A Comparative Evaluation of the Thermal Performance of Passive Facades with Variable Cavity Widths for Near-Zero Energy Buildings (nZEB): A Modeling Study

Abstract

In the current context of the transition toward climate neutrality and the pressing need to reduce energy consumption in the construction sector, nZEBs have become a central benchmark in European sustainability policies. These buildings offer multiple benefits, such as reduced operational costs, enhanced thermal comfort, and improved indoor air quality. Achieving such performance requires the integration of advanced technological solutions, including passive façades with ventilated cavities. The primary objective of this study is to investigate the influence of cavity geometry on the thermal behavior of a passive façade, through numerical simulations conducted in ANSYS Fluent 17. The study focuses on comparing five distinct configurations with varying cavity widths, aiming to identify the optimal solution in terms of heat transfer efficiency. The main contribution lies in the analysis and correlation of air temperature and velocity distributions with the cavity’s geometric parameters, highlighting the impact of channel width on thermal performance. The configuration with a 12 cm wide air channel recorded the highest heat flux at the outlet, approximately 44 times greater than the façade with a 4 cm wide channel, making it the most efficient solution. The results indicate significantly higher thermal efficiency for the configuration with a larger cavity width, contrary to initial intuitive assumptions. These insights provide a valuable framework for the optimal design of passive façades in nZEB applications and highlight the need for further research, combining numerical and experimental approaches, to develop sustainable and energy-efficient building envelope solutions.

1. Introduction

Sustainable development is a concept of balanced and responsible growth, capable of addressing global challenges such as climate change, poverty, rapid urbanization, and resource depletion, while simultaneously promoting the development of solutions tailored to human well-being and the stimulation of economic competitiveness [1]. Paradoxically, although the current level of knowledge regarding the impact of human activities on the environment is unprecedented, the pace of ecological degradation continues to accelerate. Despite the fact that science provides viable solutions for the development of sustainable societies, the implementation of a sustainable economic model is progressing slowly and unevenly, thus compromising the progress needed to ensure the well-being of future generations [2]. In recent decades, the energy sector has faced a series of major challenges regarding supply security. Growing concerns about the effects of climate change have highlighted considerable interest in implementing sustainable energy development solutions [3]. The current global context, marked by accelerated climate change and the depletion of natural resources, underscores the critical importance of scientific research in shaping sustainable solutions. The European Union’s commitments to ensuring energy security and reducing greenhouse gas emissions require a comprehensive approach that integrates economic, social, environmental, and technological dimensions. Within this framework, interdisciplinary research plays a decisive role in generating innovative solutions and laying the foundation for a sustainable trajectory for Europe’s future [4]. One of the most significant challenges facing Europe is the high energy consumption associated with the construction sector. In 2024, this sector—including both new constructions and existing buildings—accounted for approximately 40% of global energy demand and was responsible for 36% of global carbon dioxide emissions resulting from energy use [5]. Although the European Union, through Directive 2018/844/EU, has promoted the adoption of measures to support the transformation of existing buildings into nZEBs [6], there is currently no clear regulation mandating that all residential renovation works comply with the specific requirements of nZEB standards [7]. The EU’s most recent initiative on energy efficiency [8] requires Member States to develop a comprehensive report on buildings that do not meet nZEB standards and to implement concrete measures aimed at improving their energy performance [9]. The significance of this measure is highlighted by the fact that approximately 75% of buildings in the EU have low energy efficiency, that the global urban population is projected to rise to 68% by 2050, and that current renovation rates are insufficient to keep pace with these developments [10]. In this context, reducing energy consumption in the construction sector becomes a strategic priority, significantly contributing to environmental protection, the responsible management of resources, and the reduction of energy and housing costs [11].

To ensure high energy efficiency and a reduced environmental impact, the measures implemented must be aligned with each stage of the building’s life cycle—from design and construction to use and post-use phases [12]. In the process of selecting and applying the most effective solutions for enhancing energy performance and reducing environmental impact, specific methods are employed for each life-cycle stage of the building. During the design phase, the focus is placed on the use of predictive models and detailed analyses to integrate sustainable technologies, whereas in the operational phase, the strategies adopted aim to monitor consumption, by continuously optimizing energy efficiency, and adjusting to actual operating conditions [13]. In general, the designer conducts a building model simulation to assess various design options and technical solutions. This analysis is aligned with the client’s requirements and expectations, taking into account factors such as budget, energy performance, architectural appearance, and other individual preferences [14]. Maintaining a high-quality indoor environment without exceeding a reasonable budget has always been a major challenge for the construction sector. In the current context—marked by increasingly stringent regulations—clients are more frequently requesting the integration of nZEB certification requirements into building projects [15]. At the same time, access to innovative materials and technologies opens new possibilities for implementation [16]. However, this challenge leads to heightened demands regarding the level of knowledge, expertise, and practical skills required of the engineers in the field.

The passive façade has become a benchmark element in contemporary building architecture due to its multiple functional and aesthetic benefits. Beyond its modern and attractive design, this system significantly contributes to improving the thermal and visual comfort of occupants, while offering lower energy consumption compared to traditional glazing solutions. As such, it represents an effective solution for implementing energy efficiency strategies in nZEBs. The efficiency of the façade largely depends on its design geometry, as well as its thermal, physical, and optical properties, and the aerodynamic behavior of the system as a whole.

The main contributions and innovative elements of this study can be summarized as follows: detailing the stages involved in the numerical modeling of a passive façade; the configuration process of a passive façade model in ANSYS Fluent 17 (a CFD computational fluid dynamics software program); and a systematic comparative analysis of the impact of cavity width variation on temperature distribution and velocity profiles. These aspects represent a significant contribution to the understanding of complex mechanisms within passive façades. The study suggests that a wider cavity leads to superior energy efficiency. This finding—supported by the analysis of maximum temperatures reached and the potentially higher airflow—constitutes an innovative contribution that opens new directions in the design of passive façades, making it a recommended solution for nZEBs.

The paper is structured as follows: Section 2 provides a review of the literature relevant to the research topic; Section 3 details the comparative study that analyzes five distinct configurations characterized by varying passive façade cavity widths, and presents the results obtained. Section 4 includes discussion of the results and a comparative analysis of temperature and velocity graphs, while Section 5 presents the main conclusions of the study.

