Optimizing Kang-to-Room Area Ratios for Thermal Comfort in Traditional Chinese Architecture: An Empirical and Simulation-Based Approach

Abstract

Traditional Chinese Kang heating systems have been used for over two millennia in northern China, yet their thermal efficiency and optimal design parameters lack scientific validation. This study aims to establish evidence-based guidelines for Kang-to-room area ratios to enhance thermal comfort and energy efficiency in rural architecture. We conducted direct measurements in a controlled experimental house (24 m²) in Huludao City, collecting temperature and humidity data from Kang surfaces and interior spaces over five-day periods. A benchmark curve for heat flux density was developed based on specific fuelwood consumption rates (1 kg/m²). TRNSYS simulations were employed to validate experimental data and analyze thermal performance in the historical Qingning Palace (352 m²) at Shenyang Imperial Palace. The benchmark curve demonstrated high accuracy with a Mean Absolute Error of 0.46 °C and Root Mean Square Error of 0.53 °C when compared to measured temperatures over the 48 h validation period; these values are well within acceptable ranges for calibrated thermal models. Simulations revealed optimal thermal comfort conditions when heat dissipation parameters were scaled appropriately for building size. The optimal Kang-to-room area ratio ranges from 0.28 to 0.69, with the existing Qingning Palace ratio (0.34) falling within this range, validating traditional design wisdom. This research provides a scientific foundation for sustainable architectural practices, bridging traditional knowledge with contemporary thermal engineering principles for both heritage preservation and modern rural construction applications.

1. Introduction

The Kang is a unique architectural feature in northern China that integrates heating, sleeping, and daily activities, holding profound cultural significance for harmonizing energy flow and fostering balance with the environment. Its history spans over two thousand years, traceable to the Qin and Han dynasties, with early prototypes recorded in the Zuo Zhuan (“左传”in Chinese) [1] involving charcoal heaters beneath thrones and earth beds with underlying fires described in the “Compilation of the Northern Alliance of the Three Dynasties” [2]. By the Tang Dynasty (618-907 AD), it evolved into a raised brick or clay platform heated by fire, radiating warmth throughout the room (Figure 1 and Figure 2).

In modern rural households, the Kang is often supplemented with coal or electricity for thermal comfort, increasing energy consumption and highlighting the need for optimization through heat output-to-biomass fuel ratios. This promotes energy conservation, sustainability, and integration with modern technologies, aiming to minimize environmental and economic impacts.

Research on traditional Chinese Kang heating systems has evolved over the past decade from descriptive studies to performance optimization, yet gaps limit applications in sustainable rural design. Contemporary research spans fundamental thermal characterization using CFD simulations for flue gas patterns and temperature distributions [3], with Yu et al. (2020) classifying systems by cultural backgrounds and identifying types like linear, bend, and houseful Kangs (average plate temperatures 10–20 °C, standard deviation 2–10 °C) [4]. Simulation platforms like IDA-ICE [5] and TRNSYS/ANSYS have advanced energy modeling. Performance is evaluated by Chinese Standard GB7651-87 [6] for fuelwood (dry pine wood with a moisture content < 15% and a calorific value of 1.2 × 10⁷ J/kg) or straw stoves, though designs rely on craftsman experience despite widespread use in 85% of northern rural homes.

Improvement strategies include combustion optimization with smoldering and ventilation ([7], yielding 30–49% temperature increases), heat transfer enhancement via forced convection ([8], achieving 625–1170 W output), and modular modeling ([9], noting <20% efficiencies). Hybrid integrations address demands, such as combined floor-Kang systems ([10], saving 27.3% energy) and solar-Kang setups ([11], reducing pollution). Tandem models improve spatial efficiency [12].

A critical gap is the lack of validated spatial design guidelines; Zhuang et al. (2009) showed Kangs meet 50–80% heating loads [13], occupying 30–50% floor space [14], but no frameworks exist for optimal ratios across scales. Liu et al. (2024) focused on solar-coupled systems rather than heritage practices [15].

The literature reveals four key gaps: (1) quantitative frameworks for Kang-to-room ratios, relying on tradition over science; (2) multi-scale validation beyond individual buildings; (3) climate adaptability outside extreme cold regions; and (4) integrated assessments of thermal, spatial, environmental, and cultural factors. Addressing these requires interdisciplinary thermal modeling and field validation.

To bridge these gaps, this study establishes an optimal Kang-to-room ratio for sustainable rural architecture in northern China via measurements and simulations, with the following objectives: (1) develop a benchmark curve for time-dependent heat flux under controlled fuelwood rates; (2) validate it using TRNSYS for Qingning Palace; and (3) determine evidence-based ratios for thermal comfort and efficiency. These objectives interconnect to apply traditional knowledge scientifically.

2. Materials and Methods

This study utilizes two distinct buildings: a modern experimental house in Huludao City, Liaoning Province, and the historical Qingning Palace within the Shenyang Imperial Palace. Experiments and simulations were conducted using these structures. The research employs direct measurements and computational simulations, with detailed methodologies outlined in Section 2.3.

This study employs a three-phase experimental approach to establish optimal Kang-to-room area ratios. The research design includes two controlled field experiments and computational validation using TRNSYS simulations (TRNSYS 18, Solar Energy Laboratory, University of Wisconsin-Madison, Madison, WI, USA). Experiment 1 involved five-day temperature and humidity measurements (5–10 March 2023) in a purpose-built experimental house to develop a benchmark heat flux density curve. Experiment 2 conducted an additional five-day validation study (12–17 March 2023) in the same facility to verify the accuracy of the benchmark curve through comparison with simulation results. Finally, TRNSYS modeling was applied to the historical Qingning Palace to determine optimal heating parameters and validate the scalability of findings across different building scales. This comprehensive approach combines direct field measurements with computational modeling to ensure both empirical validity and theoretical robustness.

2.1. Experimental Methods

The constant heat flux methodology is grounded in fundamental heat transfer principles and dimensional analysis theory. Traditional Kang systems operate as thermal mass heating devices where heat storage and release characteristics are primarily governed by surface area rather than absolute size. The scaling approach is theoretically justified through three key principles.

Thermal Similarity Principle: Heat transfer from Kang surfaces follows established natural convection and radiation laws that are independent of absolute scale when geometric similarity is maintained. The Nusselt number correlations demonstrate that heat transfer coefficients remain consistent across different surface areas under similar temperature and environmental conditions.

Constant Energy Input per Unit Area: By maintaining constant fuel consumption per unit Kang area (1 kg/m²), we preserve the fundamental energy density characteristics that determine thermal performance. This approach ensures that the heat storage capacity per unit area remains constant, allowing for proportional scaling of thermal outputs.

Thermal Comfort Optimization: Rather than applying fixed geometric ratios, our methodology determines optimal Kang-to-room area relationships based on achieving target thermal comfort conditions (PMV = 0 ± 0.5). This thermal comfort-driven approach ensures that the scaling maintains functional equivalence across different building sizes.

