CFD Analysis of Different Ventilation Strategies for a Room with a Heated Wall

Abstract

Solar chimneys can help to reduce solar heat gain on a building envelope and to enhance natural ventilation. In this work, we proposed three configurations of two solar chimneys combined with a heated wall for the natural ventilation of a room: (I) the chimneys are connected serially, (II) the chimneys are parallel and exhaust air at two separate outlets, and (III) the chimneys are parallel, but the outlets are combined. The airflow rate achieved with each configuration was predicted with a Computational Fluid Dynamics model. The results show the effects of the heat flux in each channel and the geometries of the channels. Configuration (II) shows the highest flow rate. Particularly, the proposed configurations enhance the flow rate significantly and up to 40% when compared to the typical setup with a single channel solar chimney. The findings offer a novel design option for building façades for reducing solar heat gain and enhancing natural ventilation.

1. Introduction

Thermal insulation of building envelopes, particularly walls, is important in green and energy-efficient buildings to reduce energy demand for heating and cooling. In Viet Nam, the current regulation for energy-efficient buildings, QCVN 09:2017/BXD requires the minimum thermal resistance of $0.56 {\mathrm{m}}^2·\mathrm{K}/\mathrm{W}$ for opaque walls. To satisfy this value, concrete walls with hollow bricks must have a minimum total thickness of 220 mm, which is equivalent to two brick layers. Meanwhile, most residential buildings in Viet Nam have concrete walls with one brick layer whose total thickness of about 110 mm and the equivalent thermal resistance of $0.383 {\mathrm{m}}^2·\mathrm{K}/\mathrm{W}$. Therefore, to comply with this standard, the thermal insulation of such single layer concrete walls must be improved by adding additional insulation layers or external shading devices [1].

Among the most common methods for reducing the solar gain of building envelopes is the solar chimney. This device is based on the buoyancy effects of the air warmed by solar radiation. The buoyancy-driven airflow transports the absorbed heat in the walls and discharges to the ambient atmosphere. As a result, the thermal insulation of the building is enhanced. Miyazaki et al. [2], Al Touma and Ouahrani [3], Hong et al. [4], and Ma et al. [5] reported that the reduction in the annual energy consumption for houses and buildings with solar chimneys was between 2.3% and 77.8%. A combined solar chimney-window of a room can eliminate 11.4% of the daily heat gain [3].

As the induced flow rate is an important performance parameter of a solar chimney [6], it has been the focus of several studies. Previous works have shown that the flow rate is strongly influenced by the heat flux and the dimensions of the cavity. As the buoyancy effects are enhanced with the heat flux and the height of the air channel, the induced flow rate also increases with those two parameters [7,8,9,10,11,12,13,14,15,16,17,18]. Increasing the gap also boosts the flow rate [7,8,10,11,12,16,18]. However, when the gap is large compared to the height, there is a reverse flow at the top the air channel. The reverse flow obstructs the main flow and reduces the flow rate [8,11,19,20,21,22].

The designs of solar chimneys differ based on the types of buildings they are integrated into. In Singapore, the solar chimneys of the BCA Zero Energy Building are composed of roof cavities connected to circular tubes [23]. In Syria, the Lycée Charles de Gaulle school utilizes vertical solar chimneys on the top of two-story buildings for natural ventilation. In Viet Nam, the Deutsches Haus Ho Chi Minh City has walls with open double glass layers which function as solar chimneys. Tall buildings, such as the GSW Headquarters in Germany and Manitoba Hydro Place in Canada, were designed with large-scale solar chimneys [24]. Consequently, the performance of each solar chimney needs to be examined with its specific configuration [6].

On the building envelope, the chimney effect also takes place on a ventilated façade [25]. Air cavities behind the external claddings function as solar chimneys and increase the thermal resistance of the wall. Rahiminejad and Khovalyg [26] reported that the total effective resistance of a cladding and a cavity was up to nine times the thermal resistance of the cladding alone. Particularly, the total resistance increased with the induced flow rate in the cavity. This again confirms the important role of the flow rate.

