Solar chimneys as an element of natural ventilation in modern building practices

Myroniuk, Khrystyna; Mizernyk, Vasyl; Furdas, Yurii; Shepitchak, Volodymyr; Zhelykh, Vasyl

doi:10.17512/bozpe.2025.14.16

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Introduction

The recent architectural and construction development has been defined by the pursuit of strategies to address global energy and environmental challenges. One of the most pressing priorities for the European Union and the international community is the thermal modernization of the existing, technically outdated housing stock, with the objective of substantially reducing energy consumption associated with heating and air conditioning systems. Nevertheless, effective insulation of building envelopes is inherently linked to the necessity of maintaining a high-quality indoor microclimate. The increased airtightness of buildings following modernization often results in the disruption of conventional natural ventilation systems, thereby causing air stagnation, excessive humidity, and adverse effects on occupants’ health.

The resolution of this issue requires the integration of energy-efficient strategies capable of ensuring adequate air exchange without incurring substantial energy consumption. Traditional approaches to natural ventilation, such as stack ventilation (through vertical ducts) and cross-ventilation (through openings positioned on opposite façades), often prove inadequate in thermally modernized buildings, primarily due to the absence of a reliable pressure differential arising from variations in air density or wind effects (Myroniuk et al., 2024). Within this framework, solar chimneys emerge as a promising technology – a passive system that harnesses solar energy to generate a stable buoyancy-driven draft and thereby enhance the removal of exhaust air (Fereidoni et al., 2025; Zhao et al., 2024).

The relevance of such solutions is substantiated by numerous scientific investigations, which, both experimentally and through Computational Fluid Dynamics (CFD) modelling, have demonstrated the high effectiveness of solar chimneys in enhancing air exchange across various building typologies. Nevertheless, despite their practical potential, the large-scale adoption of these systems in contemporary construction practice remains limited. A primary barrier is the absence of straightforward engineering methodologies for their design and performance assessment. Practicing engineers currently lack standardized, accessible, and reliable tools that enable accurate prediction of a solar chimney’s ventilation capacity at the design stage, while accounting for local climatic conditions, architectural characteristics, and indoor environmental requirements. This lack of methodological certainty renders the implementation of such technologies a high-risk endeavour in professional design practice.

The purpose of this article is to analyze the current state of scientific research and the available principles for calculating solar chimneys as an element of natural ventilation and to develop practical approaches based on the proposed physical and mathematical models that can be used in engineering calculations of passive ventilation systems based on solar chimneys.

Recent studies, such as a review (Monghasemi & Vadiee, 2018) confirm that integrated solar chimney (SC) systems are a promising strategy for heating, cooling and ventilation, contributing to the reduction of energy consumption and greenhouse gas emissions. The authors emphasize the trend towards the use of complex integrated configurations, but at the same time state the lack of generalized basic principles for their ranking in terms of performance and the need for further experiments for commercialization. Experimental works, such as the study (Arce et al., 2009), provide valuable data on thermal characteristics and air flow through specific experimental SC models, determining key parameters such as the discharge coefficient (Cd = 0.52). However, such results, obtained under specific conditions, are difficult to extrapolate to arbitrary geometries and climatic conditions of the construction site.

Efforts to develop more universal tools for predicting the performance of solar chimneys are reflected in the study by Shi et al. (2016), which proposed an empirical model derived from the analysis of data obtained from various experimental setups. However, the model demonstrated a considerable mean error of approximately 14 %, with extreme deviations reaching up to 144.6 %, thereby rendering it insufficiently reliable for use in engineering design calculations. These results underscore the high complexity of the underlying physical processes and the pronounced sensitivity of system performance to specific boundary conditions, which could not be adequately captured within the framework of the generalized model.

