Optimization of a Passive Solar Heating System for Rural Household Toilets in Cold Regions Using TRNSYS

Abstract

To address the poor thermal insulation and freeze resistance of rural outdoor toilets in cold regions—key obstacles to achieving the UN Sustainable Development Goal (SDG) 6.2 and popularizing rural sanitary toilets—this study fills the literature gap of insufficient research on passive solar heating systems tailored for rural toilets in cold climates. Using TRNSYS simulation, Plackett–Burman key factor screening, single-factor experiments, and Box–Behnken response surface methodology, we optimized the system with building envelope thermal parameters and Beijing’s typical meteorological year data as inputs, taking January’s average indoor temperature as the core evaluation index. Results indicated six parameters (solar wall area, air cavity thickness, vent area ratio, vent spacing, exterior wall insulation thickness, and heat-gain window-to-wall ratio) significantly influence indoor temperature (p < 0.05). The optimal configuration was as follows: solar wall area 3.45 m², window-to-wall ratio 30%, exterior wall insulation thickness 200 mm, vent spacing 1800 mm, air cavity thickness 43 mm, and vent area ratio 5.7%. Post-optimization, the average temperature during the heating season reached 10.81 °C (79.5% higher than baseline), with January’s average, maximum, and minimum temperatures at 7.95 °C, 20.47 °C, and −1.42 °C, respectively. This solution effectively prevents freezing of flushing fixtures due to prolonged low temperatures, providing scientific support for the application of passive rural toilets in China’s cold regions.

1. Introduction

To advance UN SDG 6.2 (universal sanitation by 2030), China has vigorously promoted rural sanitary toilet renovation [1,2]. However, cold-region low temperatures cause persistent issues (e.g., pipe/fixture freezing), leaving rural sanitary toilet penetration below the national 75% average—creating a gap with SDG 6.2 targets [3,4]. Existing frost-proof measures (insulated pipes, deep septic tanks, bonded insulation) fail to ensure usability under subzero conditions [5,6,7,8], prompting scholars to propose coupling solar thermal systems with buildings to enhance cold-season heat retention.

Passive solar solutions—predominantly Trombe walls (thermosyphon heat-storage walls) enhanced by louvered absorbers, hybrid window-wall collectors, or bifacial thermal walls—have been validated to improve building thermal conditions [9,10,11,12]. Prior studies optimized key parameters for residential or general buildings: Zhang Yaya et al. [13] quantified passive solar energy distribution (insulation efficiency > window heat gain > collector efficiency); Qing Li et al. [14] screened insulation materials and glazing proportions for solar spaces; Jiang Wei refined roof insulation for modular houses via EnergyPlus [15]; Zhang Chao and Liang Xiao’s teams used TRNSYS to link thermal wall systems/insulation depth to indoor temperatures [16]; and Qi Qinghua et al. [17] identified 30–40% as Beijing’s ideal window-to-wall ratio for direct-gain solar buildings. TRNSYS further excels among thermal simulation tools for modeling solar heating systems in built environments [18].

Notably, while these studies confirm passive solar systems’ efficacy for dwellings, they focus exclusively on residential or large-scale buildings, with no targeted research on rural household toilets in cold regions. Rural toilets differ fundamentally from residences: their ultra-small volume (typically < 3 m²) creates a high surface-area-to-volume ratio that amplifies heat loss; their simple structure limits space for solar collectors; and their rural application requires low-cost, low-maintenance designs. These unique characteristics mean parameters optimized for residences (e.g., 120 mm air cavity thickness for Qinghai rural toilets) cannot be directly applied. Consequently, the critical problem of subzero temperatures and operational failures in cold-region rural household toilets remains unresolved—a gap that this study aims to address.

To fill this gap, this study integrates passive solar collectors with rural toilet cabins—tailoring the system to the toilet’s small volume and rural practicality. Using TRNSYS simulation, Plackett–Burman key factor screening, single-factor tests, and Box–Behnken parameter combination evaluation, we identify critical parameters and their optimal configuration for cold-region rural toilets. The goal is to resolve winter freezing issues and provide technical support for advancing SDG 6.2 in China’s cold rural areas.

