup

To evaluate the thermal and gas diffusion performance of the wall mockups under controlled conditions, a series of cold box experiments were conducted. This testing framework was designed to simulate a simplified indoor-outdoor boundary environment in which both CO₂ permeability and thermal transmittance could be measured simultaneously. The cold box setup aims to recreate steady indoor temperature and a CO₂ concentration difference between the inner and outer surfaces of the wall samples, thus enabling the measurement of gas diffusion and heat transfer through the porous structures. A custom built experimental cold box test apparatus was developed using an EPS cold chain packaging box, modified to host the wall mockups as its lid and integrated with monitoring instruments. The subheadings below detail the components, sealing strategy, and test protocol of this experimental setup.

Experimental setup

The experimental setup composed of an EPS cold chain packaging box is used to shape the main form of the cold box. EPS lid of this cold box is replaced with the mockups of different wall systems. The experimental setup consists of:

- Expanded Polystyrene (EPS) Box: The box’s inner dimensions are 345 mm (width), 445 mm (height) and 210 mm (depth). The EPS box wall thickness is 20 mm.

- Sealant layers: Sealing is achieved using double-sided adhesive foam tape, self-adhesive duct tape, and siliconized acrylic sealant applied at the junctions where the EPS frame of each wall mockup meets wall layers (GFCGB and glass wool). Further details on sealing protocol are provided under the next subheading.

- CO₂ and Air Temperature Measuring Device: An indoor air quality monitoring device (Testo 480) with one probe inside the cold box and another probe outside the cold box in the laboratory environment as presented on Figure 5.

- Fan: A mini fan inside the cold box provides evenly distributed temperature and CO₂ concentration (Figure 5).

- Cooling Packs: Four cooling packs, each containing 300 ml of distilled water that are frozen in the freezer at −20°C for at least 24 hours before each experiment. The dimensions of each cooling pack are 20 mm × 180 mm × 85 mm and each has a volume of 0.000306 m³. The total volume of the four cooling packs is 0.00012 m³, which is to be subtracted from the box volume to calculate the air volume inside the cold box.

- CO₂ Source: A beaker containing 25 ml acetic acid (80% purity) and 1 g sodium bicarbonate increases the CO₂ concentration level in the cold box by releasing approximately 523 mg CO₂ into the air inside the setup (Figure 5).

Figure 5.

The schematic representation of the cold box experimental setup.

Table 2 presents the instruments used in the cold box experiments and reports the ranges and accuracies for the measured parameters, as declared by the manufacturer. These specifications provide the basis for interpreting measurement uncertainty when comparing CO₂ permeability parameters and U-values across the tested wall mockups.

Table 2.

Instruments used in the cold-box experiments and their manufacturer-stated measurement specifications (measured parameter, unit, range, and accuracy; FLIR, 2025; Testo, n.d).

Instrument	Measured parameter	Unit	Range	Accuracy	Resolution
Testo 480 Digital temperature, humidity and air flow meter + Two indoor air quality probes (one in the cold box, the other in the laboratory)	CO₂ concentration inside cold box	ppm	0–10,000	From 0 to +5000 ppm CO₂ ± (75 ppm CO₂+3% of measured value)	1
	CO₂ concentration outside cold box (laboratory)	ppm		From 0 to +5000 ppm CO₂ ± (75 ppm CO₂+3% of measured value)
	CO₂ concentration outside cold box (laboratory)	ppm		From 5001 to +10,000 ppm CO₂ (150 ppm CO₂+5% of measured value)
	Air temperature inside cold box	°C	0–50	±0.3	0.1
	Air temperature outside cold box (laboratory)	°C	0–50	±0.3	0.1
	Inside cold box	hPa	+700 to +1100	±3	0.1
	Outside cold box (laboratory)	hPa	+700 to +1100	±3	0.1
FLIR E60 Infrared Camera	Surface temperature on the outer surface of the wall mockups	°C	−20 to +120	±2°C or ±2% of reading, for ambient temperature 10°C to 35°C	0.1

Sealing protocol and airtightness check

To ensure that gas exchange between the interior and exterior of the cold box occurs solely through the porous body of the wall mockup, and not through improperly sealed joints, a sealing protocol was developed through several trials (Figures 6 and 7). The primary objective of this protocol is to create a fully sealed chamber by sealing all interfaces, including the edges of the wall mockups and the junctions where they meet the cold box. The airtightness of the EPS cold chain packaging box is achieved by applying two layers of self-adhesive duct tape across all interior surfaces of the EPS box. Additionally, the EPS frame of each wall mockup, along with the interfaces between the wall mockups and the EPS box, are sealed with duct tape. Since directly removing tape adhered to EPS surfaces often damages the material, a preliminary duct tape layer is applied to protect the EPS. This approach prevents tearing during disassembly and allows for reuse of the cold box setup. Next, EPS box and the wall mockup is adhered to each other by a layer of double-sided adhesive foam tape. This foam tape layer is compressed and fixed at a minimum of three points on each joint edge using duct tape. To secure the airtightness of the joint, the outer edge where the wall mockup meets the EPS box is first wrapped with a layer of double-sided foam tape, followed by an overlayer of duct tape for enhanced sealing (Figures 6 and 7).

