The pursuit of sustainable and efficient building heating solutions has led to significant interest in harnessing solar energy, particularly in regions blessed with abundant solar resources. My research focuses on a specific and promising configuration: a solar system that utilizes photovoltaic (PV) panels to generate direct current (DC) electricity, which is then used to power electric heating films for radiant floor heating. This integrated solar system eliminates the need for power inversion and complex hydronic components, presenting a potentially simpler and more efficient pathway for clean heating. This article presents a comprehensive study, from mathematical modeling to parametric analysis, exploring the application and suitability of this DC-powered solar system in residential and office buildings.
The core principle of this solar system is direct energy utilization. In a conventional solar photovoltaic setup for heating, DC electricity from the PV panels is converted to alternating current (AC) via an inverter to power an electric boiler or heat pump, which then heats water circulated through pipes in the floor. The proposed DC solar system simplifies this chain dramatically. The DC electricity generated by the PV panels is supplied directly to the electric heating film embedded within the floor structure. This removes the inverter (and its associated ~5% energy loss), the boiler, water pumps, and pressurization units. The result is a solar system with fewer components, lower electrical losses, reduced initial investment, and minimal maintenance requirements. The efficiency of the overall solar system hinges on the synergy between the intermittent solar supply and the thermal storage capacity of the building structure, facilitated by the low-temperature radiant heating.
To accurately assess the performance of this integrated solar system, a detailed numerical model was developed. The model simulates the dynamic heat transfer within a building zone equipped with a DC-powered heating film. The following assumptions were made to formulate the mathematical framework: one-dimensional heat conduction through building envelopes, negligible effect of solar radiation on exterior surfaces for simplification, the heat output from the heating film treated as an equivalent heat flux boundary condition, and perfect thermal contact between different material layers.
Mathematical Model of the Building and Heating System
The thermal behavior of massive building elements like walls and slabs, crucial for the solar system’s energy storage, is governed by the transient heat conduction equation:
$$
\rho c \frac{\partial T}{\partial t} = \lambda \frac{\partial^2 T}{\partial x^2}
$$
Where \( \rho \) is density (kg/m³), \( c \) is specific heat capacity (J/(kg·K)), \( T \) is temperature (K), \( t \) is time (s), \( \lambda \) is thermal conductivity (W/(m·K)), and \( x \) is the spatial coordinate (m).
The boundary condition at the interior surface of the floor (where the heating film is located) is critical for modeling our solar system. It accounts for the heat flux from the film and the convective and radiative exchange with the room:
$$
\lambda \frac{\partial T}{\partial x} = q_{e}, \quad \text{at } x=0
$$
$$
\lambda \frac{\partial T}{\partial x} = h_s (T_{in} – T_s) + h_r (T_{si} – T_s), \quad \text{at } x=H_{td}
$$
Here, \( q_e \) is the equivalent heat flux from the electric film (W/m²), \( h_s \) is the natural convection coefficient (W/(m²·K)), \( T_{in} \) is indoor air temperature (K), \( T_s \) is the floor surface temperature (K), \( h_r \) is the linearized radiant heat transfer coefficient (W/(m²·K)), \( T_{si} \) is the average interior surface temperature of other room enclosures (K), and \( H_{td} \) is the thickness of the floor finishing layers (m).
The governing equation was discretized using an implicit finite-difference scheme (FDM) with interior nodes. The discrete form for an internal node \( i \) is:
$$
\rho_i c_i \frac{T_i^{t+\Delta t} – T_i^{t}}{\Delta t} V_i = \lambda_i \frac{T_{i-1}^{t+\Delta t} – T_i^{t+\Delta t}}{\Delta x} A_i + \lambda_i \frac{T_{i+1}^{t+\Delta t} – T_i^{t+\Delta t}}{\Delta x} A_i
$$
For glazing elements, a steady-state heat transfer model was applied due to their negligible thermal mass. The indoor air temperature was solved using a lumped parameter method, balancing heat gains from interior surfaces, transmission losses through the envelope, and infiltration losses:
$$
c_a \rho_a V_{in} \frac{\partial T_{in}}{\partial t} = \sum_{m=1}^{n} h_m A_m (T_m – T_{in}) + h_g A_g (T_{out} – T_{in}) + Q_{inf}
$$
A key comfort metric for radiant systems is the operative temperature (\(T_o\)), which combines air temperature and mean radiant temperature (\(T_r\)):
$$
T_o = 0.46 T_a + 0.54 T_r
$$
This was the primary output variable used to evaluate the solar system’s performance.
System Configuration and Material Properties
The solar system’s performance was evaluated for two standard building types under the climatic conditions of Xining, a city on the Tibetan Plateau with rich solar resources but cold winters. A residential room (3.2m x 3.0m x 3.0m) and an office room (10m x 5m x 4m) were modeled. The PV conversion efficiency was taken as 17%, and the heating film’s electrical-to-thermal efficiency was 98%.
Two primary floor constructions for the radiant system were investigated, which fundamentally alter the heat flow path from the film:
- Externally Insulated Slab (Construction A): Insulation is placed below the structural concrete slab. The heating film can be installed either within the slab or in the screed above it.
- Internally Insulated Slab (Construction B): Insulation is placed above the structural concrete slab but below the heating film and finishing layers. The film is always within the screed.