Experiment 1 aimed to calculate the heat flow density of the Kang. Data were collected through a 5-day investigation from 7:00 a.m. on 5 March to 7:00 a.m. on 10 March 2023. Experiment 2 was designed to validate the accuracy of heat flow density calculations in Kang’s heat dissipation simulation. Another five-day investigation was conducted at the same residence, from 7:00 a.m. on 12 March to 7:00 a.m. on 17 March. The objective of experiment 2 was to substantiate the practices devised by our practitioners, employing direct measurement methodologies to establish direct correlations for heat flux density calculations.

Subsequently, an exploration of historical wisdom led to studying the Qingning Palace (Figure 3). This palace, a notable early construction within the Shenyang Imperial Palace (1627–1636 AD), served as Emperor Huang Taiji and Empress Xiaoduan’s private dormitory during the Houjin Dynasty. To comprehensively examine its thermal characteristics, this study conducted detailed architectural surveys and developed floor plans (Figure 4), then employed Rhinoceros software (Rhino 7, Robert McNeel & Associates, Seattle, WA, USA) to create a comprehensive digital model (Figure 5). Subsequent thermal simulations and parametric analyses were conducted using the TRNSYS platform.

2.2. Experimental Materials

(1) Experimental House (Figure 6): Experiment 1 and part of experiment 2 were facilitated, controlled, and conducted within this setup. The house measures 6 m in length, 4 m in width, and 3 m in height, with a total floor area of 24 m². It features a traditional Kang bed with a surface area of 4.8 m², occupying 20% of the room area. The walls and roof are made of 240 mm thick concrete with a thermal conductivity of 1.561 W/(m·K), and the windows are 150 mm thick glass with a thermal conductivity of 1.104 W/(m·K). The positioning of measurement points is illustrated in Figure 7.

(2) Qingning Palace in Shenyang Imperial Palace (Figure 3, Figure 4 and Figure 5): As part of the UNESCO World Heritage list, Shenyang Imperial Palace served as a historical case for validation in experiment 2. The architectural drawings and dimensional data were obtained from the official architectural survey conducted by the Shenyang Imperial Palace Museum (2019) [16] and cross-referenced with the UNESCO World Heritage Site documentation (UNESCO World Heritage Centre, 2004) [17]. Floor plans and elevation drawings were verified by the authors. The specific Kang dimensions and positioning were documented through direct field measurements conducted with permission from the palace administration in accordance with heritage preservation protocols. This palace has a floor area of 352 m², with existing Kang beds covering 121 m² (approximately 34% of the room area). The palace’s walls are constructed of 500 mm thick brick with a thermal conductivity of 0.869 W/(m·K), and the roof comprises 100 mm thick tiles with a thermal conductivity of 3.704 W/(m·K).

2.3. Research Methodology

We divided the research methodology into three phases, each outlined in Figure 8.

2.3.1. Part 1: Heat Flow Density Calculation of Kang

(1)

Direct Measurements in the Experimental House

As shown in the left column of Figure 8, our initial direct measurements were conducted within the dwelling. For the Kang area of 4.8 square meters, we burned 4.8 kg of fuelwood daily at 7:00 a.m. to ensure proportional heating. Fuelwood combustion followed a standardized protocol: 4.8 kg of dry pine wood (moisture content < 15%, calorific value 1.2 × 10⁷ J/kg) was loaded into the Kang furnace at 7:00 a.m. daily. Due to its historical significance, acquiring direct data within the Qingning Palace premises proved challenging. We systematically constructed a purpose-built experimental house (Figure 6) as a controlled research facility to gather comprehensive thermal data, focusing on Kang thermal source dissipation patterns under standardized conditions. This experimental structure, measuring 6 m in length, 4 m in width, and 3 m in height with a total floor area of 24 m², was specifically designed to accommodate a traditional Kang heating system while enabling precise environmental monitoring. The facility features concrete walls and roof construction (240 mm thick, thermal conductivity 1.561 W/(m·K)) to provide consistent thermal boundary conditions, with strategically positioned measurement points (Figure 7) to capture comprehensive temperature and humidity data throughout the experimental space. The use of a standardized heat flux density approach allows for scalable analysis across different building sizes while maintaining consistent fuel consumption per unit area (1 kg/m²), providing a universal benchmark for comparing Kang performance regardless of room dimensions. This methodology enables the derivation of area ratios based on thermal comfort requirements rather than arbitrary proportions, ensuring that the Kang-to-room relationship is thermally optimized.

We positioned temperature and humidity recorders on Kang’s surface (Figure 9 and Point 4 in Figure 7) and walls at a 2-m height from the house (Points 1, 2, & 3 in Figure 7). Over 5 days, we collected and plotted temperature and humidity changes. Extracting a consistent 24 h dataset.

The sensors we used are Testo 175H1 data loggers (Part Number: 0572-1754, Testo SE & Co. KGaA, Titisee-Neustadt, Germany) throughout our experiments. These devices feature NTC thermistor temperature sensors with ±0.4 °C accuracy across the −20 °C to +55 °C range and capacitive humidity sensors with ±2% RH accuracy for the 0–100% RH range. The sensors provide 0.1 °C and 0.1% RH resolution with an IP54 protection rating suitable for building environment monitoring.

The sensors positioned at measurement Points 1, 2, and 3 were specifically designed to measure wall surface temperatures rather than floor temperatures. The Testo 175H1 features an external probe configuration that enables direct contact with wall surfaces at the specified two-meter height. The sensors were mounted using adhesive backing that ensures intimate thermal contact with the wall surface while maintaining proper orientation for accurate temperature measurement.

(2)

Thermal Flux Density Computation

The overall heat dissipation of a large-scale Kang is considered the sum of the unit-area Kang’s dissipation (Figure 10). Multiplying the Kang’s thermal flux density by its surface area determines its heat dissipation rate.

2.3.2. Part 2: Validity of Kang’s Heat Flow Density Verification Benchmark Curve

As depicted in the middle column in Figure 8, we computed a benchmark curve in experiment 1. To validate the effectiveness of this benchmark curve, we conducted a second experiment inside the testing house.

Subsequently, we selected the most stable 48 h data points from the curve. Using the meteorological data at that time and the benchmark curve data for heat flux density, we simulated the thermal environment of the house using TRNSYS software. The simulated data for the 48 h was then compared with the concurrently measured data to observe the error rate and curve fitting degree, thereby validating the effectiveness of the benchmark curve.

The specifications of the simulated building are as follows: it boasted a length of 6 m, a width of 4 m, and a height of 3 m. The thermal parameters of the outer protective structure had been methodologically configured in accordance with the present conditions. The thermal transmittance (U-value) calculations account for all thermal resistances according to ISO 6946:2017 standards [18].

For the exterior walls composed of 240 mm concrete:

U = 1/(Rsi + Rwall + Rso)

(1)

where Rsi = 0.13 m²·K/W (internal surface resistance)

Rwall = thickness/conductivity (wall thermal resistance)

Rso = 0.04 m²·K/W (external surface resistance)

Similar calculations were applied to the roof and windows, accounting for glazing, frame, and edge effects (specific values presented in Section 3.2).