Figure 6.

Sealing details of the EPS box and wall mockup using foam tape and duct tape to ensure airtight edges.

Figure 7.

Interior of the EPS cold box before mounting the wall mockup (left). Finalized setup with the wall mockup sealed and mounted onto the EPS box (right).

As the quantitative indicator of potential pressure-driven air exchange, absolute pressure was recorded simultaneously by the two Testo 480 probes throughout each experimental session: Probe A positioned inside the cold box and Probe B positioned in the laboratory environment (Figure 5). For each decay test, the pressure difference (ΔP) was evaluated as the difference between the absolute pressure values measured by Probe A and by Probe B. A probe co-location check was additionally performed by placing both probes in the same laboratory environment for 2 hours (no cold box). Under identical ambient conditions, Probe A read higher absolute pressure values than Probe B by 0.80 ± 0.05 hPa, indicating a systematic inter-probe offset.

Thermal monitoring of the cold box setup using an infrared camera enables the detection of air leakage zones as cold streaks. The significant temperature difference of ∼10°C provided between the air inside the cold box and the surrounding laboratory environment facilitates the detection of such sealing failures. Any persistent localized anomaly at the sealing line (distinct from the uniform wall-field temperature pattern) was treated as evidence of leakage and a reason for re-sealing and repetition of the experiment session. The thermal inspections are conducted at three stages: after sealing the cold-box experimental setup at the beginning, midway through, and at the end of each experiment. Additionally, sudden or step-like drops in CO₂ concentration inside the cold box (inconsistent with a smooth monotonic decay expected from diffusion-driven exchange) or a measured U-value significantly exceeding expected values, is considered indicative of potential leakage. Altogether, airtightness of the edges is verified through a triple-inspection protocol. If any leakage is detected, the corresponding experimental sessions are considered invalid.

Test protocol

The temperature (°C), CO₂ concentration levels (ppm) inside and outside the cold box experimental setup, continuously measured and recorded by an indoor air quality monitoring device (Testo 480), following the methodology of ASTM E741-24 Standard (ASTM E741-24, 2024). The tests are conducted for 5 hours which is enough to observe a period where the temperature inside and outside the cold box, and the temperature of the exterior surface of the wall mockup come to a balance and stabilized. The exterior surface temperature of the wall mockup is measured and recorded manually by using an infrared camera (FLIR E60) during the experiment at several moments where the system is expected to reach a thermal equilibrium. These data are used in relevant equations to find the measured thermal transmittance (U-value) of the wall system, as explained further in the following subheading. Each wall mock-up is tested three times to confirm the reproducibility of the results.

Data acquisition and analysis

During a decay test, the concentration difference (the driving force of diffusion) across the tested wall decreases over time, implying that the instantaneous CO₂ diffusion rate (E, mg/s) is time dependent. In this study, the effective diffusion, D_EFF, data are determined by using the data extracted from the early-time portion of the concentration decay curve, where a linear fit between the CO₂ concentration and time is provided. To achieve a single D_EFF value, the approach of using the initial slope of the decay curve yields a comparable D_EFF for different wall configurations without requiring a full transient model fit (Karanfil and Tavukçuoğlu, 2023).

First, the conversion of CO₂ concentration data collected by the CO₂ measuring device Test 480 and the CO₂ monitoring probes from ppm to mg/m³ units is done by using equation (1) and by considering a pressure of 1 atm and a temperature of 25°C in the equation (Mihelcic et al., 2021). These conditions are typical assumption for the conversions of chemicals in the air (Boguski, 2006).