Research on the interaction of solar chimneys with other architectural elements, such as the study by (Bansal et al., 1994), demonstrates a synergistic effect when integrated with wind towers, particularly under conditions of low wind velocity. Complementary numerical investigations, including the works (Benlefki et al., 2021; Suárez-López et al., 2015), provide a detailed analysis of the combined influence of thermal and dynamic effects in cross-ventilation processes, which is essential for understanding airflow behaviour in complex building systems. Similarly, the studies of (Letan et al., 2003; Nguyen & Huynh, 2024; Ziskind et al., 2002), both experimentally and numerically confirm the feasibility of employing natural convection for passive ventilation and heating in both multi-story and single-story buildings. Nonetheless, these contributions primarily emphasize proof-of-concept validation in controlled laboratory settings or isolated case studies, rather than advancing the development of universal computational methodologies applicable to design practice.

More fundamental contributions, such as those by (Rodrigues et al., 2000; Yang et al., 2013), focus on modelling natural convection in vertical channels and analysing the stack effect, which constitutes the physical foundation of solar chimney operation. These studies provide important insights into the underlying physics, including temperature and pressure distributions; however, their models frequently rely on simplified assumptions (e.g., two-dimensional flow conditions) or exhibit high computational complexity, thereby limiting their applicability during the preliminary stages of building design. Similarly, the work (Zhang & Yang, 2019) offers practical recommendations regarding the geometry of air gaps in double-skin façades, but its findings remain constrained to a specific parameter range, reducing their generalizability. Furthermore, several studies (Mizernyk et al., 2025; Mohammadi et al., 2025; Myroniuk et al., 2024; Sharon, 2023; Yue et al., 2023) have also examined specific characteristics of the elements constituting passive ventilation systems in buildings.

Thus, despite the considerable body of research devoted to solar chimneys, a critical analysis of the literature highlights a fundamental gap: the absence of standardized, reliable, and practically applicable engineering methods for their calculation. The majority of existing studies are characterized by the following limitations:

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they are predominantly localized experimental or numerical investigations, often yielding results of limited generalizability;
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they propose complex CFD models that are unsuitable for rapid application by design engineers;
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they present empirical correlations with error margins that are unacceptably high for design purposes;
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they primarily focus on demonstrating the feasibility of solar chimney concepts rather than on developing tools for large-scale design implementation.

Therefore, there exists an urgent scientific and practical need for the development of simplified yet sufficiently accurate engineering methods for predicting the performance of solar chimneys. Such methods should account for system geometry, climatic conditions, and integration with the building structure, thereby enabling the transformation of this promising technology from the subject of academic research into a standardized tool of energy-efficient construction.

1.

Materials and methods

1.1.

Research procedure

This study uses a combined theoretical and numerical approach to develop an engineering methodology for predicting the performance of ventilation systems using SD. The research procedure consists of three main stages: 1 – formulation of a mathematical model based on the fundamental principles of thermodynamics and hydrodynamics; 2 – numerical implementation and solution of the model using computational tools; and 3 – parametric analysis to assess the impact of key design and climatic variables on the system performance.

1.2.

Mathematical model

The methodology is based on a one-dimensional steady-state model that describes the heat and mass transfer processes in a vertical channel of a solar chimney. The model is based on the following system of equations derived from the conservation laws:

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Heat balance equation: The equation takes into account the absorption of solar radiation and heat transfer to the air, as well as heat loss to the environment (1) $\frac{dT}{dz} = \frac{1}{\dot{m} c_{p}} (I (z) η P - UP (T - T_{out})),$ {{dT} \over {dz}} = {1 \over {{\dot m}{c_p}}}\left( {I\left( z \right)\eta P - UP\left( {T - {T_{out}}} \right)} \right), where T is the air temperature at height, z, $\dot{m}$ {\dot m} is the mass flow rate, c_p is the specific heat capacity of air, I(z) is the intensity of solar radiation, η is the absorption coefficient of the chimney wall, P is the perimeter of the chimney channel, U is the total heat transfer coefficient, and T_out is the outdoor air temperature.
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Momentum balance equation: This equation describes the change in pressure due to the gravitational effect (thrust effect) and frictional pressure losses. (2) $\frac{dP}{dz} = - ρ g - \frac{f}{2 D_{h}} ρ V^{2},$ {{dP} \over {dz}} = - \rho g - {f \over {2{D_h}}}\rho {V^2}, where P is the static pressure, ρ is the air density, g is the acceleration of gravity, f is the Darcy friction coefficient, D_h is the hydraulic diameter of the channel, and V is the air velocity.
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Continuity equation (conservation of mass): the simplification was made so for a channel of constant cross-section A, the mass flow rate is constant. (3) $\dot{m} = ρ VA = constant,$ {\dot m} = \rho VA = constant,
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Ideal Gas Equation: Used to relate air density to air pressure and temperature. (4) $ρ = \frac{P}{RT},$ \rho = {P \over {RT}}, where R is the gas constant for air.