2.3.3. Part 3: Simulation and Analysis of the Thermal Environment of Qingning Palace

As shown in the right column in Figure 8, the simulations were conducted using the method of controlled variables. Based on the benchmark curve of the heat flux density obtained earlier, we adjusted the heat dissipation value of the Kang while keeping other indoor and outdoor parameters constant. To ensure consistent simulation of outdoor meteorological conditions, we utilized Typical Meteorological Year (TMY) weather data (weather file: CHN_Liaoning.Shenyang.543420_CSWD.epw) obtained from the EnergyPlus weather database (https://energyplus.net/weather accessed on 31 March 2023) [19]. The TMY data represent statistically typical weather conditions derived from long-term meteorological observations and provide standardized hourly parameters, including outdoor air temperature, relative humidity, solar radiation, and wind conditions. For our analysis, we selected the coldest representative day from the TMY dataset, which exhibits outdoor temperature characteristics equivalent to extreme winter conditions experienced on 20 January 2023. The selected meteorological profile ensures reproducible simulation conditions while representing the most challenging thermal performance scenario for the Kang heating system.

The scaling methodology proceeds through systematic optimization rather than simple geometric scaling. We conducted parametric studies using multiples of the experimental benchmark curve (0.5×, 1.0×, 1.5×, 2.0×, and 2.5×) to identify the heat dissipation rate that achieves optimal thermal comfort (PMV = 0 ± 0.5) in the Qingning Palace. This optimization-based approach ensures that the Kang area is determined by thermal performance requirements rather than historical precedent. The resulting optimal ratio (34% Kang-to-room area for Qingning Palace versus 20% for the experimental house) demonstrates that larger spaces require proportionally larger Kang areas to maintain thermal comfort, validating the thermal optimization approach over simple geometric scaling. Subsequently, we set up three control groups with heat dissipation values that fluctuated above and below the determined value. The TRNSYS software was used to simulate the indoor space of the Qingning Palace, and the average temperature obtained from the simulations was recorded.

Subsequently, we performed a comparative analysis of the three average temperature curves and selected the optimal heat dissipation value to plot the relationship curve between the Kang area and the combustion quantity per square meter. Furthermore, we analyzed the relationship between room area, combustion quantity, and Kang area.

Qingning Palace’s dimensions are as follows: length 22 m, width 12.5 m, and height 4 m. The thermal characteristics of the outer protective structure are set based on current conditions: The thermal transmittance calculations for Qingning Palace envelope components follow a comprehensive multi-layer analysis.

External brick walls (500 mm thick):

U = 1/(R_si + R_brick + R_so)

where R_brick = thickness/conductivity

Tile roof construction (100 mm thick):

U = 1/(R_si + R_tile + R_air + R_structure + R_so)

including air cavity and structural timber elements.

Traditional windows with 200 mm wooden frames: Glazing and frame components were analyzed separately, with a combined U-value using area weighting (specific values presented in Section 3.3).

2.3.4. Mathematical Heat Transfer Model and Assumptions

Model Assumptions:

(1)

Uniform Heat Distribution: Heat distribution across the Kang surface is assumed uniform, neglecting local variations due to flue positioning and internal geometry complexity.

(2)

Steady-State Thermal Properties: Material thermal properties remain constant over the operational temperature range, based on values in the literature for traditional building materials.

(3)

Natural Convection Regime: The Kang surface operates under natural convection conditions with Rayleigh numbers ranging from 10⁷ to 10¹⁰, confirming turbulent natural convection.

(4)

Negligible Air Infiltration: Building air leakage is minimal due to traditional construction methods, validated through blower door testing showing air changes of less than 0.5 ACH.

(5)

Gray Body Radiation: Surface emissivities are assumed constant at 0.9 for clay-based Kang surfaces, consistent with published values for similar materials.

(6)

Conductive Heat Transfer Treatment: Conductive heat transfer within the Kang structure is implicitly incorporated through measured surface temperatures rather than explicitly modeled. This approach is justified because (a) internal conduction determines the surface temperature distribution measured experimentally, (b) heat losses through conduction to foundations and adjacent structures are minimal (<10% of total heat transfer), (c) the dominant heat transfer mechanisms are convection and radiation from the heated surface, and (d) validation results confirm this approach adequately captures system behavior.

The total heat flux from the Kang surface comprises convective and radiative components, as illustrated in Figure 11.

The Kang thermal performance is modeled using fundamental heat transfer principles, combining convective and radiative mechanisms. The total heat flux density from the Kang surface is expressed as follows.

Finally, the convective heat transfer of the bed surface is calculated as follows [20]:

q = q_c + q_r

(2)

where q_c represents convective heat transfer and q_r represents radiative heat transfer.

Convective Heat Transfer Model:

The convective heat transfer from the Kang surface follows natural convection correlations for heated horizontal surfaces [21]:

$$q_c=h(t_w-t_f)$$

(3)

where t_w is the temperature of the Kang surface and t_f is the air temperature near the Kang surface.

The convective heat transfer coefficient is determined using established natural convection correlations. For horizontal heated plates with the heated surface facing upward, several well-established correlations are available in the literature. The Nusselt number can be calculated using correlations such as those developed by McAdams (1954) [22]:

$$\mathrm{h}={\displaystyle \frac{\lambda }{x}}\times N_u$$

(4)

$$N_u=0.15{\left(G_r{P}_r\right)}^{\frac{1}{3}} \mathrm{for} {10}^7<R_a{P}_r<{10}^{11}$$

(5)

where $h$ represents the heat transfer coefficient, which quantifies the amount of heat that can be transferred per second through a 1 m × 1 m surface area when the temperature difference between the fluid and the solid surface is 1 K; λ is the heat transfer coefficient of the Kang board; and x is the length of the Kang surface with the width = 1.00 m.

N_u is the Nusselt number, G_r is the Grashof number, and P_r is the Plante criterion.

This correlation was chosen because it applies to our operational Rayleigh number range (R_a = 2.1 × 10⁸ to 1.8 × 10⁹) and it accounts for turbulent natural convection typical of heated horizontal surfaces. Experimental validation shows ±8% accuracy for similar applications [23].

Radiative Heat Transfer Model:

The radiative heat exchange between the Kang surface and surrounding enclosures is calculated using the following equation [24]:

$$q_r={\sum }_{j=1}^n{\sigma }_b{\epsilon }_i{X}_{i,j}(T_i^4-T_j^4)$$

(6)

σ_b is the Stefan–Boltzmann constant, which takes the value of 5.67 × 10⁻⁸ W /(m²·K⁴); ε_i denotes the emissivity of the Kang’s surface relative to each enclosure; X_i,j denotes the emissivity of the Kang’s surface relative to each enclosure; and T_i and T_j are the absolute temperatures (in Kelvin) of the Kang’s outer surface and the inner surface of each enclosure, respectively [25].

The heat generation in the combustion chamber follows a characteristic temporal profile based on biomass combustion physics. Based on the surface heat flux measurements, we infer three distinct phases: (1) ignition and flame development (0–1 h) with gradual heat buildup, (2) active combustion (1–3.5 h) reaching peak heat generation at 3.5 h when all fuel is actively burning, and (3) thermal decay (3.5–24 h) as stored thermal energy is gradually released from the Kang thermal mass. This combustion profile directly drives the surface heat flux density pattern presented in Section 3.1, with the 3.5 h peak corresponding to inferred maximum combustion chamber heat generation.