C (in mg / m^{3}) = C (in ppm) \times MW \times \frac{P}{RT}

(1)

where,

C (in mg.m⁻³): CO₂ concentration in mg/m³

C (in ppm): CO₂ concentration in parts per million

MW: Molecular weight (44.01 g/mol for CO₂)

P: Pressure in atm (1 atm)

R: Gas constant (0.08205 L·atm/mol·K)

T: Temperature in K (25°C = 298.15 K)

The data collected by this experiment is analyzed to calculate the following parameters:

− Concentration decay rate in cold box (R, mg/m³·s): It is the initial rate presenting the fastest reduction in CO₂ concentration until the fastest concentration decay starts to slow down due to the significant decrease in the partial pressure difference between the inside and outside of the chamber. That initial period of concentration decay is considered during the regression analysis. R is the absolute slope of the best-fit linear regression of this initial period. The absolute slope of the best-fit linear regression is found by analyzing the CO₂ concentration data using a Python code (available on request) edited in Visual Studio Code Initial-gradient approach.

− CO₂ diffusion rate (E, mg/s): It is the amount of CO₂ that diffuses through a porous material in time (Jacobs, 1967; Wilson et al., 2009). The air inside the cold box (which has a very small volume of 0.03 m³) was assumed to be a well-mixed air node, supported by continuous mixing using a mini fan during measurements. The CO₂ diffusion rate is calculated by using R values obtained from the cold box experiments using equation (2).

E = R \times V

(2)

where, E: CO₂ diffusion rate, mg/s

R: CO₂ concentration decay rate measured by the cold box experiments, mg/m³·s

V: Air volume of the cold box, m³ (the volume of the cooling packs is extracted from the volume of the cold box and found 0.03212 m³)

− Effective CO₂ diffusion coefficient (D_EFF, cm²/s): It is the amount of CO₂ which crosses through the unit section area of a porous material perpendicular to the diffusion direction in unit time and at the unit concentration gradient. It is calculated using equation (3) which is based on Fick’s law (Jacobs, 1967; Wilson et al., 2009). Application of this equation assumes diffusion-dominated transport across the tested wall section (i.e. negligible pressure-driven advection). This assumption is supported by the difference (ΔP) between the absolute pressures measured by the probe inside the cold cox (Probe A) and the other probe outside the cold box (Probe B) in the laboratory environment (as explained in Section 3.2). This analysis adopts a one-dimensional effective approximation for diffusion through the wall section. Any residual three-dimensional effects are not resolved explicitly and are implicitly captured in D_EFF.

D_{EFF} = \frac{E \times L}{A (C_{IN} - C_{OUT})}

(3)

where,

D_EFF: Effective CO₂ diffusion coefficient, cm²/s

E: CO₂ diffusion rate, mg/s

L: Thickness of the building material sample, cm

A: Area of the plane perpendicular to the diffusion direction, cm²

C_IN: The CO₂ concentration in the single-chamber at the beginning of the initial period where the concentration decay is the fastest and the decay slope is linear, mg/cm³

C_OUT: The CO₂ concentration in the laboratory at the beginning of the initial period where the concentration decay is the fastest and the decay slope is linear, mg/cm³

– Calculated thermal transmittance value (U_CALCULATED, W/m²·K): The theoretical thermal transmittance values of the walls were calculated using equation (4), incorporating the layers constituting the wall assembly along with their respective thicknesses, thermal conductivity properties, and the interior and exterior thermal convection coefficients as specified in the relevant standards (Çengel and Ghajar, 2015; Sayın, 2019; TS 825, 2024).

U_{CALCULATED} = \frac{1}{\frac{1}{h_{si}} + \frac{d_{1}}{λ_{1}} + \dots + \frac{d_{n}}{λ_{n}} + \frac{1}{h_{so}}}

(4)

where;

h_si: is the inside wall surface thermal convection coefficient, 7.69 W/m²·K

h_so: is the outside wall surface thermal convection coefficient, 25 W/m²·K

d: is the thickness of the wall layers, m

λ: is the thermal conductivity of a wall layer, W/m·K

− Measured thermal transmittance value (U_MEASURED, W/m²·K):U-values were measured under steady-state laboratory boundary conditions in the cold-box apparatus with no imposed pressure difference across the wall mockup. The measured thermal transmittance values of the walls are determined by using surface temperature data extracted from infrared thermography images and microclimatic data together with relevant equation (5) defined in the literature (Albatici et al., 2015; Albatici and Tonelli, 2010).