2. Literature Review

Recent research has demonstrated that individuals residing in naturally ventilated buildings possess superior thermal self-regulation compared to those in air-conditioned environments [17], indicating a heightened adaptability to fluctuating environmental conditions. The findings emphasize the influence of physiological acclimatization when accounting for the variations in thermal comfort between the two groups. Among the methods for facilitating natural ventilation, manually opening windows remains the most accessible and widely used approach. One study explored the impact of passive façade geometry optimization on enhancing natural ventilation and indoor air quality in office settings [18]. By employing simulation tools, the study compared passive and conventional façade systems under the climatic conditions of Amman, Jordan. The findings revealed improvements in indoor air quality, pinpointed areas with reduced airflow, and identified zones of elevated turbulence, thereby informing more effective space usage. Another investigation evaluated the effectiveness of passive façade control mechanisms concerning annual energy consumption reductions [19]. Hybrid systems have been identified as the most effective solution for achieving considerable energy reductions, whereas passive systems offer an optimal compromise between performance and cost. In contexts demanding elevated thermal comfort or where they are subject to considerable climatic fluctuations, automated systems are preferable. The suitability of each system is climate-dependent: passive strategies are more effective in tropical climates, while hybrid configurations perform better in subtropical and temperate regions. Recent investigations have emphasized the advantages of combining passive façades with HVAC systems [20], particularly when integrated into the building’s southern elevation and linked to the air handling unit (AHU) to supply air preheated within the façade cavity. Research has shown that placing passive façades at a distance from the ventilation unit, in conjunction with air extraction systems, enhances indoor air circulation, ensuring a more uniform distribution of fresh air.

An experimental analysis [21] evaluating natural versus mechanical ventilation in a passive façade demonstrated that mechanical systems increase airflow and lower internal heat gains by 18.77%. However, the added energy demand of fans, typically 10–15 W, somewhat offsets these gains. To address this, an optimization framework comprising four strategies was introduced to better balance mechanical ventilation and energy use. Modifying the cavity depth yielded a 4–7% enhancement in energy efficiency. These findings underline the capacity of mechanical ventilation to limit thermal loads while proposing practical measures to optimize overall energy performance.

This study focuses on enhancing the energy efficiency of heritage buildings by employing passive façades, with an assessment of heating and cooling loads under Mediterranean and temperate oceanic climate conditions [22]. Various glass façade configurations were examined, demonstrating that the low-emissivity passive (double-layer) façade offers the highest efficiency in winter, while the reflective passive façade performs optimally during summer, achieving energy savings of up to 26.70 kWhT/m² and 4.70 kWhT/m², respectively. Natural ventilation proves beneficial only when paired with a compatible façade type; combining reflective passive façades with appropriate ventilation strategies can result in additional savings of up to 7.20 kWhT/m². In warmer regions, passive façades incorporating photovoltaic elements present a promising alternative.

Further analysis [23] explores passive façade systems from energy, exergy, exergoeconomic, and enviroeconomic standpoints, addressing system performance, payback periods, economic viability, and environmental implications. The findings underscore the interdependence between façade geometry, thermal and airflow dynamics, and system efficiency. Key design aspects—such as shading elements and glazing optical properties—play a critical role in governing heat transfer and ventilation effectiveness. Additionally, the interaction between cavity depth and airflow rate significantly influences overall system performance. In another study [24], a two-dimensional numerical model of an innovative passive façade configuration was developed. This model incorporates an optical thin-film material composed of tungsten-doped vanadium dioxide (VO₂) and an aluminum nitride (AlN) layer, selected for its high thermal absorption capacity.

A parametric study on air cavity thickness revealed a notable decrease in thermal loads during both winter and summer periods. The analysis also indicated a marked enhancement in indoor thermal comfort, with seasonal fluctuations in interior surface temperatures. A detailed investigation into the combined effects of natural convection and radiation within the cavity highlighted their substantial impact on system efficiency. In this study [25], the passive façade concept is advanced by incorporating an adaptive external layer featuring a rectilinear kirigami-inspired cut. This section can be selectively actuated to open the façade for ventilation while simultaneously reorienting the outer surface to follow the sun’s trajectory. The research aims to evaluate the potential advantages of integrating this approach into building façades. Findings demonstrated improved solar energy absorption, increased ventilation efficiency, and better indoor temperature regulation.

The research presented in [26] integrates a building energy simulation tool with a computational fluid dynamics (CFD) package to examine the thermal performance of a passive façade equipped with a solar-exposed shading device. The findings reveal that air temperature within the façade cavity increases almost linearly towards the upper section, with elevated temperatures near the shading element. Another investigation [27] involves a comparative analysis between experimental data and numerical simulations conducted in ANSYS Fluent 17, focusing on a passive façade. Optimization strategies are proposed based on temperature and airflow distribution. The study identified the presence of natural free convection and recirculation zones in the experimental model and validated the chimney effect through temperature profiles obtained from both experimental and simulated data. Additionally, a two-dimensional numerical analysis of a passive façade considering both mechanical and natural ventilation was conducted using the finite volume method [28]. The study highlights the complexity in accurately determining the heat transfer coefficient and notes that numerical outcomes are highly dependent on input parameter accuracy, the value of the convective heat transfer coefficient, and numerical approximation errors. A separate two-dimensional numerical investigation [29] explored natural convection heat transfer within a tall cavity, examining both laminar and turbulent regimes using the k-ε turbulence model. The study found that for turbulent convection, the Nusselt number rises with increasing aspect ratio, whereas in laminar flow, it declines as the aspect ratio becomes larger. In another study [30], researchers applied the zonal energy equation to simulate heat flux and temperature distribution across a passive façade. The findings confirmed that the zonal method is a practical tool for assessing façade performance, offering quick results with minimal computational effort. Concerning airflow velocity measurements in ventilated passive façades, one study [31] evaluated three conventional techniques. These included pressure-based methods at façade openings, anemometric measurements, and airflow visualization using tracer gas injection.

Several case studies have explored the benefits of passive façades in improving building energy efficiency. A selection of such studies is summarized below. In Malaysia’s tropical climate [32], east–west facing façades experience significant solar exposure, often causing overheating in rooms adjacent to glazed areas. Passive façades offer an effective approach to mitigate solar heat gains in these conditions. The findings highlight that such systems are essential in managing thermal accumulation, driven by indoor–outdoor temperature gradients and surface temperature fluctuations. Another case study conducted in Iran’s hot climate [33] compared experimental data with numerical simulations for a passive façade. The model was validated through a strong agreement between measured and simulated values. In terms of energy performance, thermographic analysis revealed energy savings between 0.27 and 0.42 kWh/m²/day, resulting from a decrease in intake air temperature for the air conditioning system to 277.15–279.15 K. In a separate study on an eight-story laboratory building featuring a passive façade in Basel [34], the system’s behavior was assessed throughout a typical summer day using CFD simulations. Measurements of surface temperatures and heat gains, including thermal loads on sensitive components, were taken. The results indicated that in warm climates with high solar radiation, passive façades using natural ventilation may be unsuitable, as structural components can overheat, potentially damaging interior elements such as shading systems. For older residential buildings exhibiting poor thermal performance in Mediterranean climates [35], enhancing thermal insulation has been demonstrated to be a more effective strategy than implementing passive façades, both in terms of reducing energy consumption and improving thermal comfort. These findings highlight the importance of tailoring renovation approaches to the unique characteristics of each building, emphasizing interventions that maximize energy efficiency and occupant comfort. A study conducted by one research group [36] performed a sensitivity analysis to assess the impact of different design aspects of glazing and shading systems on energy efficiency and indoor thermal comfort in an office building with a passive façade in Amritsar, India. The purpose of this investigation was to pinpoint the key parameters influencing building performance within the region’s climatic conditions, thereby aiding in the refinement of passive design strategies. Additionally, another study [37] explored the effects of window-to-wall ratio, glazing type, building orientation relative to solar path, and shading element placement on cooling loads and indoor thermal comfort during summer in a building situated in Taiwan. This research emphasizes the necessity of an integrated façade design approach that incorporates both orientation and shading system considerations to optimize energy performance in warm, humid climates.