The problem of the natural ventilation of a room with a wall heated by solar radiation has also been considered in many previous studies. With a simple opening at the top of the room with one vertical wall heated, Marcias-Melo et al. [27] showed that the most efficient case for removing heat was when the opening was on the top of the heated wall. To enhance the ventilation rate, Vazquez-Ruiz et al. [28] added a solar chimney to the top of the room. Their results showed the highest ventilation rate was achieved with the chimney positioned nearest to the air inlet, which was on the wall perpendicular to the heated one. In these studies, the heat from the wall was transferred directly into the room air. In addition, there was also no chimney to exploit the heat transfer on the outer surface of the wall.

Hernandez–Lopez et al. [29] utilized a chimney covering the outer surface of a heated wall to induce airflow for ventilation. Although this system successfully reduced the room air temperature by 9.1 °C, the air in the room was heated significantly because of the lack of a heat barrier on the inner surface of the heated wall. By adding a roof vertical chimney to a system identical to that of Hernandez–Lopez et al. [29], Wang et al. [30] reported that the flow rate through the wall chimney was enhanced in most cases. However, the performance of the optimized designs of the wall chimney did not change with the addition of the roof one. In addition, their system still allowed the heat transfer from the heated wall into the room.

The main research objective of this study was to exploit the heat transfer on both sides of the heated wall with two solar chimneys, covering the outer and inner surfaces of the wall, respectively. The outer chimney collects the heat loss from the outer surface of the wall while the inner chimney functions as a heat barrier to prevent the heat transfer from the wall into the room. Therefore, the proposed system can overcome the limitations of the above-mentioned works.

The performance of the proposed system was examined by a Computational Fluid Dynamics (CFD) model. CFD can provide details of the flow and thermal dynamics which are not obtained with typical building energy simulation models. Zhai and Chen [31] achieved more accurate solutions of an energy model coupled with a CFD model which could offer better predictions of heat transfer on the walls. In this study, as the performance of the proposed system depends strongly on the natural convection in the air cavity, the CFD technique was selected.

2. Description of the System

The proposed system, as seen in Figure 1, consists of two solar chimneys for a dual purpose: (i) releasing solar heat gain on a wall and preventing its transfer into the room, and (ii) natural ventilation of the room. The room has a window and a wall exposed to solar radiation (the left wall in Figure 1). The wall can be on the west or the south side of the room. Solar radiation absorbed on the wall may be conducted into the room. The conductive heat flux should depend on the thermal properties of the wall materials.

To satisfy the above two functions, the proposed system must be able to capture the heat from both sides of the wall. Accordingly, there are two air channels inside and outside of the wall. The outer channel (Channel 1) consists of a vertical section connected to a horizontal part. This channel collects warmed air along the outer surface of the wall and on the roof of the room. The horizontal part of the channel is assumed to cover half of the roof as the rest of the roof is saved for other structures. The inner channel (Channel 2) is formed by the inner surface of the wall and a partition, which is denoted as the “inner wall” in Figure 1. The two channels are arranged in three configurations, as seen in Figure 1.

Configuration (I) (Figure 1a): Channel 2 is connected to Channel 1 on its lower end. As the warm air in Channel 1 rises, air from the room enters Channel 2 from its upper opening, flows into Channel 1, and escapes to the outside environment.

Configuration (II) (Figure 1b): Channel 2 is separated from Channel 1. Air enters both channels at their lower openings and exits at their upper ends. At the outlets, the two airflows do not merge.

Configuration (III) (Figure 1c): It is similar to Configuration (II), but the upper end of Channel 2 is connected into the horizontal part of Channel 1. The airflow in Channel 2 merges with that in Channel 1 at the junction. The merged airflow escapes at the outlet of Channel 1.

Among three systems, Configuration (I) can extract stalled air and contaminant, such as smoke, in the upper zone of the room. However, this design is unfavorable for the flow in Channel 2, as it must move oppositely to the thermal effect. Configuration (II) can only suck air from the lower zone of the room, but the flows in both channels are in the same direction as the thermal effects. However, there must be an exhaust tube to discharge air in Channel 2. Configuration (III) does not require a discharge tube such as in Configuration (II).