2. Research Objects and Methodology

2.1. Research Objects

2.1.1. Passive Toilet Cabin

This study constructs a 3D model of passive toilet cabins using CAD: AutoCAD 2024 (24.3.100) based on actual rural-toilet dimensions in cold regions, with parameters of the collector system defined in accordance with passive building design standards. The structural configuration appears in Figure 1. Key parameters were as follows: 2.25 m² floor area, 1500 mm length × 1500 mm width × 2300 mm height; ventilation window: 90 mm × 900 mm × 560 mm; door: 1800 mm height × 1000 mm width; thermal wall: 2 m² surface area, 0.08 m² total vent area, 40 mm air cavity thickness; passive solar skylight: argon-filled double glazing with high transmittance; 20% roof window-to-wall ratio; 50 mm of cabin insulation thickness.

2.1.2. Passive Solar Heating System

The passive system primarily consists of a collector wall and a heat-gain window. Operating principles are illustrated in Figure 2. Incident solar radiation passes through the glazing layers. The absorber surface converts this light into thermal energy, which warms the air in the cavity. Cold air enters through the lower ventilation ports of the collector wall; as the air heats up, it rises and exits through the upper ports via density-driven convection. This achieves hot-air circulation to increase the toilet cabin temperature [19].

2.2. Experimental Methodology

2.2.1. TRNSYS Simulation Modeling

(1)

Model Development

This study developed a 3D model of the toilet cabin using SketchUP, which was then imported into TRNSYS to generate the simulation model. Thermal properties of the passive building envelope (

Table 1. Thermal parameters of the enclosure.

Name	Material	Heat Transfer Coefficient [W/(m2·K)]	Thermal Conductivity [W/(m·K)]	Specific Heat Capacity [kJ/(kg·K)]·
Envelope structure of the toilet house	Roof assembly: 20 mm fiberboard + 50 mm XPS insulation + 20 mm corrugated sheet	0.30	-	-
	Roof glazing: Thermally broken aluminum frame window	1.30
	Wall assembly: 20 mm fiberboard + 50 mm XPS insulation + 20 mm embossed metal cladding	0.40	-	-
	Windows: Thermally broken aluminum windows	2.70	-	-
	Door: 80 mm standard aluminum panel	2.70	-	-
	Floor assembly: 20 mm ceramic tile + 50 mm cement fiberboard + 50 mm XPS insulation	0.30	-	-
The collector wall of the toilet	10 mm black aluminum absorber plate	-	203	0.92
	50 mm XPS insulation	-	0.032	1.38
	200 mm high-density fiberboard	-	0.330	2.51

) and meteorological data for Beijing—sourced from Meteonorm 8 (Version 8.1)—were input into the model. The TRNSYS simulation flowchart for the solar-integrated toilet system was established (Figure 3). The hourly average temperature inside the toilet cabin during the coldest month (January) was simulated.

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Thermodynamic Simulation Framework

The core computational engine utilized TRNSYS’s TRNBuild module for thermal load analysis. This module discretized structures into thermal zones, each represented by lumped air nodes. Convective heat transfer at air nodes was governed by Equation (1):

$${\mathrm{Q}}_{\mathrm{e}}={\mathrm{Q}}_{\mathrm{s}\mathrm{u}\mathrm{r}\mathrm{f},\mathrm{e}}+{\mathrm{Q}}_{\mathrm{i}\mathrm{n}\mathrm{f},\mathrm{e}}+{\mathrm{Q}}_{\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t},\mathrm{e}}+{\mathrm{Q}}_{\mathrm{g},\mathrm{c},\mathrm{e}}+{\mathrm{Q}}_{\mathrm{c}\mathrm{p}\mathrm{l}\mathrm{g},\mathrm{e}}$$

(1)

In the formula, ${\mathrm{Q}}_{\mathrm{e}}$ is the convective heat transfer of the air node in W; ${\mathrm{Q}}_{\mathrm{i}\mathrm{n}\mathrm{f},\mathrm{e}}$ is the convective heat transfer between the air and each internal surface of the building in W; ${\mathrm{Q}}_{\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t},\mathrm{e}}$ is the convective heat transfer due to the infiltration ventilation of the building in W; ${\mathrm{Q}}_{\mathrm{g},\mathrm{c},\mathrm{e}}$ is the convective heat transfer brought by the heat source in W; and ${\mathrm{Q}}_{\mathrm{c}\mathrm{p}\mathrm{l}\mathrm{g},\mathrm{e}}$ is the convective heat transfer brought by the ventilation from the adjacent area in W.