2.3.5. TRNSYS Model Configuration and Parameters

The TRNSYS 18 simulation environment [26] was configured with the following specific model components and parameters in

Table 1. TRNSYS model components and parameters.

Parameter Category	Component	Experimental House	Qingning Palace
Building Geometry	Length (m)	6	22
	Width (m)	4	12.5
	Height (m)	3	4
	Total Volume (m3)	72	1100
	Thermal Zones	Single zone	Multi-zone
Wall Construction	Material	Concrete	Brick
	Thickness (mm)	240	500
	Thermal Conductivity (W/m·K)	1.561	0.869
	Density (kg/m3)	2400	1800
	Specific Heat (J/kg·K)	1000	900
Roof Construction	Material	Concrete	Tiles
	Thickness (mm)	240	100
	Thermal Conductivity (W/m·K)	1.561	3.704
	Density (kg/m3)	2400	2000
	Specific Heat (J/kg·K)	1000	800
Window Properties	Glass Thickness (mm)	150	200
	U-value (W/m2·K)	6.0	5.5
	Solar Heat Gain Coefficient	0.7	0.7
Kang Heat Source	Surface Area (m2)	4.8	121
	Heat Input Profile	Experimental benchmark curve	Experimental benchmark curve
	Internal Gain Distribution	100% convective	100% convective
Weather Data	Location	Huludao City, Liaoning Province	Huludao City, Liaoning Province
	Coordinates	40.7° N, 120.9° E	40.7° N, 120.9° E
	Data Format	TMY3 hourly	TMY3 hourly
	Critical Design Day	20 January 2023 (−18 °C)	20 January 2023 (−18 °C)
Simulation Control	Time Step (hours)	0.25	0.25
	Simulation Period	48 h (validation)	Annual (design analysis)
	Convergence Tolerance	0.001	0.001
	Integration Method	Modified Euler	Modified Euler

, which contains the input data for the TRNSYS model, including building geometry, material properties, Kang heat source profiles, weather data, and simulation controls. The overall model configuration and component relationships are illustrated in Figure 12.

2.3.6. Building Heat Loss Calculations and Energy Balance

To establish accurate energy balance validation, comprehensive heat loss calculations were performed for both experimental buildings using standard building physics principles. Equations (7)–(9) are based on ISO 13790:2008 [27].

Transmission Heat Loss:

The transmission heat loss through building envelope components is calculated as

Qtrans = Σ(U_i × A_i × ΔT)

(7)

where U_i represents the thermal transmittance, A_i is the surface area, and ΔT is the temperature difference across each building element.

Ventilation Heat Loss: Natural ventilation heat loss is calculated as

Q_vent = 0.33 × n × V × ΔT

(8)

where n represents air change rate (0.5 ACH for both buildings based on infiltration testing), V is the building volume, and 0.33 is the volumetric heat capacity of air.

Energy Balance Validation:

The steady-state energy balance equation is as follows:

Q_input = Q_trans + Q_vent

(9)

(specific calculations presented in Section 3.3).

The steady-state calculations above provide reference values for building thermal characteristics. However, the actual energy balance validation in this study employs TRNSYS dynamic simulations that account for temporal variations in temperature differences and thermal mass effects throughout the experimental measurement period, providing a more accurate representation of real operational conditions.

2.3.7. Rationale for Constant Heat Flux Approach

The constant heat flux rate methodology is justified by three key principles:

(1)

Thermal Equivalence: By maintaining consistent fuel consumption per unit area (1 kg/m²), we establish a standardized thermal input that can be scaled proportionally for different room sizes while preserving the fundamental heat transfer characteristics of the Kang system.

(2)

Scalability: This approach allows for direct comparison between the experimental house (24 m²) and Qingning Palace (352 m²) by using multiplier factors (4.8× and 220×, respectively) that maintain the same underlying thermal performance curve.

(3)

Design Optimization: The constant flux rate provides a basis for determining optimal area ratios based on thermal comfort requirements (PMV values) rather than direct guesswork, ensuring that the Kang size is thermally justified for any given room size.

2.4. Thermal Comfort Assessment

To validate the scaling approach, we performed dimensional analysis using the Buckingham π theorem to identify the governing dimensionless parameters. The analysis reveals that the Kang’s thermal performance is governed by three primary dimensionless groups: the modified Rayleigh number (Ra*), the geometric aspect ratio (L/H), and the thermal capacity ratio (ρcp,kang/ρcp,air). Since these dimensionless groups remain consistent between the experimental house and Qingning Palace when proper scaling is applied, the constant heat flux approach maintains thermal similarity across different scales.

Furthermore, validation through energy balance calculations demonstrates that the scaled Kang areas produce heat outputs consistent with building heat loss requirements. The constant heat flux rate methodology is justified by three key principles: (1) Thermal Equivalence: By maintaining consistent fuel consumption per unit area (1 kg/m²), we establish a standardized thermal input that can be scaled proportionally for different room sizes while preserving the fundamental heat transfer characteristics of the Kang system. (2) Scalability: This approach allows for direct comparison between the experimental house (24 m²) and Qingning Palace (352 m²) by using multiplier factors (4.8× and 220×, respectively) that maintain the same underlying thermal performance curve. (3) Design Optimization: The constant flux rate provides a basis for determining optimal area ratios based on thermal comfort requirements (PMV values) rather than direct guesswork, ensuring that the Kang size is thermally justified for any given room size. (Validation of these outputs is presented in Section 3.4.)

The Predicted Mean Vote (PMV) was calculated following Fanger’s model (ISO 7730:2005) [28] using the CBE Thermal Comfort Tool (Center for the Built Environment, University of California, Berkeley, CA, USA, https://comfort.cbe.berkeley.edu/, accessed on 15 March 2023) [29]. Boundary conditions were defined based on typical residential occupancy patterns and measured environmental conditions. Input parameters were standardized as follows: a metabolic rate of 1.0 met representing seated, quiet activities typical of residential occupancy during heating season; a clothing insulation of 1.5 clo corresponding to typical winter indoor clothing including long-sleeved shirt, trousers, sweater, and shoes, justified by traditional clothing practices in northern China during cold months; an air velocity of 0.1 m/s representing still air conditions common in residential spaces without mechanical ventilation; a relative humidity of 40% based on measured average conditions during the experimental period; air temperature values as simulated or measured for each scenario; and mean radiant temperature assumed equal to air temperature as a simplified approach for initial thermal comfort assessment, acknowledging that this assumption may underestimate radiant effects from heated Kang surfaces.

2.5. Data Analysis Methods

(1)

Statistical Analysis: Microsoft Excel (2019, Microsoft Corporation, Redmond, WA, USA) and MATLAB (R2021a, The MathWorks, Inc., Natick, MA, USA) were used for data processing, calculations, and plotting graphs.

(2)

Error Analysis: The mean absolute error (MAE) and root mean square error (RMSE) were calculated between simulated and measured temperatures.

(3)

Thermal Comfort Metrics: The Center for the Built Environment Thermal Comfort Tool was utilized to compute PMV values based on simulated indoor conditions.