The incorporation of photovoltaic (PV) panels into building façades represents a novel approach for improving energy efficiency and decreasing dependence on external energy supplies [38]. In rapidly expanding urban settings, where high-rise buildings often face constraints on rooftop areas, building-integrated photovoltaics (BIPV) have emerged as a preferred solution for on-site energy generation. PV-integrated façades not only produce electricity from renewable sources but also enhance insulation, daylight control, and visual appeal—key factors in densely populated urban environments [39]. A prominent method includes the deployment of semi-transparent photovoltaic (STPV) modules within passive façades. Research indicates [40] that STPV systems can modulate solar heat gain by permitting natural light penetration while simultaneously generating power. This approach mitigates cooling loads in summer and heating requirements in winter, proving effective across diverse climatic zones. Additionally, studies highlight that combining PV modules with dynamic elements, such as adjustable louvers, allows façades to respond to changing solar angles, thereby improving energy output and lowering cooling demands.

Advancements in the field have progressed beyond solely passive solutions, shifting focus towards innovative adaptive façade systems [41]. These systems possess the capability to modify their state in response to changes in external environmental conditions and internal comfort demands, with the goal of improving building energy efficiency. In contrast to conventional static façades, these adaptive systems dynamically regulate features such as shading, transparency, and thermal insulation in real time to optimize indoor environments, manage daylight, and reduce energy use. A prominent example is the Al Bahr Towers in Abu Dhabi [42], widely recognized as a pioneering case of adaptive façades. Drawing inspiration from the traditional Mashrabiya design, this intelligent façade employs meteorological data and sensor inputs to automatically adjust its panels, thereby delivering dynamic shading that enhances both visual and thermal comfort indoors.

The studies cited illustrate an increasing recent focus on passive façades and beyond, where numerical modeling using various simulation tools has become essential for optimizing energy performance. However, there remains a persistent need for more comprehensive understanding to support the effective design and management of these systems.

3. Methodology

3.1. The Physico-Mathematical Modeling of Heat Transfer

The physical model describing natural convection flow combined with radiation within a cavity encompasses the transport equations for mass, momentum, energy [43], and radiative transfer [44] (Equations (1)–(6)), which are solved numerically via the finite volume method [45]. The simulations are conducted for a three-dimensional, steady, and turbulent flow regime. The thermo-physical properties of the fluid are considered temperature-dependent, as the Boussinesq approximation is not applicable within the temperature range investigated [46].

The governing equations are as follows:

Continuity equation:

$${\displaystyle \frac{\partial \rho u}{\partial x}}+{\displaystyle \frac{\partial \rho v}{\partial y}}+{\displaystyle \frac{\partial \rho w}{\partial z}}=0$$

(1)

Momentum equations:

$$\begin{gathered} \overline{u}{\displaystyle \frac{\partial \rho \overline{u}}{\partial x}}+\overline{v}{\displaystyle \frac{\partial \rho \overline{u}}{\partial y}}+\overline{w}{\displaystyle \frac{\partial \rho \overline{u}}{\partial z}}=-{\displaystyle \frac{\partial \overline{P^{\mathrm{*}}}}{\partial x}}+{\displaystyle \frac{\partial }{\partial x}}\left(\mu {\displaystyle \frac{\partial \overline{u}}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(\mu {\displaystyle \frac{\partial \overline{u}}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(\mu {\displaystyle \frac{\partial \overline{u}}{\partial z}}\right)+{\displaystyle \frac{\partial \overline{u}}{\partial x}}{\displaystyle \frac{\partial \mu }{\partial x}}+ \\ {\displaystyle \frac{\partial \overline{v}}{\partial x}}{\displaystyle \frac{\partial \mu }{\partial y}}+{\displaystyle \frac{\partial \overline{w}}{\partial x}}{\displaystyle \frac{\partial \mu }{\partial z}}-{\displaystyle \frac{\partial \rho \overline{u^{\prime }}\overline{u^{\prime }}}{\partial x}}-{\displaystyle \frac{\partial \rho \overline{u^{\prime }}\overline{v^{\prime }}}{\partial y}}-{\displaystyle \frac{\partial \rho \overline{u^{\prime }}\overline{w^{\prime }}}{\partial z}} \end{gathered}$$

(2)

$$\begin{gathered} \overline{u}{\displaystyle \frac{\partial \rho \overline{v}}{\partial x}}+\overline{v}{\displaystyle \frac{\partial \rho \overline{v}}{\partial y}}+\overline{w}{\displaystyle \frac{\partial \rho \overline{v}}{\partial z}}=-{\displaystyle \frac{\partial \overline{P^{\mathrm{*}}}}{\partial y}}+{\displaystyle \frac{\partial }{\partial x}}\left(\mu {\displaystyle \frac{\partial \overline{v}}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(\mu {\displaystyle \frac{\partial \overline{v}}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(\mu {\displaystyle \frac{\partial \overline{v}}{\partial z}}\right)+{\displaystyle \frac{\partial \overline{u}}{\partial y}}{\displaystyle \frac{\partial \mu }{\partial x}}+ \\ {\displaystyle \frac{\partial \overline{v}}{\partial y}}{\displaystyle \frac{\partial \mu }{\partial y}}+{\displaystyle \frac{\partial \overline{w}}{\partial y}}{\displaystyle \frac{\partial \mu }{\partial z}}-{\displaystyle \frac{\partial \rho \overline{v^{\prime }}\overline{u^{\prime }}}{\partial x}}-{\displaystyle \frac{\partial \rho \overline{v^{\prime }}\overline{v^{\prime }}}{\partial y}}-{\displaystyle \frac{\partial \rho \overline{v^{\prime }}\overline{w^{\prime }}}{\partial z}} \end{gathered}$$