Thus, the resulting system of differential equations was represented in the form: (5) $\begin{matrix} \frac{dT}{dz} = \frac{1}{\dot{m} c_{p}} (I (z) η P - UP (T - T_{out})) \\ \frac{dP}{dz} = - g \cdot ρ - (\frac{f}{2 D_{h}}) \cdot ρ \cdot V^{2} \\ V = \frac{\dot{m}}{(ρ A)} \\ ρ = \frac{P}{(RT)} \end{matrix}$ \left\{ {\matrix{ {{{dT} \over {dz}} = {1 \over {{\dot m}{c_p}}}\left( {I\left( z \right)\eta P - UP\left( {T - {T_{out}}} \right)} \right)} \cr {{{dP} \over {dz}} = - g \cdot \rho - \left( {{f \over {2{D_h}}}} \right) \cdot \rho \cdot {V^2}} \cr {V = {{{\dot m}} \over {\left( {\rho A} \right)}}} \cr {\rho = {P \over {\left( {RT} \right)}}} \cr } } \right.

To solve the differential equations of the mathematical model, the following boundary conditions were adopted:

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At the entrance to the chimney (z = 0): T(0) = T_entry, P(0) = P_atm
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At the exit from the chimney $(z = H) : P (H) = P_{atm} - ζ_{exit} \cdot \frac{ρ V^{2}}{2}$ \left( {z = H} \right):P\left( H \right) = {P_{atm}} - {\zeta _{exit}} \cdot {{\rho {V^2}} \over 2}

where ζ_exit – local resistance coefficient at the output of the SC.

1.3.

Numerical solution procedure

The system of coupled ordinary differential equations (ODEs) was solved numerically in MATLAB R2024a using the variable-step Runge-Kutta method. This method is suitable for non-rigid systems. A user-defined function was written to define the system (ODE), which takes the current height z and the state vector Y = [T,P] as input and returns the derivatives dT/dz and dP/dz.

1.4.

Parametric analysis and input data for simulations

A series of simulations were performed to analyze the efficiency of the solar chimney under different conditions. The key parameters used for the calculation varied in ranges according to real conditions:

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solar radiation intensity (I): from 600 W/m² to 1200 W/m²;
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solar chimney height (H): from 5 m to 20 m;
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solar chimney hydraulic diameter (D_h): from 0.3 m to 1.0 m;
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solar radiation absorption coefficient (η): from 0.6 to 0.8;
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inlet air temperature (T_in): set at T_out +2 °C.

For the baseline simulation scenario, the following default values were used: H = 15 m, D_h = 0.5 m, η = 0.7, U = 5.0 W/m², T_out = 25 °C; I₀ = 800 W/m². Atmospheric pressure was assumed to be the same as for standard conditions and was constant and equal P_atm = 101 325 Pa.

1.5.

Validation method

The mathematical model was validated indirectly, as it was checked whether the results obtained on its basis correspond to existing physical principles. In this case, changes in air mass flow rate and temperature increase were compared with data obtained in previous experimental studies (Arce et al., 2009; Shi et al., 2016). In addition, the behavior of the model was checked under extreme conditions, in particular, in the absence of solar radiation and at a minimum chimney height. This was necessary to ensure its physical consistency.

2.

Results and discussion

The physical model that was taken as a basis for mathematical modeling is shown in Figure 1. The presented scheme illustrates the principle of operation of a solar chimney, which is based on the use of solar radiation energy to create natural draft. This phenomenon is based on the fundamental laws of thermodynamics and hydrodynamics.