2.6. Assumptions and Simplifications

(1)

Uniform Heat Distribution: Uniform heat distribution from the Kang’s surface was assumed, neglecting the complexity of internal flue designs.

(2)

Negligible Air Infiltration: Minimal air leakage in the experimental house and Qingning Palace was assumed due to building tightness.

(3)

Constant Material Properties: The thermal properties of materials were considered to be constant over the temperature range studied.

3. Results

3.1. Experiment 1 Data and the Heat Flow Density Results

3.1.1. Data Analysis Discussions

The operational temperature range was observed to be 15–55 °C, validated by values in the literature for traditional building materials. The comprehensive temperature and humidity data collected at all measurement locations are summarized in

Table 2. Data collection.

Location	Highest Temperature (°C)	Lowest Temperature (°C)	Average Temperature (°C)	Reference Figure
Heated Bed Surface	53.1	18.1	34.2	Figure 13
Indoor Measurement Point 1	22.0	13.7	18.7
Indoor Measurement Point 2	21.9	10.1	15.6
Indoor Measurement Point 3	22.0	13.6	18.5
Indoor Measurement Point 4	28.9	15.4	21.2

, which presents the highest, lowest, and average values recorded during the experimental period.

Figure 13 reveals distinct thermal and humidity response patterns across all measurement locations during the five-day experimental period. The Kang’s surface temperature (orange line) demonstrates pronounced diurnal cycles, reaching peak values of approximately 50 °C during active heating periods and declining to ambient levels of 30 °C during non-operational phases. This cyclic behavior confirms the effectiveness of the daily 7:00 a.m. fuel loading protocol in maintaining consistent thermal output patterns.

The indoor measurement points exhibit varied thermal responses based on their spatial positioning relative to the Kang system. Measurement Point 4, located directly on the Kang surface, shows the highest temperature variations (purple line), ranging from 15 °C to 29 °C, demonstrating the direct thermal influence of the heated platform. Points 1, 2, and 3, positioned on walls at a two-meter height, display more moderate temperature fluctuations between 13 °C and 22 °C, indicating effective heat distribution throughout the room volume.

Relative humidity measurements reveal inverse correlations with temperature patterns across all monitoring locations. During peak heating periods, relative humidity levels decrease to 30–40% at most measurement points, while rising to 60–80% during cooler periods. This relationship demonstrates the Kang system’s dual function in providing both thermal comfort and humidity regulation within the indoor environment.

The synchronized temperature and humidity variations across multiple measurement points validate the spatial representativeness of our monitoring network and confirm the uniform thermal field distribution achieved by the traditional Kang heating configuration.

3.1.2. Temperature Conversion and Calculation

Following this, we selected temperature data covering 23 h from the dataset (from 7:00 a.m. on 9 March to 6:00 a.m. on 10 March). The complete dataset is included in Supplementary Materials S1.

Heat flux density calculations were performed using the temperature data collected during the experimental period. The computational methodology followed the mathematical framework established in Section 2.3.4, with all material properties and boundary conditions specified in

Table 3. Complete calculation datasets.

Material	Thermal Conductivity (W/m·K)	Density (kg/m3)	Specific Heat (J/kg·K)	Thickness (mm)	Reference
Experimental House
Concrete (walls/roof)	1.561	2400	1000	240	Kim et al. (2003) [30]
Glass (windows)	1.104	2500	750	150	Incropera et al. (2017) [20]
Qingning Palace
Brick (walls)	0.869	1800	900	500	Vasić et al. (2010) [31]
Tiles (roof)	3.704	2000	800	100	GreenSpec [32]
Glass (windows)	1.104	2500	750	200	Incropera et al. (2017) [20]
Wood (window frames)	0.588	600	2400	200	IESVE (2021) [33]
Air Properties (18 °C)
Dry air	0.0259	1.2	1005		Lemmon & Jacobsen (1985) [34]

Note: for Tiles (roof), the thermal conductivity of 3.704 W/m·K is estimated for dense, reinforced concrete tiles common in historical roofs, where values can exceed standard clay tile ranges (typically 0.5–2.5 W/m·K) due to composite construction or high-density aggregates.

(properties sourced from the listed references). Complete calculation datasets are provided in Supplementary Materials S2.

For Wood (window frames), the thermal conductivity of 0.588 W/m·K accounts for moisture-affected or treated wood in heritage frames, where values can rise from base levels (0.1–0.2 W/m·K dry) to 0.5–0.6 W/m·K with 20–30% moisture content typical in northern China climates.

To characterize the temporal evolution of thermal output from the Kang heating system, we developed a standardized heat flux density profile based on controlled experimental conditions with 1 kg/m² daily fuelwood consumption (Figure 14). This curve serves as the fundamental boundary condition for all subsequent computational fluid dynamics simulations and represents the core thermal behavior that drives indoor environmental conditions throughout the heating cycle.

The experimental data reveal three distinct operational phases that correspond to different combustion and heat transfer mechanisms. During the initial 4.5 h period, heat flux density increases rapidly from 25 W/m² to a maximum of 82 W/m², reflecting the combined effects of active combustion and thermal energy accumulation within the Kang thermal mass. The peak at 3.5 h represents the critical transition point where active combustion ceases and stored thermal energy becomes the primary heat source. Following this peak, the system enters an exponential decay phase lasting from hours 5 to 13, during which heat flux density decreases rapidly as stored thermal energy is released through conduction and convection processes. The final phase, spanning hours 13 to 23, exhibits a gradual approach to steady-state conditions with heat flux density stabilizing near 20 W/m², indicating minimal residual heat release.

This thermal profile provides essential input parameters for numerical modeling of indoor air quality and thermal comfort conditions. By utilizing this standardized curve as the boundary condition in our computational analyses, we establish a consistent foundation for evaluating optimization strategies and design parameters for Kang heating systems. The curve enables systematic investigation of how thermal output patterns influence indoor environmental quality, air circulation patterns, and energy efficiency performance under various operational scenarios.

This curve represents the standardized thermal output profile derived from experimental measurements under controlled conditions and serves as the fundamental boundary condition for computational fluid dynamics simulations presented in subsequent analyses.

The equation describing the heat flux density as a function of time can be briefly expressed as follows:

$$T_{s\left(t\right)}=\left\{\begin{array}{c}20+15t (0<t\le 4.5)\\ 80e^{-0.3\left(t-4.5\right)}+10 (t>4.5)\end{array}\right.$$

(10)

where (t) represents time in hours, and (T_s(t)) denotes the heat flux density measured in watts (W).

3.2. Computational Model Validation Through Experiment 2 Comparison

To validate the accuracy and reliability of our computational fluid dynamics model, we conducted a comprehensive comparison between simulated and experimentally measured indoor air temperatures using data from experiment 2. This validation process serves as a critical quality assurance step that establishes the credibility of our numerical modeling approach for subsequent optimization analyses.

The validation methodology employed outdoor temperature conditions recorded during experiment 2, with heat flux boundary conditions derived from our benchmark curve scaled by a factor of 4.8 to match the experimental house configuration. Indoor air temperature simulations were performed using TRNSYS software, focusing on the central monitoring location within the experimental house as the primary validation point.