(3)

$$\begin{gathered} \overline{u}{\displaystyle \frac{\partial \rho \overline{w}}{\partial x}}+\overline{v}{\displaystyle \frac{\partial \rho \overline{w}}{\partial y}}+\overline{w}{\displaystyle \frac{\partial \rho \overline{w}}{\partial z}}=-{\displaystyle \frac{\partial \overline{P^{\mathrm{*}}}}{\partial z}}+{\displaystyle \frac{\partial }{\partial x}}\left(\mu {\displaystyle \frac{\partial \overline{w}}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(\mu {\displaystyle \frac{\partial \overline{w}}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(\mu {\displaystyle \frac{\partial \overline{w}}{\partial z}}\right)+{\displaystyle \frac{\partial \overline{u}}{\partial z}}{\displaystyle \frac{\partial \mu }{\partial x}}+ \\ {\displaystyle \frac{\partial \overline{v}}{\partial z}}{\displaystyle \frac{\partial \mu }{\partial y}}+{\displaystyle \frac{\partial \overline{w}}{\partial z}}{\displaystyle \frac{\partial \mu }{\partial z}}-{\displaystyle \frac{\partial \rho \overline{w^{\prime }}\overline{u^{\prime }}}{\partial x}}-{\displaystyle \frac{\partial \rho \overline{w^{\prime }}\overline{v^{\prime }}}{\partial y}}-{\displaystyle \frac{\partial \rho \overline{w^{\prime }}\overline{w^{\prime }}}{\partial z}} \end{gathered}$$

(4)

Energy equation [43]:

$$\overline{u}{\displaystyle \frac{\partial \rho C_p\overline{T}}{\partial x}}+\overline{v}{\displaystyle \frac{\partial \rho C_p\overline{T}}{\partial y}}+\overline{w}{\displaystyle \frac{\partial \rho C_p\overline{T}}{\partial z}}={\displaystyle \frac{\partial }{\partial x}}\left(k{\displaystyle \frac{\partial \overline{T}}{\partial x}}\right)+{\displaystyle \frac{\partial }{\partial y}}\left(k{\displaystyle \frac{\partial \overline{T}}{\partial y}}\right)+{\displaystyle \frac{\partial }{\partial z}}\left(k{\displaystyle \frac{\partial \overline{T}}{\partial z}}\right)$$

(5)

The radiative transfer equation [44] for an absorbing and scattering medium emissivity at a position $\overrightarrow{r}$ in the direction $\overrightarrow{s}$ is as follows:

$${\displaystyle \frac{dI\left(\overrightarrow{r},\overrightarrow{s}\right)}{ds}}+\left(a+\sigma \right)I\left(\overrightarrow{r},\overrightarrow{s}\right)=a{n}^2{\displaystyle \frac{\varsigma T^4}{\pi }}+{\displaystyle \frac{\sigma }{4\pi }}{\int }_0^{4\pi }I\left(\overrightarrow{r},{\overrightarrow{s}}^{\prime }\right)\Phi \left(\overrightarrow{s}{,\overrightarrow{s}}^{\prime }\right)d\Omega$$

(6)

The boundary conditions are as follows:

• Carry out a simulation of natural convection;
• The fluid flow is characterized by turbulence;
• The geometric parameters of the façade: 1.90 × 1.40 × 0.12 m;
• The effective diameter of the model’s fluid conduit: 0.221 m;
• The convective heat transfer coefficient: 8 W/m²·K;
• The emissivity of the glass’s interior surface: 0.89;
• The intensity of radiant energy flow: 60.9 W/m²;
• The temperature of the air at the entrance: 255.15 K.

The dynamic boundary layer is characterized as the zone in which the fluid velocity transitions from zero at the body’s surface to the free-stream velocity beyond which the body’s influence is negligible. The boundary layer thickness, δ, is defined as the distance y from the body’s surface where the fluid velocity reaches 0.99 of the free-stream velocity, uf.

The velocity profile within the boundary layer—representing the change in velocity tangent to the surface as a function of distance from the surface—u (y) enables the determination of the unit tangential shear stress at the surface of a body moving relative to a fluid:

$${\tau }_s\left(x\right)=\eta {\displaystyle \frac{\delta u(x,y)}{\delta y}}\left[\mathrm{N}/{\mathrm{m}}^2\right]$$

(7)

In the turbulent regime of the dynamic boundary layer, particle motion becomes irregular, characterized by three-dimensional velocity fluctuations. These turbulences enhance fluid mixing, resulting in a thicker boundary layer and more uniform velocity profiles compared to laminar flow. The emergence of velocity fluctuations and the organized structure of turbulent vortices signify the transition to turbulent flow, accompanied by a notable increase in boundary layer thickness. Enhanced mixing improves thermal (or mass) energy transfer, as convection coefficients attain higher values under turbulent conditions.

Regarding heat transfer between a fluid and a solid surface, the majority of temperature changes occur within a very thin region adjacent to the surface. Consider a fluid at temperature t_f flowing over a plate at temperature t_s. Fluid particles in direct contact with the surface reach thermal equilibrium, adopting the surface temperature. These particles then transfer energy to neighboring particles in the subsequent layer, which continue the process, establishing a thermal gradient within the fluid. This region where the temperature gradient develops is known as the thermal boundary layer. Its thickness is defined as the distance y from the surface at which 99% of the total temperature difference is observed.

The unit thermal flux q_s transferred at the contact surface can be expressed by Fourier’s law, as a function of the thermal conductivity λ_f and the temperature gradient at the surface (y = 0).

$$q_s\left(x\right)=-{\lambda }_f{\displaystyle \frac{\delta t(x,y)}{\delta y}}\left[\mathrm{W}/{\mathrm{m}}^2\right]$$

(8)

Beyond the conductive boundary layer adjacent to the surface, heat transfer within the fluid occurs through both conduction and predominantly by convective transport due to the fluid’s bulk motion. Therefore, the local convective heat transfer coefficient, α, can be expressed as:

$$\alpha \left(x\right)={\displaystyle \frac{q_s\left(x\right)}{t_s\left(x\right)-t_f}}=-{\lambda }_f{\displaystyle \frac{\delta t\left(x,y\right)}{\delta y}}*{\displaystyle \frac{1}{t_s\left(x\right)-t_f}}\left[\mathrm{W}/{\mathrm{m}}^2\right]$$

(9)

One of the earliest efforts addressing the laminar case through an integral approach for Pr > 0,6, proposing that the ratio of thermal to velocity boundary layer thickness, ∆, depends solely on the Prandtl number, was presented by [47]. The derived results demonstrated strong agreement with both experimental findings [48] and numerical solutions obtained via the similarity method [49]. Given the lack of literature on the simultaneous development of viscous and thermal layers, the current theory is formulated under the simplifying assumption that these laminar outcomes can be reasonably extended to turbulent flow conditions as follows:

$$∆\left(Pr\right)={\displaystyle \frac{{\partial }_{t\left(x\right)}}{{\partial }_{\left(x\right)}}}$$

(10)

The values of the ∆ ratio for different Prandtl numbers cover the physical situation where ∂_(x) > ∂_t(x), which correspond to common fluids such as Pr > 0.636. Therefore, using assumption (10), the integral forms of the energy and motion equations in the boundary layer are as described in [50].