U_{MEASURED} = \frac{(5.67 \times 10^{- 8}) ε (T_{SO}^{4} - T_{OUT}^{4}) + 3.8054 v (T_{SO} - T_{OUT})}{(T_{IN} - T_{OUT})}

(5)

U_MEASURED: in situ thermal transmittance value, W/m²·K

ε: thermal emissivity of the surface (unitless) which is assumed to be 0.88 for glass fiber coated gypsum board

T_SO: in situ outside surface temperature of exterior wall, K

T_OUT: in situ outside ambient temperature, K

T_IN: in-situ inside ambient temperature, K

v: in situ wind velocity near wall surface, assumed constant at 0.02 m/s

The thermal emissivity (ε) of the gypsum board and EPS are measured by using infrared thermal camera (FLIR E60) according to the method in the literature which allows measuring the thermal emissivity of a material by comparing it with a material whose thermal emissivity is already known (Barreira et al., 2021). The ε value of the gypsum board is specified as 0.88.

The aim here is to provide constant temperature inside the cold box and the material surfaces within the duration of experiments. Therefore, the experimental process of determination of the thermal performances of the tested samples is started with a trial-and-error approach to determine how long an experiment session should be and how many cooling packs are needed for different samples in order to provide steady state conditions for the cold box. Consequently four to five cold cooling packs are used in each cold box set up for in order to provide constant temperature in the cold box and the material surfaces. The experiments are conducted for 3–5 hours to discover the minimum duration where the system reaches a thermal equilibrium. This thermal equilibrium is needed for the correct measurement of the U value of a tested sample. The air temperatures inside and the outside (the laboratory environment) of the cold box are monitored and recorded every 10 seconds by Testo 480 indoor air quality monitoring device. The exterior surface temperatures of the tested samples are measured by hand by using FLIR E60 infrared thermography camera during the experiment at several moments where the system is expected to reach to a thermal equilibrium. These measured data are used in equation (5) to find the measured thermal transmittance value, U_MEASURED (W/m²·K). The reported U values are derived from in-situ surface temperature measurements under steady boundary conditions and therefore include experimental variability associated with sensor accuracy, surface contact, and spatial temperature non-uniformity. To quantify repeatability, each wall configuration was tested three times, and U-values are reported as “mean ± standard deviation.”

The U value measurements were obtained under controlled, steady-state cold box conditions without imposed pressure difference across the wall mockups. Transient outdoor temperatures and wind-induced pressure gradients that may modify in situ heat transfer and air transport mechanisms in real façades are out of the scope of this study. In short, the thermal performance parameter in this study is limited to steady-state U values measured in the laboratory.

An uncertainty analysis was performed for both the measured D_EFF and U-values in accordance with the Guide to the Expression of Uncertainty in Measurement (GUM; JCGM 100:2008, 2008). Type A uncertainty components were taken from the repeatability (standard deviation) of three replicate runs per wall mockup. Type B uncertainty components were derived from measuring device specifications (Table 2) and geometric tolerances of the exposed area (A), diffusion length (L), and cold-box air volume (V). For D_EFF, the regression uncertainty of the early-time linear decay slope and the ppm to mg·m⁻³ conversion uncertainty associated with absolute pressure and temperature assumptions were included. For the measured U values, Type B components included surface temperature, emissivity, near-surface air velocity, and the indoor/outdoor air temperature terms in equation (5). Standard uncertainties were propagated using sensitivity coefficients. The combined standard uncertainty was computed by root sum of squares, and the expanded uncertainty (U) was obtained with a coverage factor k = 2 (≈95% confidence). The considered uncertainty sources are summarized in Appendix 1 for D_EFF and Appendix 2 for the U values.

Results

The airtightness of the experimental setup, comprising an expanded polystyrene (EPS) cold-chain packaging box with its original EPS lid, was verified through repeated preliminary CO₂ permeability tests. The CO₂ concentration inside the box was continuously monitored until it stabilized around 8000 ppm (14,400 mg/m^3; Figure 8).

Figure 8.

CO₂ concentration decay results for EPS lid: Experiment 1 (left), Experiment 2 (middle), Experiment 3 (right): CO₂ concentration data inside the cold box (C_IN) and laboratory environment (C_OUT) measured and recorded by the indoor air quality measurement device (Testo 480).