It is assumed that there is ignorable heat conduction through the roof and the inner wall into the room. This is practically possible by using roof materials with good thermal resistance. The heat transfer between two walls of Channel 2 is mainly under radiation mode, which can be reduced significantly by using polished materials.

The performance of the configurations in Figure 1 was examined with a Computational Fluid Dynamic (CFD) model. The induced flow rate through the room was computed at different dimensions of the chimneys. To model the effects of the thermal resistance of a building wall, different heat flux ratios in two channels were also considered.

The remainder of this paper is divided into three parts. The computational model is described in the section, “CFD Model”. The main findings are reported in the section, “Results and Discussion”. Lastly, the section “Conclusions” summarizes the main results.

3. CFD Model

For assessing the ventilation performance of the configurations in Figure 1, the airflow rate in each case was computed with a model based on Computational Fluid Dynamics (CFD). CFD has been employed extensively for simulations of indoor air and ventilation [9,14,15,28,32,33,34,35,36]. Following the CFD models for solar chimneys in the literature, a two-dimensional model was built with the following assumptions:

• The flow and heat transfer were steady;
• The flow was incompressible and turbulent;
• The ambient air was at atmospheric pressure;
• The flow in a solar chimney becomes turbulent when the Rayleigh number, $Ra=g\beta q_t{L}^4/\nu \alpha \lambda$, is above ${10}^{10}$ [8,22,33]. In this study, the Rayleigh number was about ${10}^{12}-{10}^{13}$. Accordingly, the flow in the cavity was assumed to be turbulent.

The governing equations in the Reynolds-Averaged Navier–Stokes (RANS) forms are as follows:

$$\frac{\partial \left(\rho u_i\right)}{\partial x_i}=0$$

(1)

$$\frac{\partial \left(\rho u_i{u}_j\right)}{\partial x_j}=-\frac{\partial p}{\partial x_i}+\frac{\partial }{\partial x_j}\left(\mu \left(\frac{\partial u_j}{\partial x_i}+\frac{\partial u_i}{\partial x_j}\right)-\rho \overline{u_i^{\prime }{u}_j^{\prime }}\right)-\rho g_i\beta \left(T-T_r\right)$$

(2)

$$\frac{\partial \left(\rho u_{i}T\right)}{\partial x_i}=\frac{\partial }{\partial x_i}\left(\frac{\lambda }{c_p}\frac{\partial T}{\partial x_i}-\rho \overline{u_i^{\prime }{T}^{\prime }}\right)$$

(3)

The turbulence terms ($-\rho \overline{u_i^{\prime }{u}_j^{\prime }}$ and $\rho \overline{u_i^{\prime }{T}_j^{\prime }}$) in Equations (3) and (4) were solved with the RNG $k-ϵ$ model. Common RANS turbulence models (standard $k-\omega$, standard $k-\epsilon$, RNG $k-\epsilon$, Low Reynolds number $k-\omega$) were successfully used for simulations of solar chimneys [9,17,37,38]. Particularly, Gan [9] and Hinojosa et al. [37] reported that the RNG $k-\epsilon$ model offered the best performance at $Ra\approx {10}^{10}-{10}^{12}$, which is close to the Rayleigh numbers in this study. Therefore, the RNG $k-ϵ$ model was selected. Details of the formulations can be seen in [9,14,15,28,32,33,37].

Based on the above formulations, a numerical model was built for the configurations in Figure 1. Its main components included the computational domain, mesh, discretization methods for the governing equations, and suitable boundary conditions. All these settings were conducted with the CFD software ANSYS Fluent, the version for Academic 2021R2.

Figure 2 shows the computational domain of configuration (II). It was composed of the room, two channels, and the extensions to the ambient space beyond the window of the room and the outlet of Channel 1. The extensions of the domain for simulations of the natural convection flow in a heated cavity was first proposed by Gan [9], and later applied in the works by Gagliano et al. [39], Pasut and De Carli [40], Deblois et al. [41], Tong and Li [42], and Nguyen and Wells [14,15]. These extensions are important as they ease the adaption of the flow to the local dynamic conditions at the openings of the cavity. Accordingly, more accurate solutions can be obtained [9,40].