The local Nusselt number ${Nu}_x$ is defined by

$${Nu}_x={\displaystyle \frac{{\phi }_{w}x}{{\theta }_w\lambda }}$$

(11)

Introducing ${\Pi }_{\Delta }$ as a function of the ∆ boundary layer ratio

$${\Pi }_{\Delta }={\Delta }^{{\displaystyle \frac{8}{7}}}\left({\displaystyle \frac{7}{72}}-{\displaystyle \frac{7}{60}}\Delta +{\displaystyle \frac{21}{253}}{\Delta }^2-{\displaystyle \frac{14}{435}}{\Delta }^3+{\displaystyle \frac{7}{1332}}{\Delta }^4\right)$$

(12)

both the dynamical boundary layer and the Nusselt number result from the Prandtl number (Δ is only Pr dependent) and are expressed by

$${\displaystyle \frac{\delta }{x}}=0.0448{\left({Ra}_x^{*}\right)}^{-{\displaystyle \frac{1}{14}}}{\left[{\displaystyle \frac{{Pr}^{-\frac{16}{3}}}{∆{\left({\Pi }_{∆}\right)}^{10}}}\left(1+{\displaystyle \frac{0.0823}{({\Pi }_{∆}){Pr}^{\frac{10}{15}}}}\right)\right]}^{{\displaystyle \frac{1}{14}}}$$

(13)

$${Nu}_x=0.0631{\left({Ra}_x^{*}\right)}^{{\displaystyle \frac{2}{7}}}{\left[{\displaystyle \frac{{\Pi }_{∆}^{\frac{1}{2}}{Pr}^{\frac{1}{2}}}{∆}}\left(1+{\displaystyle \frac{0.0823}{({\Pi }_{∆}){Pr}^{\frac{10}{15}}}}\right)\right]}^{-{\displaystyle \frac{2}{7}}}$$

(14)

${Ra}_x^{*}$ is the local modified Rayleigh number defined by

$${Ra}_x^{*}={\displaystyle \frac{g\beta {\phi }_u{x}^4}{\lambda v^2}}Pr.$$

(15)

3.2. Overview of the ANSYS

The simulation of physical processes using specialized commercial software constitutes an advanced scientific method employed to analyze fluid flow, heat and mass transfer, as well as other related phenomena, through the numerical solution of fundamental equations. This technique provides essential support throughout the entire lifecycle of a building, from the initial conceptual design to the detailed engineering of structural elements and up to the identification and resolution of potential operational issues. Moreover, numerical simulation complements traditional experimental methods, significantly contributing to the reduction in time, effort, and costs required for testing and obtaining experimental data.

Addressing a problem within the field of fluid mechanics involves essential steps: defining the mathematical model, selecting an appropriate numerical method, developing the computational algorithm, and verifying the accuracy of the obtained results. Thermal analysis plays a crucial role in this process, as it enables the determination of temperature distribution and key thermal parameters such as heat loss, temperature variations, and heat fluxes [27]. In the context of increasing demands for building energy efficiency, there is a growing use of specialized software for thermal system modeling and computational fluid dynamics (CFD) analysis. These tools provide detailed, essential information during the design phase, contributing to the optimization of building energy performance.

The simulation methodology in ANSYS Fluent 17 is based on solving conservation differential equations, complemented by semi-empirical models addressing aspects such as turbulence, pressure, cavitation, heat transfer, and chemical species transport. These equations are discretized using techniques such as finite difference, finite element, finite volume, or boundary element methods. The simulation domain is divided into a mesh, and the nodal equations are solved as an integrated global system.

Within the finite volume method [51], the equations are solved for small control volumes, where conservation laws govern the transport of physical properties. This approach is computationally intensive because the balance of transported quantities must be maintained between adjacent volumes. The Navier–Stokes equations form the foundation of most fluid flow simulations, and their simplified variants, such as the Euler equations and potential flow, are obtained by neglecting specific terms. CFD is part of computer-aided design (CAD) and computer-aided engineering (CAE), utilizing computational power to analyze fluid behavior and their interactions with system boundaries or walls. The accuracy and speed of solutions depend on available processing resources, and the validity of results is confirmed through comparison with experimental data or real-world measurements.

3.3. Setting Up the Passive Facade

The development of a passive façade model within the ANSYS Fluent 17 environment requires a sequence of essential steps, beginning with the precise specification of the system’s geometry. This is followed by discretizing the computational domain into discrete elements, defining the relevant boundary conditions, and specifying the physical properties of the materials involved. Subsequently, the numerical simulation is performed, with the final stage consisting of a detailed interpretation of the obtained data.

3.4. The Geometric Model

To optimize the nodal discretization mesh, the study domain was delineated using the Geometry module of the ANSYS Fluent 17 software. The geometric configuration of the model was limited to the fundamental components of the passive façade: the external glazed layer, consisting of a single glass pane with a thickness of 6 mm; the internal glazed assembly, composed of two glass panes with thicknesses of 6 mm and 5 mm, respectively, separated by a 16 mm air gap; and the internal cavity, characterized by a distance of 0.12 m between the glazed surfaces. This strategy simplifies the analytical process, reducing the computational model’s complexity without compromising the fidelity of the obtained results. The assessment of the radiative balance was conditioned by the intensity of solar radiation (both direct and diffuse components), the specific orientation of the façade, the view factors characterizing the radiative interaction between the various building elements of the façade, as well as the radiative properties of the materials. For this investigation, a radiative heat flux value of 66.90 W/m² was adopted, representative of the Moldova region in January with southern exposure [52]. From this incident radiant energy, it was considered that 10% is reflected by the surface, and another 10% is absorbed by the material, under an external ambient temperature of 255.15 K [53].

3.5. Creating the Discretization Mesh

After defining and graphically representing the analysis domain, the discretization phase is carried out. For two-dimensional studies, the domain is often segmented using triangular or quadrilateral elements, whereas for three-dimensional configurations, tetrahedra, hexahedra, triangular prisms, quadrilateral pyramids, or irregular polyhedra are employed. The application of discretization with irregular polyhedra significantly reduces the number of cells required to achieve higher accuracy [54], although the volume of nodes and, consequently, the computational resource demand remains substantial. Therefore, for the present model, regular cubic hexahedra were chosen. Therefore, the discretization was performed using regular hexahedrons in the form of cubes.

The solution process for the system of equations requires locating the constituent elements of the mesh, composed of cells, nodes, edges, and faces, organized within a connectivity matrix. In the case of structured meshes, characterized by a uniform distribution of nodes, this matrix can be dynamically generated, avoiding the need for separate storage. Conversely, unstructured meshes become essential for modeling complex geometries or integrating imported meshes, allowing adaptive refinements based on results obtained during simulation.