$${{\mathrm{Q}}_{\mathrm{r},\mathrm{w}\mathrm{e}}=\mathrm{Q}}_{\mathrm{g},\mathrm{r},\mathrm{e},\mathrm{w}\mathrm{e}}+{\mathrm{Q}}_{\mathrm{s}\mathrm{o}\mathrm{l},\mathrm{w}\mathrm{e}}+{\mathrm{Q}}_{\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g},\mathrm{w}\mathrm{e}}+{\mathrm{Q}}_{\mathrm{w}\mathrm{a}\mathrm{l}\mathrm{l}-\mathrm{g}\mathrm{a}\mathrm{i}\mathrm{n}}$$

(2)

In the formula, ${\mathrm{Q}}_{\mathrm{r},\mathrm{w}\mathrm{e}}$ is the radiant heat gain for the temperature node on the wall surface in W; ${\mathrm{Q}}_{\mathrm{g},\mathrm{r},\mathrm{e},\mathrm{w}\mathrm{e}}$ is the radiant heat exchange between the internal heat source and the wall in W; ${\mathrm{Q}}_{\mathrm{s}\mathrm{o}\mathrm{l},\mathrm{w}\mathrm{e}}$ is the heat absorbed by the wall from solar radiation through the window in W; ${\mathrm{Q}}_{\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g},\mathrm{w}\mathrm{e}}$ is the long-wave radiation between the building envelopes in W; and ${\mathrm{Q}}_{\mathrm{l}\mathrm{o}\mathrm{n}\mathrm{g},\mathrm{w}\mathrm{e}}$ is the internal heat source of the wall in W.

2.2.2. Key Factor Screening Experiment

Screening experiments involving 7 factors at 2 levels were conducted using Design-Expert® Software, Version 13 (13.0.7), totaling 12 runs. Screened factors were as follows: A—exterior wall insulation thickness, B—roof insulation thickness, C—window—to—wall ratio, D—collector wall area, E—vent spacing (inlet/outlet), F—air cavity thickness, and G—vent area ratio. The experimental design appears in

Table 2. Plackett–Burman design for critical factors.

Treatment	A Exterior Wall Insulation Thickness (mm)	B Roof Insulation Thickness (mm)	C Window-to-Wall Ratio (%)	D Collector Wall Area (m2)	E Vent Spacing (Inlet/Outlet) (mm)	F Air Cavity Thickness (mm)	G Vent Area Ratio (%)
1	100	100	20	3.45	1000	100	6
2	100	300	60	3.45	1000	20	2
3	300	300	60	2	1000	20	6
4	100	300	20	3.45	1800	20	6
5	100	100	20	2	1000	20	2
6	300	100	60	3.45	1800	20	2
7	300	300	20	3.45	1800	100	2
8	100	300	60	2	1800	100	6
9	300	100	60	3.45	1000	100	6
10	300	300	20	2	1000	100	2
11	100	100	60	2	1800	100	2
12	300	100	20	2	1800	20	6

.

2.2.3. Optimal Parameterization Experiment

Based on screening results, single-factor experiments were used to determine optimal parameters for A, D, and C, with mean cabin temperature and material cost as dependent variables. The test matrix was as follows: exterior wall insulation thickness (A) increased from 100 mm to 300 mm in 50 mm increments; D (collector wall area) ranged from 2 m² to 3.45 m² in 0.725 m² increments; and C (window-to-wall ratio) increased from 20% to 60% in 10% increments, totaling 13 experimental groups.

Following initial optimization, single-factor tests were used to investigate vent spacing (E), air cavity thickness (F), and vent area ratio (G), with mean, maximum, and minimum cabin temperatures as dependent variables to define feasible ranges for Box–Behnken RSM implementation. The experimental design was set as follows: the vent spacing (E) was gradually increased from 1000 mm to 1800 mm at a 200 mm increment; the air cavity thickness (F) was gradually increased from 20 mm to 100 mm at a 20 mm increment; and the vent area ratio (G) was gradually increased from 2% to 6% at a 1% increment. A total of 15 experimental groups were conducted.

Final optimization employed Box–Behnken RSM to determine the global optima of E, F, and G. The 3-factor, 3-level design with 17 runs is detailed in

Table 3. B-BD for vent spacing, air cavity thickness, and vent area ratio.