Details of the dimensions in Figure 2 are presented in

Table 1. The main dimensions of the room and the solar chimneys.

Dimension	Value (m)	Dimension	Value (m)
H	2.0	G2	0.05–0.2
W	1.9	hi	0.1
L1	2.1	li	0.1
L2	1.0	h	0.4
G1	0.05–0.2

. Similar settings of the computational domains and dimensions were also applied to the other configurations.

Figure 2 also displays the mesh structure. A non-uniform mesh of rectangular cells was used. The mesh size decreases toward the solid walls. It was smallest next to the surfaces of the channels. To find an appropriate mesh pattern in each case, different mesh sizes were tested and the airflow rate through the room was compared.

Table 2. Mesh independence test.

Test	No. of Cells	Max. Mesh Size (mm)	Min. Mesh Size (mm)	${\mathit{y}}^{+}$	Q (kg/s)	Difference (%)
1	16,460	90	1.1	3.9	0.05121	1.26
2	42,820	57	0.55	2.25	0.05118	1.32
3	120,665	42	0.29	1.3	0.05153	0.64
4	152,250	38	0.23	1.1	0.05169	0.32
5	184,620	35	0.2	0.95	0.05186	0.00

shows a test for Configuration I. The number of cells increased from 16,460 to 184,620, and the maximum non-dimensional distance of the first nodes on the heated walls, or $y^{+}={\Delta }_1{u}_{\tau }/\nu$, decreased from 3.9 to 0.95. The flow rate obtained at each grid resolution was compared to that of the finest one (Test 5 in Table 2). It was found that with $y^{+}<1.5$, the flow rate changed less than 1.0% when the mesh was refined. This observation agrees with the results by Zamora and Kaiser [22]. Therefore, a mesh yielding $y^{+}<1.5$ was selected. The corresponding maximum and minimum cell sizes were below 42 mm and 0.29 mm, respectively.

The boundary conditions are also presented in Figure 2. On the open boundaries of the extended regions, the pressure and temperature were applied with those of the ambient atmosphere which are zero-gauge pressure and 20 °C, respectively. The turbulence level at the open boundaries was assumed to be low, with an intensity of 2.0%. The heat source was distributed on the right and the left walls of Channels 1 and 2, respectively. Two walls of each channel also exchanged radiative heat transfer which was calculated with the S2S model bundled in ANSYS Fluent. It was assumed that there was no heat transfer on other solid surfaces.

The Finite Volume Method was employed for the discretization of the governing equations with the following settings:

-

SIMPLEC method for the coupling of pressure and velocity;

-

PRESTO! method for the pressure interpolation on the mesh faces;

-

Second order scheme for all equations.

These settings were also employed for simulations of solar chimneys in previous studies [9,14,15,42,43].

The experiment by Burek and Habeb [7] was used to validate the CFD model. The chimney was a vertical rectangular cavity which was open to the ambient air at the upper and lower ends. Its side walls were enclosed. The height of the chimney was 1.025 m. The width was 0.925 m. The gap changed from 0.02 m to 0.11 m. The heat source was distributed on one wall of the air channel at the flux of $600 \mathrm{W}/{\mathrm{m}}^2$, which was around the median value in Singapore [23] and Vietnam [44]. The back side of the air channel was well insulated. The air velocity was measured at the center of the air channel near the inlet. The mass flow rate was then computed from the air velocity, the cross-sectional area of the cavity, and the air density.

In the experiment, as the chimney was stand-alone, air freely entered the air cavity, rose due to the thermal effect, and escaped to the ambient atmosphere from the top of the air cavity. To reproduce the experimental conditions, the computational domain also covered both the air cavity and ambient air. The extensions from the cavity walls to the external domains were 10 times of the cavity gap, as proposed by Gan [9]. The boundary conditions of atmospheric temperature and pressure were applied on the external boundary. The heat flux, which was the same as in the experiment, was applied on one side of the air cavity. The rest of the setup was the same as described above.