Regardless of the discretization technique adopted, a system of linear equations is obtained for steady-state problems, while a set of differential equations requiring linearization processes is necessary for unsteady phenomena analysis [55]. The solution of these systems can be achieved through either direct or iterative solving methods.

Regardless of the discretization technique adopted, a system of linear equations is obtained for steady-state problems, while a set of differential equations requiring linearization processes is necessary for unsteady phenomena analysis [55]. The solution of these systems can be achieved through either direct or iterative solving methods.

The mesh inside the DSF varied for each of the 5 cases, as presented in

Table 1. Number of cells for each of the 5 configurations.

Crt. Nr	Channel Width (D)	Number of Cells
1	4	519,246
2	6	742,000
3	8	1,038,492
4	10	1,260,000
5	12	1,483,560

, and was made fine and structured near the wall to satisfy the turbulence model condition (Y⁺ = 1). This mesh becomes coarser away from the wall in order to optimize the computational time.

3.6. Establishing Analysis Models

In ANSYS Fluent 17, the pressure-based solver was selected due to its versatility across various applications and its numerical efficiency, despite requiring approximately 1.5 to 2 times more memory than the density-based method. During the initial simulation phase, the standard k-ω turbulence model was employed [56], which involves solving transport equations for the turbulence kinetic energy (k) and the specific dissipation rate (ω). This model is suitable for accurate boundary layer analysis and flows with low Reynolds numbers but necessitates fine mesh discretization near solid surfaces to yield reliable results.

Due to inconclusive initial findings, the transient SST k-ω model was subsequently implemented [57]. This model integrates the shear stress transport (SST) mechanism to combine the advantages of two distinct modeling approaches. The SST k-ω model demonstrates superior capability in accurately capturing boundary layer phenomena, extending down to the viscous sublayer, and performs efficiently in low Reynolds number flows without requiring additional damping functions. Although the SST model significantly improves velocity profile predictions and flow separation under adverse pressure gradients [58], it demands increased mesh density near solid boundaries. For radiative heat transfer analysis, the surface-to-surface (S2S) model was chosen, as it can simulate one-, two-, and three-dimensional geometric configurations, including cylindrical shapes through body-fitted coordinates (BFC). The S2S model facilitates radiative heat transfer simulation in both laminar and turbulent regimes and allows the specification of imposed heat flux, temperature, or radiative properties on surfaces [59]. Its operation is based on subdividing surfaces into zones of uniform temperature, requiring the evaluation of geometric or view factors to quantify radiative heat flux exchange.

Regarding the solution methods, a model using a velocity–pressure coupling scheme (coupled) was selected, as it enables faster convergence compared to a solver that does not couple velocity and pressure. In this analysis, an important factor is the interpolation of numerical methods, which is necessary for evaluating diffusion fluxes, calculating velocity gradients, and applying higher-order discretization schemes. The least-squares cell-based method was chosen, as it is recommended for hexahedral meshes. For pressure analysis, the body force weighted method was selected, as it is the most suitable in the case of natural convection with a high Rayleigh number.

Numerical solution strategies included a velocity–pressure coupling scheme, favored for optimizing the convergence rate compared to segregated methods. Interpolation techniques, essential for evaluating diffusion fluxes, velocity gradients, and within higher-order discretization schemes, constituted a key element of the analysis. For geometries discretized with hexahedral elements, the “Least-Squares Cell-based” method was selected, while the “Body Force Weighted” method was applied for pressure field calculation, recognized for its efficiency in simulating natural convection phenomena at significant Rayleigh numbers.

Regarding momentum evaluation, the upwind scheme was implemented, known for its simplicity and robustness, although it introduces more pronounced numerical dissipation dependent on flow properties. The precision difference between first-order and second-order discretization methods is considerable, with the second-order upwind scheme ensuring superior accuracy. For a rapid estimation of the flow field—including variables such as velocity, pressure, temperature, turbulence, and volume fractions—hybrid initialization was employed initially. This technique combines various methods and is based on Laplace’s equation.

To meet the convergence criteria, the simulator performed a sufficient number of iterations to achieve convergence, a criterion assessed by verifying the fulfillment of conservation equations at the cell level within predefined residual tolerances, ensuring a global balance of conserved physical quantities, and stabilizing the values of variables of interest. Residuals, indicators of imbalances in the numerical solution, correlate with numerical errors but do not represent a direct equivalence. In our case, the convergence residual value of 0.001 was chosen.

The simulations for the passive façade were conducted under steady-state conditions, meaning that a constant thermal and fluid dynamic equilibrium over time was assumed, without transient variations in temperature or air velocities within the ventilated cavity. This approach allows for simplification of the numerical modeling, reducing both computation time and simulation complexity, given that the heat transfer and natural convection processes reach a stable state after a certain period.

The chosen relaxation factor is essential for ensuring stable and efficient convergence in numerical simulations, and the recommended values can vary significantly depending on the specific nature of the problem studied and the flow dynamics analyzed. Generally, to prevent numerical oscillations and facilitate gradual solution stabilization, moderate values of relaxation factors are preferred. Thus, in this case, a uniform value of 0.5 was selected for the relaxation of pressure, velocity, and energy, reflecting an optimal compromise between convergence speed and maintaining numerical algorithm stability.

3.7. Setting the Boundary Conditions

• Carry out a simulation of natural convection;
• The fluid flow is characterized by turbulence;
• The geometric parameters of the façade: 1.90 × 1.40 × 0.12 m;
• The effective diameter of the model’s fluid conduit: 0.221 m;
• The convective heat transfer coefficient: 8 W/m²·K;
• The emissivity of the glass’s interior surface: 0.89;
• The intensity of radiant energy flow: 60.9 W/m²;
• The temperature of the air at the entrance: 255.15 K.

3.8. Approaches for Data Collection and Analysis

In order to clarify the mechanisms of heat transfer and to assess the energy efficiency of passive façade systems, the investigation focuses on the analysis of the velocity and temperature field distributions within the cavity. These fields are governed by the convective heat transfer coefficients, whose values are determined by the ventilation strategy implemented within the cavity (in this case, natural ventilation) and the level of solar radiation exposure.

3.8.1. Temperature Field Distribution

Once the simulation process was completed and the predefined convergence criteria were met, the analysis focused on the temperature distribution across the façade surface. To examine thermal variations within the cavity, cross-sectional views were generated at key locations of the model—namely, the inlet, the central region, and the outlet. Figure 1 presents the passive facade model, configured within the ANSYS Fluent 17 environment, upon which the numerical simulations were performed. The visual representations generated by the software illustrate the temperature differences shown in the XY plane (as presented in Figure 2) in the graphs of Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9, and in the ZY plane (as depicted in Figure 6).