For rigorous comparison, we selected the most stable 48 h temperature dataset from experiment 2 and calculated corresponding average temperatures for each measurement interval. These experimental values were systematically compared with TRNSYS-simulated average temperatures for the same spatial zone and temporal period. The validation results demonstrate the model’s capability to accurately predict indoor thermal conditions under typical Kang heating system operation.

The comparison reveals strong agreement between simulated and measured indoor air temperatures throughout the complete heating cycle (Figure 15). Both temperature profiles exhibit identical thermal behavior patterns, with synchronized minimum temperatures occurring at the 8th hour (12.7 °C simulated versus 12.6 °C measured, representing a deviation of only 0.1 °C). Peak temperatures on the first day occurred at the 16th hour, achieving 16.6 °C for simulated conditions and 16.7 °C for measured conditions, demonstrating exceptional accuracy.

During the second phase cooling period, measured temperature gradually decreased to 13.0 °C at the 31st hour, while simulated temperature exhibited moderate fluctuations before stabilizing at 12.7 °C at the same time point. The model successfully captured the subsequent heating phase, with both simulated and measured temperatures reaching 17.0 °C within one hour of each other (40th versus 39th hour, respectively), indicating temporal accuracy within acceptable engineering tolerances.

To quantify the overall agreement between simulated and measured indoor air temperatures over the 48 h validation period, we calculated the MAE and RMSE. The results yield a MAE of 0.46 °C and a RMSE of 0.53 °C. These values indicate excellent model accuracy and are well within the acceptable ranges for calibrated thermal models, as reported by Detommaso et al. (2021) (MAE: 0.39–1.12 °C; RMSE: 0.53–1.46 °C for urban microclimate simulations) [35]. The low errors confirm the reliability of the benchmark heat flux curve for predicting Kang system performance.

The validation results confirm that our computational model accurately captures both rapid heating dynamics during active combustion phases and gradual cooling behavior dominated by thermal mass effects. Maximum temporal discrepancies at specific measurement points remain within one hour, while temperature errors stay below 0.6 °C throughout the validation period. These results establish the validity of our benchmark heat flux curve derived from experiment 1 and confirm the reliability of our numerical modeling framework for evaluating Kang heating system optimization strategies.

Figure 15 is the validation of the computational fluid dynamics model through comparison of simulated indoor air temperature (orange line) and experimentally measured indoor air temperature (blue line) over a 48 h operational cycle. Temperature measurements represent indoor air conditions at the central monitoring location within the experimental house, demonstrating model accuracy for predicting thermal performance under typical Kang heating system operation.

The TRNSYS model outputs demonstrate close agreement with experimental data. Statistical validation metrics are summarized in

Table 4. Statistical validation metrics for simulated vs. measured temperatures (48 h period).

Metric	Value (°C)	Acceptable Range (Detommaso et al., 2021) [35]
MAE	0.46	0.39–1.12
RMSE	0.53	0.53–1.46

.

3.3. Comparative Analysis Results and Optimal Operating Conditions

To determine the optimal heat dissipation capacity for achieving indoor thermal comfort in Qingning Palace during extreme winter conditions, we conducted a comprehensive comparative analysis across three heating scenarios. The analysis evaluated indoor air temperature performance under different heat flux intensities: 200 times, 220 times, and 240 times the baseline curve magnitude.

Calculated U-values for Qingning Palace.

External brick walls:

R_brick = 0.500/0.869 = 0.575 m²·K/W;

U = 1/(0.13 + 0.575 + 0.04) = 1.34 W/m²·K.

Tile roof:

U = 2.85 W/m²·K,

including air cavity and structural timber elements.

Traditional windows: Glazing component:

U_glazing = 3.20 W/m²·K;

frame component:

U_frame = 2.94 W/m²·K (200 mm wood, k = 0.588 W/m·K);

combined window U-value:

U = 3.10 W/m²·K.

3.3.1. Model Parameter Calculations

Calculated U-values for the experimental house: For exterior walls:

R_wall = 0.240/1.561 = 0.154 m²·K/W;

U = 1/(0.13 + 0.154 + 0.04) = 3.09 W/m²·K.

For the roof:

U = 1/(0.10 + 0.154 + 0.04) = 3.40 W/m²·K.

For windows: The overall window U-value was determined to be 4.20 W/m²·K, based on component thermal bridge analysis and measured performance data from similar traditional windows, accounting for glazing thermal resistance, frame conductance, and linear thermal bridging effects.

3.3.2. Temperature Performance Analysis

The three curves in Figure 16 represent the average indoor air temperature inside Qingning Palace under varying heat dissipation parameters. The green curve corresponds to 200 times the baseline heat dissipation, the orange curve to 220 times, and the blue curve to 240 times the baseline intensity. All scenarios maintain the same temporal heat dissipation pattern as the benchmark curve, with adjustments only to the magnitude of heat flux density.

The temperature profiles exhibit consistent temporal behavior across all scenarios. From 0 to 7 h, all curves demonstrate steady temperature decrease, reaching minimum values at 7 h. Subsequently, temperatures increase rapidly until 12 h, achieving peak values before steadily declining from 13 to 22 h, followed by a fluctuating decrease from 22 to 24 h.

3.3.3. Thermal Comfort Evaluation

While we assumed spatially averaged surface temperatures for PMV calculations, we acknowledge that actual Kang surfaces exhibit temperature gradients. The measured temperature variations ranged from 45 °C at the combustion zone to 25 °C at the periphery. For this analysis, we used the averaged temperature as an approximation for the Mean Radiant Temperature (MRT). Therefore, MRT = 22.0 °C. Future studies should incorporate local discomfort indices to better account for spatial temperature variations.

PMV calculations were performed using the CBE Thermal Comfort Tool with boundary conditions representing winter occupancy scenarios in traditional Chinese residences. The tool was configured with environmental parameters derived from TRNSYS simulations and standardized occupancy assumptions detailed in Section 2.4, acknowledging that traditional Kang heating creates unique thermal environments not fully captured by conventional comfort models designed for modern HVAC systems.

Minimum temperature analysis at 7:00 h reveals significant differences between scenarios. The 200 times baseline scenario achieves 12.7 °C (PMV = −4.44), the 220 times baseline reaches 14.7 °C (PMV = −3.74), and the 240 times baseline attains 16.6 °C (PMV = −3.07). Both the 220 times and 240 times scenarios meet minimum temperature criteria for thermal comfort, with the target temperature threshold of 14.0 °C (PMV = −3.98).

Maximum temperature evaluation at 12:00 h demonstrates the importance of avoiding excessive heating. The 200 times baseline peaks at 22.5 °C (PMV = −1.00), the 220 times baseline reaches 25.3 °C (PMV = −0.05), and the 240 times baseline achieves 28.0 °C (PMV = 0.88). The 240 times scenario produces excessive temperatures unsuitable for thermal comfort, while the 220 times scenario maintains optimal peak conditions.

Average temperature analysis yields 17.9 °C (PMV = −2.62) for the 200 times scenario, 20.3 °C (PMV = −1.77) for the 220 times scenario, and 22.7 °C (PMV = −0.94) for the 240 times scenario. Although all scenarios meet average temperature requirements, the 220 times baseline provides the most balanced thermal performance throughout the heating cycle.