The computed flow rate was compared to the measured data. The comparison is displayed in Figure 3. It shows that the predicted flow rate agrees well with the measured one. The discrepancies were from 0% at G = 40 mm to 9.7% at G = 20 mm. Considering possible measurement errors in the experiment, this maximum difference is acceptable. Therefore, the CFD model is considered reliable.

4. Results and Discussion

The ventilation performance of the proposed configurations was evaluated in two cases:

Firstly, $G_2$ were fixed to 0.1 m while $G_1$ changed. Other dimensions are presented in Table 1. The total heat flux in the two channels was $q_t=600 \mathrm{W}/{\mathrm{m}}^2$. The heat flux in Channel 1, $q_1$, and Channel 2, $q_2$, changed, but $q_1+q_2=q_t$. The flow rate was computed for different ratios of $q_2/q_1$ to model different heat fluxes conducted through the building wall depending on its thermal conductivity.

Secondly, the effects of changing the heat flux and the gap $G_2$ of Channel 2 were evaluated.

4.1. Changing G₁

The flow velocity and temperature for $q_1=500 \mathrm{W}/{\mathrm{m}}^2$ and $q_2=100 \mathrm{W}/{\mathrm{m}}^2$ are presented in Figure 4 ($G_1=G_2=0.1 \mathrm{m}$). It is assumed that a total solar radiation flux of $q_t=600 \mathrm{W}/{\mathrm{m}}^2$ is transmitted through the outer glass and absorbed in the building wall; then a heat flux of $q_1=500 \mathrm{W}/{\mathrm{m}}^2$ is transferred into Channel 1 and $q_2=100 \mathrm{W}/{\mathrm{m}}^2$ is conducted through the wall and transferred into Channel 2. Figure 4a shows that for Configuration (I), the airflow moves down in Channel 2, then along Channel 1, and discharges to the ambient air from the outlet of Channel 1. The flow temperature increases along the flow path as it receives more heat. In Figure 4b for Configuration (II), the air from the room enters both channels. As more heat is supplied to Channel 1 ($q_1>q_2$), the flow speed in Channel 1 is higher. In addition, the temperature at the outlet of Channel 1 is also higher. In Figure 4c for Configuration (III), the airflows in both channels merge at the junction. As a result, the flow speed from the junction to the outlet of Channel 1 is higher than those in other parts of the channels. The lower-temperature flow in Channel 2 penetrating Channel 1 is seen to obstruct the flow in Channel 1.

As the induced flow rate was calculated at the window of the room, it is the total flow rate, Q, through both channels. In Configuration (I), it is also the flow rate through Channels 1 and 2, i.e., $Q=Q_1=Q_2$. In Configurations (II) and (III), it is the sum of $Q_1$ and $Q_2$.

The induced flow rates, Q, of three configurations are plotted in Figure 5, Figure 6 and Figure 7. In Figure 5 for Configuration (I), the flow rate is higher as the gap increases. Significant improvement of the flow rate of up to 51% is obtained when the gap changes from 0.05 m to 0.1 m. However, increasing the gap from 0.1 m to 0.2 m only increases the flow rate by 8%. As $q_2$ increases, the flow rate does not change significantly, and the change is only within 6%. This is because, although $q_2$ increases, the total heat flux, $q_t$, that the flow receives in Configuration (I) is constant. Accordingly, a minor change in the flow rate with $q_2$ can be expected.

Figure 6a shows the airflow rate of Configuration (II). The flow rate is higher for the larger gap $G_1$. As $q_2$ increases, the flow rates first increase then decrease. The maximum flow rate happens when $q_2$ is from 300 to 500 $\mathrm{W}/{\mathrm{m}}^2$. In Figure 6b, the airflow rate in Channel 2 is compared to the total one and plotted as the functions of the ratio of $q_2/q_t$. At a given $q_2/q_t$, the ratio of $Q_2/Q$ is lower for the higher gaps. It may be that because as $G_1$ is small, the flow in Channel 1 experiences more flow resistance, resulting in a lower flow rate in Channel 1. $Q_2/Q$ also increases with $q_2$, as more heat is supplied to Channel 2.