Treatment	E (mm)	F (mm)	G (%)
1	1800	40	6
2	1400	40	4
3	1400	40	4
4	1400	20	6
5	1800	60	4
6	1400	60	2
7	1400	40	4
8	1800	40	2
9	1400	60	6
10	1400	20	2
11	1000	60	4
12	1800	20	4
13	1400	40	4
14	1000	20	4
15	1000	40	6
16	1000	40	2
17	1400	40	4

.

3. Results and Analysis

3.1. Key Factor Screening

The significance ranking of factors is presented in

Table 4. Analysis of variance (ANOVA) for key factor screening tests.

Source of Variance	Sum of Squares	Mean Square	F-Value	p-Value	Significance Ranking
A	1.33	1.33	52.30	0.0019	3
B	0.0481	0.0481	1.89	0.2414	7
C	6.42	6.42	252.01	<0.0001	2
D	19.35	19.35	759.26	<0.0001	1
E	0.2523	0.2523	9.90	0.0346	6
F	0.4563	0.4563	17.90	0.0134	5
G	0.6912	0.6912	27.11	0.0065	4
total regression	28.56	4.08	160.05	0.0001	significant

Note: The term is significant when p < 0.05, and p < 0.01 is highly significant.

. Statistical hierarchy of thermal impact is as follows: D (p < 0.01) > C (p < 0.01) > A (p < 0.01) > G (p < 0.01) > F (p < 0.05) > E (p < 0.01) > B (NS). Six parameters demonstrated statistically significant impacts (p < 0.05), with B being non-significant (p > 0.05). Parameters A, D, C, and E exhibited highly significant influences (p < 0.01). These findings align with Zhang Chao et al.’s research [16]. Conversely, Jiang Wei’s study identified roof insulation as critical for temperature regulation in modular buildings [15]. The divergence stems from spatial constraints: miniature cabin volumes (2.25 m²) attenuate roof insulation efficacy.

3.2. Optimal Parameters of Key Factors

3.2.1. Optimal Parameter Determination of Exterior Wall Insulation Thickness (A), Collector Wall Area (D), and Window-to-Wall Ratio (C) of the Toilet House

Figure 4 illustrates single-factor analysis. Exterior wall insulation thickness (A): Temperature rises linearly at 100–200 mm (key inflection point), with diminishing returns beyond 200 mm (Figure 4a). This aligns with XPS insulation’s thermal conductivity (0.032 W/(m·K)), as 200 mm thickness reduces the envelope heat transfer coefficient to ≤0.3 W/(m²·K) (Table 1) while avoiding high cost [15,20]. Window-to-wall ratio (C): A sharp temperature surge occurs at 20–30% (Figure 4b); beyond 30%, nighttime heat loss through glazing (heat transfer coefficient = 1.3 W/(m²·K)) offsets daytime solar gains, making 30% the cost–benefit optimal ratio. Collector wall area (D): Temperature and cost increase linearly with D, and 3.45 m² (maximum available south-facing wall area) is selected to balance radiation absorption and usable toilet space (Figure 4c). The cost–benefit-optimized configuration from single-factor analysis was A = 200 mm, C = 30%, and D = 3.45 m².

3.2.2. Optimal Parameter Determination of Vent Spacing (E), Air Cavity Thickness (F), and Vent Area Ratio (G) of the Solar Collector Wall

Figure 5 identifies feasible ranges for vent spacing (E), air cavity thickness (F), and vent area ratio (G) for subsequent Box–Behnken response surface analysis. Vent spacing (E): 1000–1800 mm was determined as the feasible range, with 1400 mm as the midpoint; temperature growth slows significantly beyond 1400 mm, indicating limited gains from wider spacing (Figure 5a). Air cavity thickness (F): 20–60 mm was selected (midpoint = 40 mm), as temperatures peak at 40 mm and decline sharply with thicker cavities (due to airflow stratification in small toilet spaces, Figure 5b). Vent area ratio (G): 2–6% was set as the range (midpoint = 4%), as 2–4% brings substantial temperature gains while 4–6% shows diminishing returns (Figure 5c).

Response surface outcomes for vent spacing, cavity thickness, and vent area ratio appear in

Table 5. The effects of vent spacing, air cavity thickness, and vent area ratio on toilet room temperature.