The selection of these temperature sections was intentional, with the primary objective of highlighting the thermal contrasts in the five analyzed scenarios. Subsequently, specific details will be presented for the cases with cavity widths of 4 cm, 6 cm, 8 cm, 10 cm, and 12 cm.

A detailed examination of the graphical representation presented in Figure 2 reveals a remarkable uniformity of the thermal values recorded at the inlet section across all five analyzed configurations. This homogeneity in the temperature distribution within the inlet zone makes it difficult to visually distinguish any significant variations between the different studied cases.

3.8.2. Velocity Field Distribution

After completing the simulation process and meeting the convergence criteria, the graphical representations illustrate the velocity values recorded within the façade channel. These values were analyzed at specific cross-sections located at the inlet (z = 0 m), the mid-plane (z = 0.95 m), and the outlet of the façade (z = 1.90 m). The strategic selection of these sections aimed primarily to highlight the differences between the five investigated scenarios. The following sections (Figure 10, Figure 11, Figure 12, Figure 13, Figure 14 and Figure 15) will detail the results obtained for the five analyzed cases in the XY and ZY planes, respectively.

3.9. Values for the Thermal Flux in ANSYS Fluent 17

Table 2. Values determined by ANSYS Fluent 17.

Ansys Fluent 17 Values
Channel Width	Inlet Temperature	Outlet Temperature	Mass Flow	Heat Flux
cm	K	K	kg/s	kW	W
4	255	273.77	6.32 × 10−12	1.1923 × 10−7	0.0001192
6	255	274.74	2.43 × 10−11	4.8280 × 10−7	0.0004828
8	255	275.53	1.42 × 10−10	2.9202 × 10−6	0.0029202
10	255	276.21	2.04 × 10−10	4.3587 × 10−6	0.0043587
12	255	276.82	2.39 × 10−10	5.2304 × 10−6	0.0052305

presents the numerical results, obtained using Ansys Fluent 17, for the air inlet temperature in the cavity (fixed at 255 K), the air outlet temperature, the mass flow rate of air through the cavity, and the transferred heat flux.

4. Results

Analyzing graphical representations of temperature in the XY plane, a clear dependence of the temperature profile on the cavity width can be observed. The curves indicate a general tendency for the central temperature within the cavity to decrease as its width increases. This phenomenon suggests an influence of the air gap size on the thermal transfer capacity and on the internal convective regime. A non-uniform horizontal temperature distribution (along the X+ axis) is noticeable, with higher values near the boundary layers (X+ ≈ 0 and X+ ≈ 1) and lower values in the central region (X+ ≈ 0.5). This pattern is typical of natural convection phenomena, where heated air near warm surfaces (assuming the extremities correspond to zones of significant thermal transfer) tends to rise, generating convective currents that influence the thermal distribution inside the cavity. The formation of thermal boundary layers near the walls is likely the cause of the elevated temperatures observed in these areas.

Evaluating the graphical representations presented of the temperature contours in the ZY plane reveals a general trend in increasing temperature along the horizontal direction of the outlet section (from Y+ = 0 to Y+ = 1). This increase suggests thermal energy accumulation as the fluid traverses the cavity and interacts with its surfaces. Significant thermal stratification is observed depending on the cavity width. For larger cavity widths, higher temperatures are recorded throughout the outlet section profile. This finding indicates a direct influence of the cavity size on its capacity to retain and transfer heat. A wider cavity may allow for more extensive development of convective currents or reduce thermal losses to the exterior, resulting in elevated outlet temperatures.

Analyzing the presented graphs, which illustrate the velocity profile in the XY plane for the mid-section, a significant variation in velocity magnitude is observed as a function of the channel width. As the channel width increases, a general trend of higher maximum velocities attained in the mid-section becomes evident. This positive correlation suggests a direct influence of the channel geometry on the internal fluid flow regime within the façade. Wider channels may facilitate more vigorous air circulation, possibly due to reduced flow resistance or changes in buoyancy forces that drive natural convection. The velocity profiles for all five channel widths exhibit a shape characteristic of flow within a channel, with reduced velocities near the walls (at X+ ≈ 0 and X+ ≈ 1) due to viscous effects, and a peak velocity in the central region (around X+ ≈ 0.5). This parabolic or quasi-parabolic distribution is typical for laminar flows or for the central region of weakly turbulent flows in channels.

A flattening of the velocity profile is observed in the central zone of the channel for larger widths (d = 10 cm and d = 12 cm), indicating a more uniform velocity distribution in this region. This flattening may suggest a more developed convective flow or a transition toward a flow regime less influenced by wall-induced viscous effects in wider channels. The absolute values of velocity remain relatively low (in the order of 10⁻⁹ m/s), which indicates the phenomenon of natural convection with limited intensity, determined by temperature differences and the dimensions of the channel.

Analyzing the presented graphs, which illustrate the velocity profiles in the ZY plane, a parabolic velocity distribution is observed within the channel for all five investigated widths. The velocity is minimal (approaching zero) in the immediate vicinity of the channel walls (at Y+ ≈ 0 and Y+ ≈ 1) due to the no-slip condition, and reaches a maximum value at the channel’s center (Y+ ≈ 0.5). The magnitude of the maximum velocity attained at the channel center varies significantly with its width. A positive correlation is found between channel width and the fluid’s maximum velocity. Wider channels (d = 10 cm and d = 12 cm) enable considerably higher maximum velocities compared to narrower channels (d = 4 cm and d = 6 cm). This observation suggests that the channel dimension directly influences the intensity of the airflow or fluid flow within the passive façade. It is also noted that the slope of the velocity profile near the walls is steeper for narrower channels, indicating a greater velocity gradient in that region. This suggests more pronounced viscous shear forces near the surfaces for channels with a smaller internal distance.

The mass flow rate of air through the cavity exhibits an increasing trend with channel width, although not perfectly linear. The lowest mass flow-rate value is recorded for a 4 cm width (6.32 × 10⁻¹² kg/s), while the highest is for a 12 cm width (2.39 × 10⁻¹⁰ kg/s). This increase in mass flow rate is attributed to the reduction in flow resistance within wider channels, thereby promoting more intense natural convection. The transferred heat flux also shows a significant increase with channel width. Expressed in kW, it ranges from 1.1923 × 10⁻⁷ kW (0.0001192 W) for 4 cm to 5.2304 × 10⁻⁶ kW (0.0052305 W) for 12 cm. This increase indicates that a wider cavity facilitates the transfer of a greater amount of heat, which is a direct consequence of the higher outlet temperature and increased mass flow rate.

