Clean Energy from First Principles

Solar Heating

Absorbs solar radiation to produce low-grade thermal energy for domestic hot water, space heating, and industrial process heat without concentration.

Fundamental Principle

Natural Asymmetry Exploited

The temperature difference between the Sun's surface (~5800K) and the Earth (~300K), exploited at the low-temperature end of the thermal spectrum. Solar heating systems absorb solar radiation and convert it directly to thermal energy at temperatures suitable for domestic hot water (40-80°C), space heating (30-60°C), and low-temperature industrial processes (up to ~150°C).

The physical quantity out of equilibrium is the radiative flux from the Sun. A surface at ambient temperature (~300K) would emit ~450 W/m² according to Stefan-Boltzmann, but receives ~1000 W/m² of solar irradiance at midday, creating a net energy gain that can be captured as useful heat.

Unlike concentrated solar thermal (which achieves high temperatures via optical concentration for electricity generation) or photovoltaics (which extract electrical work via the photovoltaic effect), solar heating systems operate without concentration or electrical conversion. They accept the full solar spectrum and convert it to low-grade heat through straightforward absorption. This simplicity is both a strength (low cost, high reliability) and a limitation (the heat is useful only for thermal loads, not electricity).

Ultimate Source

Nuclear fusion in the Sun's core, identical to all solar technologies. The solar constant of ~1361 W/m² above Earth's atmosphere is reduced to ~1000 W/m² at the surface under clear skies, with further reductions from clouds, atmospheric scattering, and collector orientation.

For solar heating, the relevant quantity is Global Horizontal Irradiance (GHI) or Global Tilted Irradiance (GTI), which includes both direct and diffuse radiation. Unlike concentrated solar thermal and concentrated photovoltaics, flat-plate solar heating collectors can utilise diffuse radiation (scattered by clouds and atmosphere), making them effective in a wider range of climates including temperate and partly cloudy regions.

The source is effectively inexhaustible. Global solar thermal heating capacity could expand by orders of magnitude without approaching any resource limit. The constraint is economics and competition from other heating technologies, not fundamental energy availability.

Key Physics

Radiation absorption:

A solar collector absorbs incident radiation according to its absorptivity α. For a selective absorber coating (high absorptivity in the visible/near-IR, low emissivity in the thermal IR):

$$Q_{absorbed} = \alpha \cdot G \cdot A_c$$

where G is incident irradiance (W/m²) and A_c is collector area (m²). Modern selective coatings achieve α ≈ 0.92-0.96 in the solar spectrum.

Thermal losses:

The collector loses heat to the environment via:

  1. Radiation: Proportional to (T_c⁴ - T_amb⁴), reduced by low-emissivity coatings
  2. Convection: Proportional to (T_c - T_amb), reduced by glazing and vacuum insulation
  3. Conduction: Through collector edges and back, reduced by insulation

The overall heat loss coefficient U_L (W/m²K) characterises total losses per unit area per degree temperature difference:

$$Q_{loss} = U_L \cdot A_c \cdot (T_c - T_{amb})$$

Typical values:

Hottel-Whillier-Bliss equation:

Qu=FR⋅Ac⋅[τα⋅G−UL⋅(Ti−Tamb)]Q_u = F_R \cdot A_c \cdot [\tau\alpha \cdot G - U_L \cdot (T_i - T_{amb})]

where F_R is the heat removal factor (ratio of actual heat removal to maximum possible), τα is the transmittance-absorptance product of the glazing and absorber, T_i is the inlet fluid temperature, and T_amb is ambient temperature.

η=QuG⋅Ac=FR⋅τα−FR⋅UL⋅(Ti−Tamb)G\eta = \frac{Q_u}{G \cdot A_c} = F_R \cdot \tau\alpha - F_R \cdot U_L \cdot \frac{(T_i - T_{amb})}{G}

This linear relationship (efficiency decreasing with temperature rise above ambient, normalised by irradiance) is the fundamental performance characteristic of non-concentrating solar thermal collectors.

Stagnation temperature:

Tstag=Tamb+τα⋅GULT_{stag} = T_{amb} + \frac{\tau\alpha \cdot G}{U_L}

For a flat-plate collector with U_L = 4 W/m²K, τα = 0.8, and G = 1000 W/m²:

$$T_{stag} = T_{amb} + \frac{0.8 \times 1000}{4} = T_{amb} + 200°C$$

Evacuated tubes can reach stagnation temperatures exceeding 300°C, creating overheat protection challenges.

Conversion Mechanism

Energy Capture and Conversion

Solar heating systems capture solar radiation and convert it to thermal energy in a heat transfer fluid (water, water-glycol mixture, or air). This is the simplest and most direct solar energy conversion: photons are absorbed by a dark surface, their energy thermalises immediately, and the resulting heat is transferred to a working fluid.