Treatment	E (mm)	F (mm)	G (%)	Average Temperature of Toilet Room (°C)	Maximum Temperature of Toilet Room (°C)	Minimum Temperature of Toilet Room (°C)
1	1800	40	6	7.87	20.36	−1.40
2	1400	40	4	7.65	19.81	−1.51
3	1400	40	4	7.61	19.76	−1.58
4	1400	20	6	7.39	19.89	−1.83
5	1800	60	4	7.54	19.31	−1.47
6	1400	60	2	6.93	17.89	−1.75
7	1400	40	4	7.65	19.81	−1.51
8	1800	40	2	7.35	19.13	−1.65
9	1400	60	6	7.58	19.46	−1.44
10	1400	20	2	7.05	19.09	−2.00
11	1000	60	4	7.28	18.69	−1.59
12	1800	20	4	7.53	20.19	−1.77
13	1400	40	4	7.60	19.81	−1.51
14	1000	20	4	7.09	19.19	−1.98
15	1000	40	6	7.57	19.70	−1.52
16	1000	40	2	7.01	18.35	−1.81
17	1400	40	4	7.62	19.74	−1.62

. Using Design-Expert 10, quadratic regression models were developed for three significant responses: mean toilet temperature (WD), maximum temperature (HWD), and minimum temperature (LWD). These models are expressed in Equations (3)–(5).

$$\mathrm{W}\mathrm{D}=7.63+0.1675\mathrm{E}+0.0338\mathrm{F}+0.3175\mathrm{G}-0.0450\mathrm{E}\mathrm{F}+0.0775\mathrm{F}\mathrm{G}-0.2393{\mathrm{F}}^2-0.1492{\mathrm{G}}^2$$

(3)

$$\mathrm{H}\mathrm{W}\mathrm{D}=19.79+0.3825\mathrm{E}-0.3762\mathrm{F}+0.6188\mathrm{G}-0.0950\mathrm{E}\mathrm{F}+0.1925\mathrm{F}\mathrm{G}-0.0693{\mathrm{E}}^2-0.3637{\mathrm{F}}^2-0.3688{\mathrm{G}}^2$$

(4)

$$\mathrm{D}\mathrm{W}\mathrm{D}=-0.155+0.0762\mathrm{E}+0.1662\mathrm{F}+0.1275\mathrm{G}-0.1582{\mathrm{F}}^2-0.0508{\mathrm{G}}^2$$

(5)

In the formula, E is the spacing of ventilation openings in mm; F is the thickness of the air cavity in mm; and G is the area ratio of ventilation holes in %.

Statistical analysis (

Table 6. Model ANOVA for vent spacing, air cavity thickness, and vent area ratio.

Source of Variance	Average Temperature of Toilet Room (°C)			Maximum Temperature of Toilet Room (°C)			Minimum Temperature of Toilet Room (°C)
	Sum of Squares	F-Value	p-Value	Sum of Squares	F-Value	p-Value	Sum of Squares	F-Value	p-Value
E	0.2245	275.88	<0.0001	1.17	374.20	<0.0001	0.0465	28.08	0.0011
F	0.0091	11.20	0.0123	1.13	362.07	<0.0001	0.2211	133.49	<0.0001
G	0.5356	658.35	<0.0001	3.06	979.20	<0.0001	0.1300	78.51	<0.0001
EF	0.0081	9.96	0.0160	0.0361	11.54	0.0115	0.0020	1.22	0.3054
EG	0.0004	0.4917	0.5058	0.0036	1.15	0.3189	0.0004	0.2415	0.6382
FG	0.0240	29.53	0.0010	0.1482	47.39	0.0002	0.0049	2.96	0.1291
E2	0.0030	3.70	0.0957	0.0202	6.46	0.0386	0.0000	0.0078	0.9322
F2	0.2410	296.24	<0.0001	0.5819	186.03	<0.0001	0.1054	63.66	<0.0001
G2	0.0938	115.28	<0.0001	0.4634	148.15	<0.0001	0.0108	6.55	0.0376
residual	0.0057			0.0219			0.0116
lack of fit (LOF)	0.0036	2.25	0.2249	0.0174	5.13	0.0742	0.0011	0.1362	0.9334
pure error	0.0021			0.0045			0.0105
aggregate	1.17			6.73			0.5372

) verifies E/F/G parameters exert extremely significant influences on mean thermal performance (p < 0.0001). For the mean temperature model (WD), p < 0.0001, indicating extreme significance between predictors and response. Lack-of-fit p = 0.2249 (NS) validates model adequacy. R² = 0.9951 and adj-R² = 0.9889 approach unity, with adequate precision of 42.5689. HWD model: p < 0.0001, lack-of-fit p = 0.0742 (NS), R² = 0.9967, adj-R² = 0.9926, precision 57.3795. LWD model: p < 0.0001, lack-of-fit p = 0.9334, R² = 0.9784, adj-R² = 0.9507, precision 19.6220. These metrics confirm the exceptional predictive accuracy across all regression models.