The flow rate of Configuration (III) in Figure 7a is enhanced significantly, up to 3.2 times, when $G_1$ increases from 0.05 m to 0.2 m. However, for the gaps of $G_1=0.1 \mathrm{m}$ and $G_2=0.15$ m, the flow rate of $G_1=0.1 \mathrm{m}$ is higher for $q_2<250 \mathrm{W}/{\mathrm{m}}^2$; otherwise, the flow rate of $G_1=0.15 \mathrm{m}$ is higher. Figure 7b shows that at all values of $q_2/q_t$, increasing the gap $G_1$ from 0.05 m to 0.2 m demonstrates a clear decrease of $Q_2/Q$. However, increasing $G_1$ from 0.1 m to 0.15 m results in an increase of $Q_2/Q$.

Previous studies have shown a consistent increase in the airflow rate versus the air gap [7,8,10,11,12,16,18]. Therefore, it is expected that when the gap $G_1$ increases, the flow rate in Channel 1, $Q_1$, gradually dominates over $Q_2$. This point is obvious for Configuration (II) in Figure 6b, and Configuration (III) with $G_1=0.05 \mathrm{m}$ and $0.2 \mathrm{m}$ in Figure 7b. To explore why the flow rate in Configuration (III) does not always increase as $G_1$ increases from 0.1 m to 0.15 m in Figure 7b, the streamlines for $q_2=100 \mathrm{W}/{\mathrm{m}}^2$ of Configuration (III) are displayed in Figure 8. It shows that when the flow in Channel 2 merges with the one in Channel 1 in the marked region in Figure 8, the effective flow areas of both flows decrease significantly. As a result, a higher flow resistance is expected at the junction and downstream of it. In addition, the presence of the recirculation area in the marked region in Figure 8 may also cause the complex behavior of the airflow rate in the cases of $G_1=0.1 \mathrm{m}$ and 0.15 m in Figure 7. Similar effects were also reported by Zamora and Kaiser [22] and Kim et al. [20].

Comparing the mass flow rates in Figure 5, Figure 6a and Figure 7a shows that the total flow rate is always the highest with Configuration (II) and the lowet with Configuration (I). With $G_1=0.2$ m, the maximum flow rate of Configurations (I), (II), and (III) are 0.057, 0.109, and 0.1 kg/s, respectively.

4.2. Changing the Total Heat Flux

Figure 9 shows the induced flow rate as the heat flux changes for $G_1=G_2=0.1$ m. The flow rate, Q, is normalized by that with $q_2=0$, $Q_0$. The ratios of $Q/Q_0$ for different heat fluxes of each configuration match well. The maximum scatter is for Configuration (II), and only about 4%. Consequently, the aero-thermal behaviors of the flows are seen to be identical for different values of $q_t$.

Figure 9 also shows that, for all configurations, increasing $q_2$ results in higher, or identical, flow rates compared with those for $q_2=0$. The least enhancement of 4% is with Configuration (I) and a slight decrease of 2.0% is seen for Configuration (III) at $q_2/q_t=0.9$. The maximum increase of 40% is seen with Configuration (II). The ratios of $q_2/q_t$ where the $Q/Q_0$ peaks are 0.75, 0.55, and 0.35 for Configurations (I), (II), and (III), respectively.

4.3. Changing G₂

As seen in Figure 5, Figure 6, Figure 7 and Figure 9, Configuration (II) offers the highest flow rate among the three configurations. Therefore, it is selected to examine the effects of changing Channel 2’s gap, $G_2$. Figure 10 presents the flow rate of Configuration (II) as $G_2$ and $q_2$ change. As expected, Q increases with $G_2$ (Figure 10a). The flow rate also peaks at a specific $q_{2,c}$ for each $G_2$. On the other hand, $q_{2,c}$ also increases with $G_2$. They are 200, 300, 400, and 500 $\mathrm{W}/{\mathrm{m}}^2$ for $G_2=$ 0.05, 0.1, 0.15, and 0.2 m, respectively. Figure 10b reveals that the ratio of $Q_2/Q$ becomes higher as $G_2$ increases. However, the increasing rate of $Q_2/Q$ versus $G_2$ decreases with $G_2$. For example, at $q_2/q_t=0.5$, increasing $G_2$ from 0.05 m to 0.1 m boosts $Q_2/Q$ up to 27%, but increasing $G_2$ from 0.15 m to 0.2 m enhances $Q_2/Q$ by only 6%. In conclusion, raising $G_2$ increases not only the total flow rate but also $q_{2,c}$ and the flow rate, $Q_2$, in Channel 2.