5. Discussion

The comparative analysis of temperature distribution in the XY and ZY planes reveals a significant dependence of the thermal field on the geometry of the passive façade cavity. In the XY plane, the observed temperature difference between the configuration with the minimum cavity width (4 cm) and that with the maximum width (12 cm), amounting to 10.20% at the outer extremity, highlights the influence of the air channel dimension on the overall heat transfer. Larger cavity widths promote higher maximum temperatures in this region, suggesting an increased heat transfer capacity. In the ZY plane, the temperature profile exhibits the staged evolution characteristic of a thermal boundary layer. The initial linear decrease over the first 0.2 normalized units (Y+) indicates the dominance of conductive heat transfer within the viscous sublayer. The subsequent zone, ranging from 0.2 to 0.8 (Y+), marked by a stable thermal gradient, corresponds to a transitional or buffer region where convective effects become more pronounced, although without significant thermal stratification. The final linear increase toward the maximum value reflects the influence of thermal boundary conditions at the outer edge of the boundary layer.

A comparative analysis of the velocity profiles, presented for the five distinct widths of the passive facade’s channel, reveals a consistent parabolic velocity distribution. This classic hydrodynamic profile shape is a clear indication of the “stack effect.” According to this thermo-gravitational principle, warm, less-dense air rises within the cavity, generating a low-pressure zone at its base and a high-pressure zone at the top, thereby driving the upward airflow.

The peak velocity values exhibit a directly proportional correlation with the channel width. Wider channels allow for the development of significantly higher maximum velocities. This observation suggests that channel width is a critical geometric parameter in determining the heat transfer rate through the passive façade, thereby directly affecting its thermal performance. A wider channel offers lower hydrodynamic resistance, facilitating an increased volumetric flow rate under the action of driving forces. Moreover, the analysis of the velocity gradient near the channel walls reveals a steeper slope for narrower channels. This pronounced gradient indicates higher intensity of viscous shear forces in that region, a consequence of stronger interaction between fluid layers in confined geometries. The increase in viscous shear affects the momentum transfer, which in turn impacts the heat transfer by reducing its effectiveness.

The study brings a potentially innovative perspective by demonstrating that a larger cavity width (12 cm in this case) leads to significantly superior thermal efficiency, manifested by an outlet heat flux approximately 44 times greater compared to the 4 cm variant. This contradicts a possible initial intuition that a narrower cavity might be more efficient for convective heat transfer or that an optimal limit might exist at a smaller width. This finding offers new perspectives for the optimal design of passive facades.

A correlation is identified between channel width, outlet temperature, mass flow rate, and heat flux. The increase in heat flux with channel width suggests a greater capacity of the façade to preheat incoming air during the cold season or to evacuate heat during the warm season. At the same time, the extremely low mass flow rates indicate a slow flow regime dominated by natural convection, characterized by relatively weak driving forces.

6. Conclusions

The conclusions drawn from the detailed analysis of temperature distribution and velocity profiles within the cavity of the passive façade highlight a complex interdependence between the geometry of the air channel and the system’s energy efficiency. Specifically, cavity width emerges as a critical design parameter, exerting a direct influence on both the internal thermal and hydrodynamic regimes, and consequently affecting the façade’s overall performance in terms of energy conservation. A clear correlation is observed between the width of the passive façade cavity, the air mass flow rate, and the transferred heat flux. As the channel width increases, there is a corresponding increase in both the mass flow rate of air circulating through the cavity and the amount of heat transferred. The comparative analysis of the temperature fields in the XY plane demonstrated that a greater cavity width (12 cm) results in higher maximum temperatures at the outer edge of the façade, suggesting enhanced thermal transfer to the interior and reduced heat loss to the exterior. This observation, combined with the higher total thermal variation observed in wider cavity configurations, indicates an increased sensitivity of the thermal regime to air channel dimensions.

From a fluid dynamics perspective, the parabolic velocity profiles—characteristic of a laminar flow regime—indicate a direct dependence of velocity magnitude on cavity width. Wider channels allow for higher maximum velocities, which imply an increased volumetric airflow through the façade. Greater airflow, driven by natural convection, contributes to more uniform temperature distribution within the cavity and more efficient heat removal in the warm season or preheating of incoming air during the cold season—both essential for optimizing the building’s energy performance. These characteristics not only reduce the energy demand for heating or cooling but also enhance indoor comfort and building sustainability.

Although the “stack effect” is a well-known concept, its detailed demonstration and explanation, through parabolic velocity profiles and direct correlation with increased heat flux within the specific context of passive facades with varying widths, adds further confirmation and a deeper understanding of its vital role in the energy performance of these systems.

Even though studies on ventilated cavities exist, such an explicit and quantified comparative analysis of the direct influence of only cavity width across multiple profiles (temperature, velocity, heat flux, mass flow rate) for five distinct configurations contributes to a superior understanding of the processes and phenomena occurring within the cavity of a passive facade. This allows for the precise identification of the most efficient configuration within the specific context investigated.

The work not only analyzes but also translates its results into practical recommendations, directly emphasizing that passive facades with optimized cavities (in this case, 12 cm) are an efficient and recommendable solution for achieving nZEB standards. This direct link between research and practical applications for modern buildings adds significant value.

The present study focused on the influence of cavity width; however, the energy performance of a passive façade can vary significantly depending on the specific climatic context and other construction parameters of the building. A detailed quantification of specific energy benefits under various scenarios was not undertaken. The study primarily relies on numerical simulations. The authors emphasize the necessity of validating these simulations through experimental studies that evaluate the performance of passive façades under real and diverse climatic conditions by monitoring relevant physical parameters. Moreover, this study does not include an in-depth analysis of material and manufacturing costs, long-term durability, or the environmental impact associated with different passive façade configurations. Such an evaluation would be essential to provide a comprehensive perspective on the overall sustainability of the proposed solution.

The study offers an original perspective on how variations in the air channel width of the passive façade influence the thermal field in the XY and ZY planes. The identification of a temperature difference exceeding 10% between extreme configurations confirms the essential role of this geometric parameter in optimizing heat transfer.

The staged evolution of the temperature profile (conduction in the viscous sublayer, buffer zone, and peripheral convective influence) is rarely documented in the literature on passive façades. This detailed description of the thermal boundary layer contributes to a deeper understanding of heat transfer behavior in narrow cavities.

The study also highlights that the cavity width affects not only the distribution of velocity and temperature, but also integrative parameters such as mass flow rate and heat flux, providing a quantitative basis for the optimal design of passive façades based on seasonal climate conditions. The results support the use of wider cavities to enhance the energy performance of façades, either by preheating the air during the cold season or by efficiently evacuating heat during the warm season. This direction has direct applicability in the design of nZEBs

Future studies could investigate the optimization of cavity width in correlation with other climatic and construction parameters to quantify specific energy benefits and to establish optimal design recommendations. In addition to cavity width, other geometric parameters may significantly impact performance. Future investigations could include the analysis of the influence of cavity height, the size and shape of inlet/outlet openings, as well as the presence of internal elements (e.g., baffles, absorption components). A multidimensional parametric analysis would enable the identification of optimal geometric combinations.