The CO₂ concentration decay data obtained from the cold box experiment on Wall 00, Wall 01, and Wall 02 are presented on Figures 9 –11, respectively. The CO₂ concentration decay rates for the cold box experimental setups with EPS lid, Wall 00, Wall 01, and Wall 02 are measured as 0.13 ± 0.02, 1.05 ± 0.09, 1.06 ± 0.04, and 1.23 ± 0.06 mg/m³·s, respectively. Based on the GUM propagation (JCGM 100:2008, 2008), including the expanded uncertainties of D_EFF (k = 2), the corresponding D_EFF values are calculated as 0.00020 ± 0.00007, 0.035 ± 0.007, 0.040 ± 0.010, and 0.054 ± 0.008 cm²/s, respectively, The results show that the EPS lid exhibits a very low, negligible decay rate, resulting in a concentration peak in the cold box exceeding 14,400 mg/mg³ (approximately 8000 ppm), representing the gas impermeable material options. On the other hand, Wall 00, Wall 01, and Wall 02 display significantly high CO₂ permeability that results in the concentration levels in the cold box below 2000 mg/m³ (approximately 1100 ppm) by the end of the 5-hour experiment. Comparing the results for the wall samples with drilled millimetric pores, namely Wall 01 and Wall 02, to the Wall 00 which has no perforation on its GFCGB layers, 2 mm perforation at 5 cm intervals increases the D_EFF value of the wall by 14% and the same perforation at 1 cm intervals increases it by 54%.

Figure 9.

CO₂ concentration decay results for Wall 00: Experiment 1 (left), Experiment 2 (middle), Experiment 3 (right): CO₂ concentration data inside the cold box (C_IN) and laboratory environment (C_OUT) measured and recorded by the indoor air quality measurement device (Testo 480).

Figure 10.

CO₂ concentration decay results for Wall 01: Experiment 1 (left), Experiment 2 (middle), Experiment 3 (right): CO₂ concentration data inside the cold box (C_IN) and laboratory environment (C_OUT) measured and recorded by the indoor air quality measurement device (Testo 480).

Figure 11.

CO₂ concentration decay results for Wall 02: Experiment 1 (left), Experiment 2 (middle), Experiment 3 (right): CO₂ concentration data inside the cold box (C_IN) and laboratory environment (C_OUT) measured and recorded by the indoor air quality measurement device (Testo 480).

Figures 12 –14 present the air temperatures inside the cold box and the laboratory environment, measured and recorded by using the Testo 480 indoor air quality measurement device, alongside the exterior surface temperatures of the Wall 00, Wall 01, and Wall 02 mockups, respectively, measured manually with a FLIR E60 thermal imaging device. Each figure illustrates the temperature profiles across the three experiments (left to right), enabling a comparative evaluation of the thermal performance of the different wall configurations under identical test conditions.

Figure 12.

Air temperatures inside the cold box and laboratory environment measured and recorded by the indoor air quality measurement device (Testo 480), along with the manually measured (using FLIR E60) exterior surface temperature of the Wall 00 mockup for Experiment 1 (left), Experiment 2 (center), and Experiment 3 (right).

Figure 13.

Air temperatures inside the cold box and laboratory environment measured and recorded by the indoor air quality measurement device (Testo 480), along with the manually measured (using FLIR E60) exterior surface temperature of the Wall 01 mockup for Experiment 1 (left), Experiment 2 (center), and Experiment 3 (right).

Figure 14.

Air temperatures inside the cold box and laboratory environment measured and recorded by the indoor air quality measurement device (Testo 480), along with the manually measured (using FLIR E60) exterior surface temperature of the Wall 02 mockup for Experiment 1 (left), Experiment 2 (center), and Experiment 3 (right).

The thermal transmittance (U-value) results for the different wall configurations and material samples are summarized in Table 3, together with the CO₂ permeability test results. Wall 00, consisting of unperforated GFCGBs and 100 mm glass wool insulation (two layers of 50 mm-thick exterior wall insulation panels), has a U_CALCULATED (theoretically calculated) value of 0.32 W/m²·K and the measured U-value of 0.32 ± 0.01 W/m²·K, indicating good agreement between the theoretical and experimental results. The measured U-values of all the tested mockups are in the range of 0.32–0.36 W/m²·K (Table 3). In addition to run-to-run standard deviations, expanded uncertainties of measured U values (k = 2) are 0.321 ± 0.151 W·m⁻²·K⁻¹ for Wall 00, 0.357 ± 0.307 W·m⁻²·K⁻¹ for Wall 01, and 0.328 ± 0.159 W·m⁻²·K⁻¹ for Wall 02. Therefore, within the present cold-box method, U-value differences among the perforation variants are not statistically distinguishable.

Table 3.

The data achieved by the cold box experimental setup: CO₂ decay rate, effective CO₂ diffusion coefficient (D_EFF ± repeatability), theoretically calculated U-value (U_CALCULATED) and the measured U-value (U_MEASURED ± repeatability).