The model includes a solar chimney, in which the incoming air (T_in) is heated, an exhaust air duct (“chimney”) with a height (H), in which a pressure drop is created due to the difference in densities of the heated outgoing (T_out) and cold incoming air. Heat (Q) is generated in the solar chimney due to solar radiation (I), thereby creating a convective flow, which is used to organize passive air exchange in the building.

Figure 2 presents the results of analytical studies based on the mathematical model of the solar chimney. For clarity, they are presented in the form of graphical dependencies obtained in the MATLAB R2024a environment.

Mathematical modelling in the MATLAB R2024a environment allowed us to analyze the influence of solar radiation in the range of 600 W/m² – 1200 W/m² on the operation of the solar chimney. The results obtained showed a stable increase in the air temperature at the outlet – from 45 °C to 65 °C, which indicates the effective use of thermal energy in the channel. The pressure at the inlet and outlet changed slightly, maintaining a constant difference that forms natural draft.

The mass air flow rate remained at 0.5 kg/s, and the outlet velocity was about 2.5 m/s – 2.7 m/s, indicating the stability of the hydrodynamic characteristics regardless of the change in the magnitude of solar radiation. Temperature profiles along the height of the channel demonstrated an increase in the temperature gradient with increasing solar radiation, which is also confirmed by the visualization of the 3D distribution.

The main modelling results are presented in Table 1.

Table 1.

Results of mathematical modelling of the operating parameters of a solar chimney at different intensities of solar radiation (own research)

I [W/m²]	T_in [°C]	T_out [°C]	ΔT [°C]	$\dot{m}$ {\dot m} [Kg/s]	V [m/s]
600	30.0	42.5	12.5	0.51	2.30
700	31.7	46.2	14.5	0.51	2.33
800	33.3	49.9	16.5	0.51	2.36
900	35.0	53.5	18.5	0.51	2.39
1000	36.7	57.2	20.6	0.51	2.41
1100	38.3	60.9	22.6	0.51	2.44
1200	40.0	64.6	24.6	0.51	2.47

Thus, the results of the modelling confirm that the solar chimney is capable of providing a stable air exchange within the room, demonstrating a clear correlation between the temperature parameters and the level of solar radiation. This finding highlights the solar chimney’s effectiveness as a component of passive ventilation systems for energy-efficient buildings, particularly those that have undergone thermal modernization and feature high airtightness.

On the basis of the analytical investigations conducted, a simplified engineering methodology for calculating the parameters of a solar chimney has been developed, grounded in a mathematical model. The principal stages of this methodology are as follows:

1.

Determination of heat balance

The principle of operation of a solar chimney is based on the perception of solar radiation, which heats the chimney wall. From the heated surface, heat is transferred to the air flow inside the chimney. The heat flow from solar radiation is found by the formula (6) $Q = I \cdot A \cdot η,$ Q = I \cdot A \cdot \eta , where I is the intensity of solar radiation [W/m²]; A is the area of the chimney absorber on which solar radiation falls [m²]; η is the coefficient of useful use of solar energy.

Thermal energy obtained from solar radiation causes heating of the air flow in the chimney. The amount of heat released for heating the air was determined from the dependence: (7) $Q = \dot{m} \cdot c_{p} \cdot (T_{in} - T_{out}),$ Q = {\dot m} \cdot {c_p} \cdot \left( {{T_{in}} - {T_{out}}} \right), where $\dot{m}$ {\dot m} is the mass flow rate of air [kg/s], c_p is the specific heat capacity of air at constant pressure [J/(kg·K)], T_in is the air temperature at the inlet to the chimney, T_out is the air temperature at the outlet from the chimney.

2.

Determination of stack effect (draft)

After the heat is transferred from the heated surface of the solar chimney to the air flow inside the chimney, air movement occurs due to the difference in density of the external and internal air. The stack effect (draft) is determined by the formula: (8) $Δ P_{g} = g \cdot H \cdot \frac{ρ_{out} - ρ_{in}}{1 + β},$ \Delta {P_g} = g \cdot H \cdot {{{\rho _{out}} - {\rho _{in}}} \over {1 + \beta }}, where: g – acceleration of free fall [m/s²]; H – chimney height [m]; ρ_out − ρ_in – air density [kg/m³]; β – correction factor that takes into account the heterogeneity of temperatures and pressures in the channel.