The thermophysical properties of the main materials used in the building envelope and floor constructions are summarized in the table below. These properties are vital inputs for the numerical model of the solar system’s thermal performance.
| Material | Density (kg/m³) | Specific Heat (J/(kg·K)) | Thermal Conductivity (W/(m·K)) |
|---|---|---|---|
| Aerated Concrete Block | 500 | 400 | 0.110 |
| EPS Insulation | 20 | 1386 | 0.041 |
| Concrete | 2500 | 920 | 1.740 |
| Cement Screed | 1800 | 1050 | 0.930 |
| Marble Tile | 2800 | 817 | 2.910 |
Analysis of Heating Characteristics and Floor Construction Impact
Initial simulations of the basic solar system operation, using Construction A with the film placed at the slab-screed interface, revealed its inherent characteristics. The thermal mass of the building structure provided valuable damping, reducing indoor temperature swings compared to the outdoor variation. The solar system’s operation raised the average indoor temperature by approximately 3°C above the natural (unheated) room temperature on a typical winter day. However, a deep dive into the heat flow paths exposed a significant limitation of Construction A for this DC solar system.
Investigating different installation depths (\(H\)) of the heating film within Construction A showed that placing the film closer to the floor surface yielded higher operative temperatures. More critically, the analysis of heat distribution revealed that a substantial portion of the electrical energy supplied by the solar system was being stored as low-grade heat in the massive structural slab below the insulation, rather than being delivered to the room. For a film at H=0.15m, only about 9% of the heat output contributed directly to raising the indoor temperature, while a staggering 56% was stored in the structural concrete. This represents a major inefficiency in the solar system’s ability to convert PV electricity into usable thermal comfort.
| Heat Flow Path | Construction A (External Insulation) | Construction B (Internal Insulation) |
|---|---|---|
| Upward into Room | ~9% | ~69% |
| Stored in Structural Slab | ~56% | ~18% |
| Downward Loss (through insulation) | ~35% | ~13% |
This finding led to the evaluation of Construction B, the internally insulated slab. By placing the insulation beneath the film but above the structural slab, the heat flow path is dramatically optimized for the solar system. As shown in the table above, the proportion of heat entering the room skyrocketed to 69%, while the low-grade storage in the structural slab was reduced to 18%. This configuration ensures that the majority of the DC electricity generated by the solar system is effectively utilized for space heating, significantly enhancing the system’s responsiveness and efficiency. Consequently, for a residential building using Construction B, the indoor operative temperature on a typical day ranged from 17.3°C to 21.0°C, comfortably within the acceptable thermal comfort range. The rule still applies that within Construction B, placing the film closer to the floor surface provides slightly better performance.
Application in Office Buildings and Key Design Parameter
The solar system was also simulated for a typical office building, which has a larger window-to-wall ratio, higher ceilings, and different occupancy patterns (daytime use only). Using the optimized Construction B, the operative temperature during a typical day ranged from 13.3°C to 17.9°C. While lower than the residential case due to higher transmission losses, this range is generally adequate for daytime occupancy, especially since the operation period of the solar-powered film aligns well with office hours.
A critical design parameter for sizing this solar system is the ratio of the total PV panel area (\(A_{pv}\)) to the total floor area covered by the heating film (\(A_{film}\)). This “area ratio” directly determines the available solar-derived electrical power per square meter of heated floor. Simulations were conducted for the office building with varying area ratios, and the results are highly instructive.
| Area Ratio (A_pv / A_film) | Average Operative Temp. (°C) | Approx. Temp. Increase per +0.5 Ratio | Peak Floor Surface Temp. |
|---|---|---|---|
| 0.5 | 5.5 | +7°C | Safe |
| 1.0 | ~12.5 | Safe | |
| 1.5 | ~19.5 | Approaching Limit | |
| 2.0 | ~26.5 | Risk of Overheating |
The relationship between the area ratio and the average indoor operative temperature is remarkably linear for this solar system. However, a crucial constraint emerges: the floor surface temperature. As the area ratio increases, so does the heat flux from the film, raising the risk of the floor surface exceeding comfort or safety limits (typically considered to be around 29°C). The analysis indicates that for the studied climate and construction, an area ratio of 1.5 represents a practical upper limit to avoid surface overheating while still achieving good heating performance. This provides a clear and simple guideline for designing the solar system.
Seasonal Performance and Conclusions
An extended simulation over the entire heating season (October 15 to April 15) for Xining was performed, assuming the solar system operates without electrical storage or grid connection. The results indicate that the DC-powered electric heating film solar system can largely meet the basic thermal demand throughout the season. The operative temperature generally remained within an acceptable band. It was noted that during the shoulder seasons (early and late heating season), there is a potential for indoor overheating if the system runs continuously, suggesting the need for operational controls or zoning.
In summary, this investigation into the solar photovoltaic DC-powered electric heating film radiant heating system yields several key conclusions for its effective application:
- Optimal Floor Construction: The internally insulated slab construction (Construction B) is strongly recommended. It fundamentally improves the efficiency of the solar system by minimizing the storage of low-grade heat in the structural mass and directing most of the generated heat upward into the occupied space.
- Film Placement: Within the chosen construction, placing the electric heating film closer to the floor surface enhances thermal performance, leading to higher operative temperatures.
- Building Suitability: The solar system can provide thermal comfort in both residential and office buildings. Its operation pattern is particularly well-suited for office buildings with daytime occupancy.
- Critical Design Parameter: The ratio of PV panel area to heated floor area (\(A_{pv}/A_{film}\)) is a paramount design variable. It has a near-linear relationship with the achieved indoor operative temperature. To prevent floor surface overheating, this ratio should generally not exceed 1.5 under similar climatic and construction conditions.
The continuous reduction in the cost of photovoltaic panels has significantly improved the economic viability of such direct-use solar systems. By eliminating the inverter and hydraulic subsystems, the proposed DC solar system offers a pathway toward simpler, more reliable, and efficient solar-powered heating. This study demonstrates that with proper design—focusing on floor construction and the PV-to-load area ratio—this integrated solar system can provide a comfortable indoor thermal environment, making it a promising solution for clean heating in sun-rich, cold regions.