Tested samples	Layer configuration	Thickness (mm)	D_EFF (cm²/s)	U_CALCULATED (W/m²·K)	U_MEASURED (W/m²·K)
EPS lid	10 mm EPS	10	0.00020 ± 0.00003	1.20	N/A
Glass wool	2 × 50 mm glass wool	100	N/A	0.33	N/A
Wall 00	12.5 mm GFCGB (no pores) + 2 × 50 mm glass wool + 12.5 mm GFCGB (no pores)	125	0.035 ± 0.003	0.32	0.32 ± 0.01
Wall 01	12.5 mm GFCGB (with 2 mm-pores at 5 cm intervals) + 2 × 50 mm Glass Wool + 12.5 mm GFCGB (with 2 mm-pores at 5 cm intervals)	125	0.040 ± 0.005	N/A	0.36 ± 0.02
Wall 02	12.5 mm GFCGB (with 2 mm-pores at 1 cm intervals) + 2 × 50 mm Glass Wool + 12.5 mm GFCGB (with 2 mm-pores at 1 cm intervals)	125	0.054 ± 0.003	N/A	0.33 ± 0.02

Considering that the millimetric perforations are limited to the 12.5 mm GFCGB lining layers and the dominant thermal resistance performance is dominantly governed by the 100 mm glass wool core. The calculated U-values using equation (4): Wall 00 (with unperforated lining layers) yields a U value of 0.317 W·m⁻²·K⁻¹, while the 100 mm glass-fiber insulation board alone (without the two GFCGB layers) yields 0.330 W·m⁻²·K⁻¹ (Table 3). As a result, only minor differences in steady-state U-value are expected among the perforation variants under the tested conditions. Across all experiments on EPS lid, Wall 00, Wall 01, and Wall 02, the measured mean ΔP remained in the range of 0.91 ± 0.06 to 1.05 ± 0.09 hPa. The overall average ΔP value of 1.00 ± 0.08 hPa, measured by the experiments, lies within the device accuracy (±3 hPa) and comparable to the inter-probe bias (0.80 ± 0.05 hPa). Therefore, no pressure difference could be confirmed beyond measurement uncertainty, and the experiments are treaded as near-isobaric conditions. Under these conditions, CO₂ transmission through the wall body is interpreted as diffusion-dominated, driven by the CO₂ concentration (partial-pressure) gradient, while acknowledging that a small residual advective component cannot be fully excluded without a dedicated airflow/leakage quantification.

Discussion

The experimental findings of this study provide a basis for evaluating the functional role of breathable wall assemblies in enhancing indoor air quality without compromising thermal insulation. This discussion interprets the results in the context of current building science literature, particularly the emerging perspective that solid wall components can serve as active regulators of air exchange. The implications for design practice, material performance, and future research directions are explored in the following sections.

Contribution of millimetric perforation to breathing wall design principles

The findings of this study offer new empirical validation for the conceptual shift, in which solid components of building envelopes are no longer regarded as passive barriers but as active elements contributing to environmental regulation (Karanfil and Tavukçuoğlu, 2023). Regarding the competing demands of energy efficiency and indoor air quality in building design, the proposed multi-layered breathing insulated exterior wall system has significant potential to be used as a design element to enhance indoor air quality.

Wall 01 and Wall 02, which have 2 mm perforations at 5 and 1 cm intervals respectively, show significant improvements in CO₂ permeability, 14% and 54% higher D_EFF values, respectively, compared to the unperforated Wall 00. In particular, the cold-box experiments demonstrate that increasing the pore frequency results in a significant increase in D_EFF, indicating that gas permeability is highly sensitive to the perforation patterns on the lining layers of a wall system. On the other hand, the GUM propagation results show that the expanded uncertainty of D_EFF (k = 2) is approximately ± 19% for Wall 00, ±26% for Wall 01, and ±14% for Wall 02. This level of uncertainty is relatively high and indicates that small differences in D_EFF, especially between Wall 00 and Wall 01, may not be reliably distinguishable within the measurement precision of the present setup. Therefore, D_EFF should be interpreted conservatively as an “apparent” effective coefficient under the tested boundary conditions.

For U_MEASURED values, the expanded uncertainties are dominated by the temperature terms, resulting in broad overlap among all tested wall mockups. Therefore, the measured U-value differences should be stated as “no detectable change within measurement uncertainty”. Although, the similarity of measured U-values between Wall 00 and Wall 02 is consistent with the contribution of the lining layers to total U value of the wall system: The thermal resistance is dominated by the 100 mm glass wool core, while the contribution of the two 12.5-mm GFCGB lining layers to the overall U value is only 4%. Because the perforations are limited only to the lining layers, their influence on steady-state conductive heat transfer is expected to be limited. In addition, from a geometric standpoint, drilling pores at 5 and 1 cm intervals is expected to increase the porosity of GFCGB by 0.1% and 2.7%, respectively. Within this context, the small decrease in measured U value from Wall 01 to Wall 02 may reflect this slight porosity increase in the lining material, although the magnitude of the difference remains comparable to the method’s variability, which can arise from local temperature non-uniformity and minor differences in boundary stability between experimental sessions. Finally, the uncertainty propagations quantify measurement and parameter uncertainty but do not bound any residual advective transport. Thus, D_EFF should be interpreted as an apparent effective coefficient measured under almost isobaric conditions, and any generalization to real-life building envelopes exposed to wind or stack pressures should be made cautiously.