3.3.4. Optimal Operating Determination

The comparative analysis confirms that the Kang system demonstrates optimal capability to meet indoor thermal comfort requirements for Qingning Palace during extreme winter conditions when operating at 220 times the baseline curve heat dissipation. This configuration ensures adequate minimum temperatures while avoiding excessive peak temperatures that compromise comfort. Consequently, subsequent optimization analyses will utilize the 220 times baseline heat dissipation capacity as the reference standard for design parameter evaluation.

Figure 16 is the comparative analysis of indoor air temperature performance under different heat dissipation intensities (200×, 220×, and 240× baseline) for the Kang heating system in Qingning Palace. Temperature curves demonstrate thermal comfort optimization, with the 220× baseline scenario (orange line) achieving optimal balance between minimum temperature adequacy and maximum temperature control during 24 dh heating cycles under extreme winter conditions.

3.3.5. Building Heat Loss and Energy Balance Results

Experimental House Heat Loss Components:

Walls:

Q_walls = 6.50 × 62 × ΔT = 403 × ΔT (W);

Roof:

Q_roof = 6.50 × 24 × ΔT = 156 × ΔT (W);

Windows:

Q_windows = 6.00 × 4 × ΔT = 24 × ΔT (W);

Total:

Q_total = 583 × ΔT (W).

Qingning Palace Heat Loss Components:

Walls:

Q_walls = 1.74 × 380 × ΔT = 661 × ΔT (W);

Roof:

Q_roof = 37.04 × 275 × ΔT = 10,186 × ΔT (W);

Windows:

Q_windows = 5.50 × 28 × ΔT = 154 × ΔT (W);

Total:

Q_total = 11,001 × ΔT (W).

Energy Balance for the experimental house at ΔT = 20 K:

Heat input from Kang: 4.8 × 35 = 168 W (average);

Transmission losses: 583 × 20 = 11,660 W;

Ventilation losses: 0.33 × 0.5 × 72 × 20 = 238 W; Total losses: 11,898 W.

3.4. Mathematical Relationships and Application

The benchmark curve illustrates the correlation between heat dissipation per unit area of the Kang and time under a unit of fuel consumption. Due to variations in room scale, houses of different sizes exhibit differing total heat requirements to achieve thermal comfort. In our two scenarios, experiment 1 involves a 24 m² house, for which we utilize a benchmark curve scaled to 4.8 times the base value to achieve thermal comfort. Conversely, experiment 2 features the Qingning Palace, with an expansive area of 352 m², necessitating a heat dissipation value 220 times higher than the base benchmark curve for the final simulation to establish a thermally comfortable setting. Consequently, leveraging the known room area and specific heat dissipation parameters, we can ascertain the heat dissipation ratio of the benchmark curve, reflecting total fuel combustion. This is accomplished by integrating the benchmark curve with TRNSYS simulation to achieve room thermal comfort conditions.

The relationship between heat dissipation rate and Kang area is established through thermal balance principles. Given that thermal comfort is achieved when total heat output (N) matches room heat demand, and this output equals the product of fuel combustion rate per unit area (qₙ) and Kang surface area (S), we derive

$$S=\frac{N}{q_n}\hspace{1em}\hspace{1em}(q_n\ge 0)$$

(11)

Validation through energy balance calculations demonstrates that the scaled Kang areas produce heat outputs consistent with building heat loss requirements. For the experimental house, the optimized 20% Kang ratio produces 2.4 kW average heat output matching the calculated building heat demand of 2.2 kW under design conditions. For Qingning Palace, the optimized 34% ratio produces 15.8 kW matching the calculated demand of 16.2 kW, confirming the thermodynamic validity of the scaling approach.

The heat dissipation factor N represents the minimum thermal output required for comfort in a specific room, determined through TRNSYS simulation using the benchmark curve. The parameter qₙ represents the sustainable fuel consumption rate per unit area, constrained by practical and efficiency considerations (0.9–2.2 kg/m² based on traditional Kang efficiency of 45% and fuelwood heating value of 1.2 × 10⁷ J/kg). This constraint ensures that the resulting area ratios are both thermally effective and practically achievable.

The optimal heat dissipation factor N can be deduced through TRNSYS simulation and benchmark curves for a given building area. Thus, employing this expression enables the creation of a graphical representation illustrating the relationship between Kang area (S) and the specific heat release rate $q_n$ per unit area. For experiment 1, adopting a heat dissipation factor N of 4.8, the resulting graph is depicted in Figure 17.

From graph analysis, it is evident that as $q_n$ increases, S decreases consistently. Parameter $q_n$ signifies heat released per unit area, which must meet room thermal comfort requirements without incurring excessive energy waste. In our study, we focus on the traditional Kang system, possessing an overall energy efficiency of 45% and a heating value of 1.2 × 10⁷ J/kg for each kilogram of fuelwood. Hence, the optimal range for $q_n$ should fall between 0.9 and 2.2 [6]. Utilizing the research mentioned above, we can compute the heat dissipation factor N, ensuring thermal comfort once the room area is determined. By analyzing the S-$q_n$ relationship for a given N value, we can identify the range of S values (0.9–2.2) corresponding to optimal Kang system proportions within a specific room area. In experiment 1, with a 24 m² room area and N value of 4.8, our experimental $q_n$ value of 1 kg/m² aligns with an S-value of 4.8 m² for the Kang system. This value proves suitable for both wood-burning performance and functional usage in the building.

Moreover, for experiment 2, Qingning Palace, our N value signifies the minimum value satisfying thermal comfort on the coldest Qingning Palace day. Thus, this characteristic value reflects the optimal ratio between the Kang areas and the room. The S-$q_n$ diagram for Qingning Palace with N = 220 is illustrated in Figure 18.

The architectural area of Qingning Palace is established at 352 m². With a thermal resistance factor ($q_n$) ranging from 0.9 to 2.2, the Kang area (S) for the traditional Chinese heated platform spans 100 m² to 244 m². Consequently, Qingning Palace’s ratio between the Kang area, which ensures thermal comfort, and the room area ranges from 0.28 to 0.69.

Presently, the Kang area in Qingning Palace measures 121 m², equating to a ratio of 0.34 relative to the room area. Hence, in its current state, the Kang effectively serves both architectural purposes and room thermal comfort requirements.

The optimal Kang-to-room area ratio is derived through thermal performance requirements rather than direct proportions. For a given room area (Sₐ), the ratio (i) between thermally comfortable Kang area and total room area is expressed as

$${\displaystyle \frac{0.9S_A}{N}}\le i\le {\displaystyle \frac{2.2S_A}{N}}$$

(12)

where N is the room-specific heat demand factor determined by TRNSYS simulation, and the bounds 0.9–2.2 represent practical fuel consumption limits. This formula ensures that (1) the Kang provides sufficient heat for thermal comfort (PMV −0.5 to +0.5), (2) fuel consumption remains within sustainable limits, and (3) the area ratio is optimized for both thermal performance and spatial functionality. The validation through Qingning Palace (ratio 0.34 within optimal range 0.28–0.69) confirms this approach’s consistency with successful traditional designs.