In the coldest month of January, aiming at the comprehensive maximum value of the average temperature, the highest temperature, and the lowest temperature inside the toilet house, the regression equation was solved to find the optimal solution. As shown in Figure 6, the optimal combination of the three significant parameters is a ventilation hole spacing of 1800 mm, an air cavity thickness of 43 mm, and a ventilation hole area ratio of 5.7%.

3.3. Comprehensive Performance of Optimized Passive Solar Toilet System

The TRNSYS simulation platform was used to simulate the hourly variations in indoor temperature between the original passive rural household toilet and the optimized rural household toilet during the heating season, as shown in Figure 7.

The optimized toilet cabin has an average temperature of 10.81 °C during the heating season—79.5% higher than the baseline. In January (the coldest month), the optimized cabin’s average temperature is 7.95 °C, maximum is 20.47 °C, and minimum is −1.42 °C; these values are 4.74 °C, 6.87 °C, and 4.95 °C higher than the baseline, respectively. Subzero hours: 22h (3% total) for optimized vs. 167 h (22.4%) for baseline. The solution effectively eliminates flushing system freeze-ups from sustained hypothermia, guaranteeing functional sanitation in harsh winters.

4. Discussion

4.1. Influence Mechanism of Key Parameters on the Thermal Environment of Toilet Houses

Based on the experimental results, the solar collector wall area, exterior wall insulation thickness, and window-to-wall ratio of the heat-gain window are the core parameters influencing the toilet cabin temperature (p < 0.01), and their mechanism of action is highly consistent with the heat transfer laws of passive buildings. As the “heat source core” of the system, when the area of the solar collector wall increases from 2 m² to 3.45 m², the average temperature of the toilet house shows a linear increase (Figure 4c). This is because a larger heat-collecting area can absorb more solar radiation, heat the airflow in the air cavity through the black heat-absorbing coating, and then raise the indoor temperature via convective heat transfer through ventilation holes [16,21]. However, limited by the small space characteristics of rural household toilets (only 2.25 m²), the area of the solar collector wall cannot be expanded infinitely. The optimal value of 3.45 m² not only ensures radiation absorption efficiency but also avoids the compression of toilet space caused by an excessively high wall proportion while balancing material costs (as reflected by the matching between cost growth rate and temperature increase in Figure 4c).

The influence of exterior wall insulation thickness shows the characteristic of diminishing marginal returns: the temperature rises linearly when the thickness ranges from 100 mm to 200 mm, and the growth rate slows down after exceeding 200 mm (Figure 4a). This is attributed to the low thermal conductivity of the XPS insulation board (0.032 W/(m²·K)). When the thickness increases to 200 mm, the heat transfer coefficient of the toilet house envelope structure drops below 0.3 W/(m²·K) (Table 1). Further increases in thickness make a limited contribution to reducing heat loss but significantly increase material costs. This pattern indicates that excessive pursuit of high insulation thickness in rural toilet renovation may result in resource waste [15,20]. The optimized thickness of 200 mm not only meets thermal requirements but also aligns with the economic affordability of rural areas.

The optimal window-to-wall ratio of the heat-gaining window is 30%, which is consistent with the research conclusion (30–40%) of Qi Qinghua et al. [17] on direct-gain solar buildings in Beijing. However, it differs significantly from the 60% proposed by Luo Wei et al. [22] for Lhasa. The core reason lies in regional climate differences: Beijing has a temperate monsoon climate with a low solar altitude angle and an annual solar radiation (approximately 5000 MJ/m²) much lower than that of Lhasa (approximately 7000 MJ/m²). If the proportion of heat-gaining windows is too high (e.g., 60%), substantial heat dissipation will occur at night due to the high thermal conductivity of glass (1.3 W/(m²·K), Table 1), which instead reduces the average temperature [23]. In contrast, a 30% proportion enables efficient solar radiation intake during the day and minimizes heat loss at night through the thermal insulation performance of double-layer argon-filled glass, achieving a balance between “heat collection and heat preservation.”