The results reinforce the argument that “permeability” should not be viewed as a flaw, but rather as a potential functional attribute, provided it is carefully quantified and optimized for both gas and heat transfer performance. The observed performance trade-offs (higher diffusion at minimal thermal cost) support a redefinition of building envelope expectations in line with breathing wall principles.

The present findings under the tested conditions suggest that the tested millimetric perforation changes the U-value of the wall system only insignificantly. Notably, the measured U values (0.32–0.36 W·m⁻²·K⁻¹) do not exceed the recommended maximum U value (0.40 W·m⁻²·K⁻¹) for the walls in Mediterranean climate zones (Maduta et al., 2023). In colder climates, where lower U-values are targeted while promoting gas permeability, the same perforated lining concept can be adapted to various multi-layered compositions with increased insulation thickness.

Crucially, unlike previous studies that measured gas permeability in individual building materials, this study applies the D_EFF parameter to multi-layered wall systems, integrating industrially available materials such as GFCGB and glass wool. This marks an important shift from material-scale analysis to envelope-scale performance evaluation.

When compared to existing research on porous materials, the D_EFF values obtained in this study demonstrate a significantly higher rate of CO₂ diffusion. For example, the D_EFF values of adobe and autoclaved aerated concrete samples had been reported as in the range of 0.012–0.0138 cm²/s (Karanfil and Tavukçuoğlu, 2023). Similarly, values for gypsum board, porous fiberboard, and highly-porous limestone range from 0.014 to 0.034 cm²/s (Namoulniara et al., 2016; Niemelä et al., 2017). On the other hand, the multi-layered wall systems tested here achieve D_EFF values ranging from 0.035 cm²/s for the unperforated Wall 00 to 0.054 cm²/s for the most permeable configuration, Wall 02. The D_EFF values of these wall systems tested in this study do not only fall within but also exceed the upper bounds reported in the literature for single-material considerations. The higher CO₂ permeability signals the effectiveness of breathing envelope systems with perforation in enhancing envelope-scale gas permeability. This expands the range of design possibilities for passive indoor air quality regulation and supports the viability of breathing building envelope systems as an IAQ design element in architectural practice.

Practical and technological implications

The proposed perforated GFCGB strategy presents a low-tech and scalable solution with the potential to reduce reliance on mechanical ventilation systems, especially in resource-constrained or post-pandemic design contexts. By promoting CO₂ diffusion across the wall section, the system contributes to improved IAQ without inducing airflow, preserving occupant comfort and wellbeing. Additionally, the use of industrially available materials such as GFCGB and glass wool enhances the constructability and adaptability of the system.

Importantly, the experimental design in this study applies the D_EFF parameter in multi-layered wall systems for the first time. This contributes to a broader framework in which thermal and diffusive behaviors are jointly considered in building envelope evaluations.

These findings signal the need to re-evaluate conventional design paradigms and consider the role of permeability as a strategic choice in envelope design. A building envelope can be designed in many different ways. One approach may prioritize an airtight enclosure to protect people from polluted outdoor air, whereas another approach may support a breathing facade to use clean air for passive self-ventilation. In both cases, the effective CO₂ diffusion coefficient of wall systems, measured in this study, plays a key role. This parameter deserves to be a research interest in future scientific research to guide informed decision-making across diverse architectural strategies.

Future research directions

The results pave the way for further computational and field studies to optimize these systems for real-world applications and diverse climatic conditions. Building on the promising outcomes of the laboratory-scale experiments, future work should focus on extending this research into advanced simulation-based investigations. In particular, computational fluid dynamics (CFD) modeling can enable the assessment of the breathing wall system under diverse environmental and architectural conditions. These simulations will provide deeper insight into the system’s self-ventilation behavior and thermal performance across a range of building geometries and climates. In addition, the D_EFF values obtained in this study can serve as empirical inputs for multi-scale modeling approaches. For instance, they can be used to calibrate pore-network models that simulate gas transport through complex porous geometries, or to define boundary conditions in CFD simulations that assess coupled heat and mass transfer across wall assemblies. Integrating these experimentally derived D_EFF values into simulation tools would enable more accurate prediction of performance across varying geometries, materials, and environmental conditions, thereby enhancing the scalability and generalizability of breathing envelope design strategies.