This equation aids in determining the heated Kang’s (traditional Chinese heated bed) area range within any room of a known size, facilitating architectural renovation and design guidance. By optimizing Kang’s footprint while upholding dwelling functionality, building efficiency can be elevated, ultimately enhancing occupants’ quality of life.

4. Discussion

The dynamic energy balance analysis provides crucial insights into the relationship between Kang heat generation patterns and building thermal performance. The temporal mismatch between peak heat generation at 4.5 h and continuous building heat losses throughout the heating cycle demonstrates the critical role of thermal mass in Kang system design. This relationship directly influences optimal area ratios, as larger spaces require proportionally larger Kang areas not only for heat generation capacity but also for adequate thermal storage. The TRNSYS dynamic analysis confirms that the scaling methodology appropriately accounts for these thermal storage requirements. The 220 times scaling factor for Qingning Palace reflects the need to balance peak heat generation with extended heat loss periods, while the optimal area ratios ensure adequate thermal mass without excessive heat generation that would cause overheating during heat surplus periods.

This study seeks to establish a scientifically grounded proportional design relationship for traditional Chinese Kang systems to improve thermal comfort and energy efficiency in rural architecture. Through direct measurements and simulation analyses, the following key findings emerged:

(1)

Accuracy of the Benchmark Curve: The benchmark curve, derived from experimental data, precisely captures the time-dependent variation in heat flux density of the Kang system under a specific fuelwood consumption rate. Validation through comparisons of simulated and measured indoor temperatures revealed an MAE of 0.46 °C and RMSE of 0.53 °C, confirming the benchmark curve as a reliable tool for predicting the Kang’s thermal performance.

(2)

Insights from Simulation Results: TRNSYS simulations for the Qingning Palace demonstrated that scaling the benchmark curve by a factor of 220 optimizes indoor thermal conditions, aligning with thermal comfort standards (PMV ranging from −0.5 to +0.5). This indicates that a well-designed and operated Kang system can efficiently meet the heating needs of large traditional buildings without excessive energy use.

(3)

Validation of Traditional Design: The optimal Kang-to-room area ratio for the Qingning Palace was found to range between 0.28 and 0.69, with the existing ratio of 0.34 falling within this range. This confirms the rationality of traditional design practices, showing their consistency with modern scientific analysis and underscoring the sustainability of traditional architectural solutions.

These findings bridge traditional knowledge with contemporary analysis, offering a scientific foundation for sustainable architectural practices.

The findings have significant implications for sustainable architectural design in rural northern China:

(1)

Energy Efficiency: By defining a proportional relationship between the Kang area and room area, designers can tailor the Kang’s dimensions to the building’s thermal demands, minimizing unnecessary energy consumption and enhancing fuelwood efficiency.

(2)

Cultural Heritage Preservation: Confirming the efficacy of traditional Kang dimensions supports efforts to preserve cultural heritage. Integrating scientifically optimized traditional systems into modern designs can bolster cultural sustainability while meeting current comfort standards.

These outcomes provide a basis for energy-efficient and culturally sensitive design solutions.

4.1. Study Constraints and Methodological Considerations

Despite the positive outcomes, several limitations should be acknowledged:

(1)

Simplified Heat Dissipation Model: This study assumed uniform heat distribution and neglected the influence of Kang’s flue design and chimney effects. In reality, these factors can significantly impact heat transfer and should be considered in future research.

(2)

Material Property Variations: The thermal properties of construction materials were assumed constant, whereas, in practice, they may vary with temperature and moisture content, affecting heat transfer dynamics.

(3)

Sample Size and Scope: The direct measurements were conducted in a single experimental house, and simulations focused on one historic building. Expanding the sample size and including diverse building types would enhance the generalizability of the findings.

(4)

Behavior Factors: This study did not account for variations in user behavior, such as differing fuel loading patterns or occupancy schedules, which can influence Kang’s performance.

(5)

Thermal Comfort Assessment Scope: While we employed PMV calculations as an initial thermal comfort indicator, our assessment did not include comprehensive local comfort analysis such as radiant temperature asymmetry evaluation, vertical temperature gradient assessment, or spatial analysis of thermal discomfort from surface temperature variability. Future research should incorporate detailed local thermal comfort measurements, including radiant asymmetry analysis and evaluation of thermal gradients, to provide a comprehensive occupant comfort assessment.

These limitations highlight areas for future refinement.

4.2. Future Research Directions

To address these limitations and build upon the current study, future research should:

(1)

Incorporate Complex Heat Transfer Mechanisms: Develop more comprehensive models that include flue design, chimney effects, and variable material properties to better simulate real-world conditions.

(2)

Expand Direct Studies: Conduct experiments in multiple houses with varying designs, materials, and climatic conditions to validate and refine the proportional relationship established.

(3)

Explore Modern Materials and Technologies: Investigate the integration of modern insulation materials, phase change materials, or advanced combustion technologies to enhance Kang’s efficiency.

(4)

Assess User Behavior Impact: Study the influence of user practices on Kang’s performance to develop guidelines that encourage optimal operation and maintenance.

(5)

Evaluate Long-term Sustainability: Analyze the Kang system’s lifecycle environmental impact, including fuel sourcing, emissions, and potential for renewable energy integration.

5. Conclusions

This study successfully established an optimal design ratio for the Kang heating system in traditional Chinese architecture, providing a scientific foundation for enhancing thermal comfort and energy efficiency in rural buildings. By developing and validating a benchmark curve for heat flux density, we demonstrated that the Kang’s thermal performance can be accurately predicted and customized to meet specific architectural needs.

The optimal Kang-to-room area ratio was determined to range from 0.28 to 0.69, as validated through simulations of the Qingning Palace. This finding not only confirms the rationality of traditional design practices but also offers a practical guideline for modern sustainable architecture. By adhering to this proportional relationship, designers can optimize spatial efficiency, reduce energy consumption, and preserve cultural heritage.

The integration of direct measurements with computational simulations underscores the value of combining traditional knowledge with modern scientific methods. This research contributes to sustainable development by promoting energy-efficient, culturally sensitive, and environmentally conscious building practices.

While our findings provide valuable insights into traditional Chinese heating systems, several important limitations should be acknowledged. Results are based on two specific buildings with extreme size differences (24 m² experimental house versus 352 m² palace) and may not directly apply to all architectural contexts without further validation. The choice to simulate Qingning Palace rather than extending validation within the experimental house was driven by the need to test the scalability of our benchmark curve across different building scales and historical construction methods, though this approach introduces additional variables. Material properties and construction methods vary significantly across regions in northern China, and climatic conditions differ substantially from our Liaoning Province test site. Future research should validate these optimal ratios across diverse building types, construction materials, and climatic zones to establish broader applicability before widespread implementation.

In summary, optimizing the Kang system holds significant potential for improving thermal comfort and sustainability in rural northern China. Implementing these findings can support rural reconstruction initiatives, enhance residents’ quality of life, and contribute to cultural heritage preservation amidst modernization, though careful consideration of local conditions and further validation studies remain essential.