The density of the air leaving the solar chimney and entering the solar chimney is found by the formulas: (9) $ρ_{out} = \frac{P}{R \cdot T_{out}},$ {\rho _{out}} = {P \over {R \cdot {T_{out}}}}, (10) $ρ_{in} = \frac{P}{R \cdot T_{in}},$ {\rho _{in}} = {P \over {R \cdot {T_{in}}}}, where: P – atmospheric pressure [Pa]; R – gas constant for air (R = 287 J/(kg·K); T_out, T_in – absolute air temperature at the outlet and inlet of the solar chimney [K].

3.

Pressure loss calculation

Airflow within the solar chimney channel is subject to pressure losses resulting from frictional interaction with the channel walls, as well as from flow resistance caused by ventilation grilles, openings, and directional changes. These hydraulic losses can be quantified using the following equation: (11) $Δ P = (\frac{f \cdot H}{D_{h}} + \sum ζ) \cdot \frac{ρ \cdot V^{2}}{2},$ \Delta P = \left( {{{f \cdot H} \over {{D_h}}} + \sum \zeta } \right) \cdot {{\rho \cdot {V^2}} \over 2}, where: f – coefficient of friction resistance, D_h – hydraulic diameter of the channel [m], ∑ ζ – sum of local resistance coefficients, ρ – air density [kg/m³], V – air velocity in the channel [m/s].

4.

Checking the operating conditions of the chimney

The condition for the operation of a solar chimney is the ratio of gravitational head to hydraulic pressure losses. The condition for the effective operation of a solar chimney is the excess of gravitational head ΔP_g over pressure losses in the channel ΔP (12) $Δ P_{g} \geq Δ P,$ \Delta {P_g} \ge \Delta P,

5.

Determination of mass air flow rate

The mass air flow rate is calculated using the formula: (13) $\dot{m} = ρ \cdot V \cdot A_{duct},$ {\dot m} = \rho \cdot V \cdot {A_{duct}}, where A_duct – cross-sectional area of the solar chimney channel [m²].

Accordingly, the volumetric air flow rate is calculated as: (14) $\dot{V} = \frac{\dot{m}}{ρ},$ \dot V = {{{\dot m}} \over \rho },

Thus, the proposed simplified engineering calculation method enables a step-by-step assessment of the solar chimney’s performance in terms of its air exchange capacity. This approach is particularly significant for the design and evaluation of passive ventilation systems incorporating solar chimneys in energy-efficient buildings, especially those that have undergone thermal modernization.

Conclusions

This article provides a critical review of contemporary research and presents the results of mathematical modelling of a solar chimney performed in the MATLAB R2024a environment. The modelling enabled a quantitative evaluation of the dependence of key parameters – such as air temperature, pressure drop, mass flow rate, and air velocity – on the intensity of solar radiation within the range of 600 W/m² – 1200 W/m². The results indicate that, with increasing solar radiation, the air temperature at the channel outlet rises from 42.5 °C to 64.6 °C, while the mass flow rate and air velocity remain nearly constant, thereby confirming the stability of the system’s hydrodynamic characteristics.

The practical contribution of this work lies in the development of a simplified engineering methodology for calculating the performance of a solar chimney, which accounts for the heat balance, gravitational pressure, pressure losses, and mass airflow rate. The proposed approach enables designers to perform rapid and accurate evaluations of solar chimney efficiency at the building design stage, eliminating the necessity for complex CFD modeling.

Consequently, the study confirms the feasibility and practical value of employing solar chimneys as components of passive ventilation systems in energy-efficient buildings. Future research should focus on the experimental validation of the proposed methodology under real operating conditions and its incorporation into standardized design frameworks for natural ventilation systems in thermally modernized buildings.

Solar chimneys as an element of natural ventilation in modern building practices

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