Moreover, the integration of simulation outputs into a decision-support tool is recommended. Such a tool could assist architects and engineers by suggesting optimal wall configurations tailored to specific indoor air quality requirements, user comfort needs, and spatial constraints. This would substantially enhance the practical application of the proposed breathing building envelope system and promote its adoption in the design of healthier, energy-conscious, and climate-responsive buildings.

Conclusion

This study proposed a novel multi-layered, breathing, and insulated wall system designed to improve indoor air quality through passive ventilation, and it assessed its performance. By integrating millimetric perforations into the lining layers of a porous wall structure, the system enables enhanced CO₂ diffusion while maintaining thermal resistance. The research applies new parameters and suggests methods for assessing the permeability of opaque building envelope components, offering a pathway to more sustainable, health-conscious, and thermally efficient building designs. To summarize, this study:

- Introduced a practical cold box experimental setup that measures both the effective CO₂ diffusion coefficient (D_EFF) and thermal transmittance (U-value) of multi-layered wall systems.

- Generated reference data for D_EFF values of wall systems with varying perforation densities, creating a foundation for future modeling and simulation.

- Demonstrated that 2 mm millimetric perforations on GFCGB layers significantly improve CO₂ permeability (by up to 54%) without compromising thermal performance.

- Validated the concept of breathing yet insulated envelopes, showing that vapor and gas diffusion can occur passively through solid walls designed with intended gas permeability.

- Established D_EFF as a critical design parameter for evaluating and comparing wall systems, whether the design objective is an airtight or a breathing envelope.

- Inspires applications of perforation-based diffusion enhancement in product design, simulation methods, performance assessment protocols, and material innovation.

As a result, this research reveals the potential of millimetric perforation designs within insulated breathing wall systems as a low-tech yet effective solution to the dual challenge of indoor air quality and energy efficiency, contributing a paradigm shift in how solid building envelope components are conceived, modeled, and applied in architectural practice.

Footnotes

Appendix

Appendix 2.

Uncertainty sources considered in the measured U-value calculation, their classification, and rationale.

Uncertainty source	Symbol	Type (A/B)	How it was quantified in this study
Repeatability of U measurements	from U_run to U_final (final reported value)	Type A	Standard deviation of U-values obtained from three repeated runs per wall mockup (n = 3), representing experimental repeatability under nominally identical conditions.
Surface emissivity	ε	Type B	Manufacturer datasheet uncertainty for emissivity. Treated as a standard uncertainty assuming a rectangular distribution and propagated via:
Surface emissivity	ε	Type B	$c_{ε} = \frac{\partial U}{\partial ε}$
Air velocity near surface	v	Type B	Instrument accuracy from anemometer datasheet. Converted to standard uncertainty and propagated via:
Air velocity near surface	v	Type B	$c_{v} = \frac{\partial U}{\partial v}$
Surface temperature	T _SO	Type B	Infrared camera temperature resolution (±0.1°C). Converted to standard uncertainty and propagated analytically via: $c_{T_{SO}} = \frac{\partial U}{\partial T_{SO}}$
Air temperature inside the cold box	T _IN	Type B	Testo 480 temperature accuracy (±0.3°C). Treated as standard uncertainty and propagated via the sensitivity coefficient: $c_{T_{IN}} = \frac{\partial U}{\partial T_{IN}}$
Laboratory air temperature outside the cold box	T_OUT in numerator and denominator	Type B	Testo 480 temperature accuracy (±0.3°C). Affects both numerator and denominator; propagated using the sensitivity coefficient: $c_{T_{OUT}} = \frac{\partial U}{\partial T_{OUT}}$
Well-mixed air assumption	Conceptual (affecting temperatures)	Not assigned	Assumed valid due to continuous fan operation. Any residual non-uniformity is reflected indirectly in run-to-run repeatability (Type A), not propagated as a separate uncertainty term.
Possible weak air movement through perforations	Conceptual (affecting interpretation)	Not assigned	Addressed qualitatively through pressure monitoring and cautious interpretation of results. Not treated as a quantitative uncertainty term in GUM propagation.

Acknowledgements

Authors would like to thank Fatih Ulutaş for providing gypsum board and glass wool samples, Murat Sayın for technical support, Mert Karanfil for coding support. The authors received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Başak Yüncü Karanfil

Ayşe Duman

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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