4.2. Multi-Parameter Synergistic Effect of the Passive Solar Heating System

The interaction between ventilation hole spacing, air cavity thickness, and ventilation hole area ratio (Table 6) reveals the “synergistic optimization logic” of the passive solar heating system. The temperature reaches its optimal value when the ventilation hole spacing is 1800 mm. This is because if the spacing is too small (e.g., 1000 mm), the airflow in the air cavity tends to form a “short-circuit circulation,” preventing hot air from fully spreading to the entire toilet house. In contrast, a spacing of 1800 mm allows airflow to rise evenly along the solar collector wall and cover the entire toilet house space through the upper ventilation holes [16].

The optimized air cavity thickness of 43 mm differs from the 120 mm reported in the study by Zhang Chao et al. on rural toilets in Qinghai, and the reason lies in the toilet house volume. The toilet house space in this study is only 2.25 m², and a 43 mm air cavity can form a stable “thermal convection layer.” An excessively thick cavity (e.g., 60 mm) will cause airflow stratification, with hot air stagnating in the upper part of the cavity and failing to effectively exchange with the cold indoor air. In contrast, the toilet houses in the Qinghai study have larger spaces, requiring a thicker air cavity to ensure airflow dynamics [23].

The optimal ventilation hole area ratio of 5.7% reflects the balance between “ventilation efficiency and heat loss control”: when the ratio is too low (e.g., 2%), the air convection rate is slow, and heat in the heat-collecting cavity cannot be transmitted to the indoor space in a timely manner; when the ratio is too high (e.g., 6%), hot air inside the toilet house is prone to leakage through the ventilation holes at night, leading to a decrease in the minimum temperature (Figure 5c) [21]. This result indicates that the passive solar heating system does not rely on single-parameter optimization. Instead, it requires multi-parameter synergy to form a closed loop in the three links of “heat collection–convection–heat preservation” to maximize the improvement of the thermal environment effect.

4.3. Long-Term Feasibility of the Optimized Passive Solar Heating System

The long-term feasibility of the system is critical for its practical promotion in rural toilet renovation in cold regions. The optimized passive solar heating system exhibits strong long-term viability: its core components—XPS insulation boards (closed-cell structure, 25–30-year service life per GB/T 10801.2-2021 [24]), anti-corrosion absorber plates, thermally broken frame double glazing, and PVC vents with adjustable shutters—are resistant to freezing-thawing cycles and extreme temperatures (−30 °C to 60 °C), ensuring reliable operation for over 20 years. Operating on natural solar radiation and convection, it requires zero operational energy and minimal maintenance (annual glass cleaning and vent inspection, <2 h/year, manageable by rural households). Economically, the additional 800–1200 CNY per toilet cost is fully covered by national subsidies (1000–3000 CNY/household in cold regions), and it eliminates annual anti-freezing expenses (100–200 CNY) of conventional toilets, delivering cumulative savings over 20+ years. Additionally, multi-parameter synergy (insulation + solar collection + ventilation) prevents complete system failure from minor component issues, further enhancing long-term stability supporting sustainable promotion in rural cold regions.

5. Conclusions

This study optimizes passive solar heating systems for cold-region rural toilets, addressing the gap of toilet-specific solutions. Key findings: six parameters (solar wall area, etc., p < 0.05) significantly affect temperature; the optimal configuration (collector wall area 3.45 m², window-to-wall ratio 30%, etc.) lifts heating season average temp to 10.81 °C (79.5% higher than baseline), with January’s mean 7.95 °C, eliminating fixture freezing.

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Practical implications: The extra cost per toilet of CNY 800–1200 fits national subsidies (CNY 1000–3000 per household); widely available components (XPS insulation, aluminum absorber plates) and simple installation suit rural construction capacity. It can be scaled to other cold regions (e.g., 10–15% larger solar walls in Heilongjiang), supporting China’s rural sanitation plans and carbon goals.

(2)

Future research: Integrate passive heating with low-cost thermal storage (e.g., PCMs in air cavities) to cut subzero hours; use CMIP6 data to optimize for climate change; and conduct rural field trials to refine user-centric designs (e.g., detachable collector walls), boosting adoption.