4.4. Discussion

The fact that Configuration (II) offers the highest flow rate among three proposed configurations, as seen in Figure 5, Figure 6, Figure 7 and Figure 9, agrees well with the experiments by Macias-Melo et al. [27] and Vaquez-Ruiz et al. [28]. They reported that for a room with a heated wall, the highest airflow rate is obtained when the opening or the roof vertical solar chimney is right on top of the heated wall. However, as there was not a barrier wall inside the room in their models, heat is transferred into the whole room in their experiments.

Hernadez-Lopez et al. [29] investigated a wall solar chimney for a room 2.55 m high. Their configuration is also without an internal barrier wall. They showed an airflow rate of 0.0144 kg/s/m for a gap of 0.1 m, and a heat flux of 363 $\mathrm{W}/{\mathrm{m}}^2$. Configuration (II) in this study at $400 \mathrm{W}/{\mathrm{m}}^2$ and a gap of 0.1 m for both channels offered the maximum flow rate of 0.0805 kg/s/m when $q_1=q_2=200 \mathrm{W}/{\mathrm{m}}^2$. As the flow rate in this study is about 5.6 times higher than that in Hernadez-Lopez et al. [29], it clearly shows the advantage of using a heat barrier wall inside a room, i.e., the “inner wall” in Figure 1.

A comparison of Figure 6 and Figure 9 shows that changing either $G_1$ or $G_2$ while the other is fixed, results in identical maximum flow rates. The difference between the two cases is the value of $q_{2,c}$ where the flow rate is peak. The ratio of $q_{2,c}/q_t$ decreases with $G_1$ while it increases with $G_2$. Therefore, in practical designs, it is optional to increase $G_1$ or $G_2$ to achieve the desired ventilation rate. Channel 2 takes space inside the room but should have less construction cost as it is structurally simpler than Channel 1.

5. Conclusions

Three configurations consisting of two solar chimneys for a room’s natural ventilation with a heated wall were proposed and examined numerically. The flow rate in each channel, and the total flow rate through both channels, were evaluated. In most cases, the flow rate increases with the channel gaps. When the heat flux, $q_2$, in Channel 2 increases, the airflow rate of Configuration (I) changes insignificantly, but those of the two other configurations increase, peak, then decrease. The ratio of $Q_2/Q$ increases with $q_2/q_t$ but decreases with $G_1$ when $G_2$ is fixed. When $G_1$ is fixed and $G_2$ changes, $Q_2/Q$ increases with both $q_2/q_t$ and $G_2$.

Among the three proposed configurations, Configuration (II) offers the highest flow rate, which is 91% and 9% higher than those of Configurations (I) and (III), respectively. As $q_2$ increases, the maximum increase in the flow rate of Configuration (II) (40%) is also higher than those of Configurations (I) (4%) and (III) (8%). Therefore, the best ventilation performance is seen with Configuration (II). In addition, with Configuration (II), changing either $G_1$ or $G_2$ results in similar maximum flow rates.

Based on these findings, design engineers may consider various solutions for natural ventilation and solar load-reducing methods of rooms or houses with solar-heated walls, as follows:

For exhausting stalled air in the upper zone of the room, Configuration (I) is preferred, but the ventilation rate decreases to about 52% of that of Configuration (II). Moreover, as the performance of Configuration (I) does not depend on $q_2$, it eases the selection of the material of the building wall.

For maximizing the ventilation rate, Configuration (II) is the best choice. However, as Configuration (III) performs closely to Configuration (II) and the handling of the outlet is simpler, Configuration (III) is preferred.

In future works, experiments with the proposed configurations can be conducted. Such experiments can offer real heat flux ratios, $q_2/q_1$, in each channel obtained with real wall materials.