The primary physical interaction is absorption of electromagnetic radiation by the collector surface, followed by heat conduction to the fluid and convective heat transfer within the fluid.

Physical Processes

1. Optical absorption

Solar radiation passes through transparent glazing (glass or polymer) and strikes the absorber surface. The absorber is typically a metal sheet (copper or aluminium) with a selective coating that:

This selectivity is achieved through thin-film coatings (e.g., black chrome, cermet coatings, titanium nitride oxide) that exploit the wavelength dependence of optical properties. Typical selective surfaces achieve solar absorptance α_s ≈ 0.92-0.96 and thermal emittance ε ≈ 0.05-0.15.

2. Heat conduction

Heat conducts from the absorber surface through the metal sheet to fluid channels (typically copper tubes soldered or welded to the absorber). The thermal resistance of this path depends on:

The collector efficiency factor F' characterises how close the mean absorber temperature is to the fluid temperature; well-designed collectors achieve F' > 0.9.

3. Convective heat transfer to fluid

Heat transfers from the tube wall to the flowing fluid. The heat transfer coefficient depends on:

Water and water-glycol mixtures have good heat transfer properties. Typical flow rates are 0.01-0.02 kg/s per m² of collector area.

4. Heat loss suppression

Losses are minimised by:

Collector Types

Unglazed collectors:

Glazed flat-plate collectors:

Evacuated tube collectors:

Evacuated flat-plate collectors:

Conversion Chain

$$\text{Solar radiation} \xrightarrow{\text{glazing}} \text{Transmitted light} \xrightarrow{\text{absorber}} \text{Surface heat} \xrightarrow{\text{conduction}} \text{Fluid heat} \xrightarrow{\text{storage/use}} \text{Useful thermal energy}$$

Principal losses occur at:

  1. Optical stage (~10-20%): Glazing reflection and absorption, absorber reflectance
  2. Thermal stage (highly variable): Radiation, convection, and conduction losses; depends strongly on operating temperature and collector type
  3. System stage (~5-15%): Pipe losses, storage tank losses, heat exchanger losses (for indirect systems)

Overall system efficiency (useful heat delivered / incident solar energy) ranges from 30-60% depending on application, climate, and system design.

Theoretical Limits

Primary Efficiency Limit

For a non-concentrating solar thermal collector, the maximum instantaneous efficiency approaches the optical efficiency τα when operating at ambient temperature (no thermal losses). This limit is typically 75-85% for glazed collectors.

However, the useful efficiency falls as operating temperature increases. The fundamental trade-off is:

  • Higher temperatures are more useful (higher exergy content)
  • Higher temperatures incur greater thermal losses

For domestic hot water at 60°C and ambient at 20°C, achievable efficiencies are:

For space heating at 40°C, efficiencies can reach 50-70% for flat plates.

Origin of the Limit

The limit arises from the second law of thermodynamics applied to heat transfer:

  1. Thermal losses scale with temperature: Heat flows from hot to cold. A collector at temperature T_c in ambient T_amb loses heat at rate proportional to (T_c - T_amb) for convection/conduction, and (T_c⁴ - T_amb⁴) for radiation.

  2. No concentration means no temperature boost: Without optical concentration, the maximum absorber temperature is limited by the balance between absorbed solar flux (~800-1000 W/m² at most) and thermal losses. This caps achievable temperatures at ~150-200°C for evacuated collectors, ~100-150°C for flat plates.

  3. Carnot considerations: If the collected heat were used to drive a heat engine (as in solar thermal electricity), the Carnot efficiency at these temperatures would be very low (15-30%). This is why solar heating is used for thermal loads directly rather than electricity generation.

The Hottel-Whillier-Bliss equation captures these physics exactly: efficiency is linear in the reduced temperature (T_i - T_amb)/G, with slope determined by thermal losses and intercept determined by optical efficiency.

Key Design Tradeoffs

Glazing layers:

Selective coatings:

Collector area vs. storage:

Operating temperature:

Relation to Thermodynamic Bounds

The Carnot efficiency between the Sun (5800K) and ambient (300K) is ~95%, but this is irrelevant for solar heating because:

  1. Solar heating collectors do not concentrate sunlight and cannot approach solar temperatures
  2. The goal is thermal energy delivery, not work extraction
  3. The relevant comparison is to the fuel displaced, not to theoretical maximum work

For heating applications, the appropriate figure of merit is the solar fraction: the fraction of heating load met by solar energy. Well-designed systems achieve solar fractions of 50-80% for domestic hot water and 20-50% for space heating in temperate climates.

Compared to the alternative of using PV electricity to drive a heat pump:

This comparison has shifted in favour of PV + heat pump as PV costs have fallen, though solar thermal retains advantages in specific applications.

Practical Limitations

Material Constraints

Absorber materials:

Selective coatings:

Glazing:

Insulation:

None of these materials are scarce. Scaling to hundreds of GW_th is not constrained by material availability.

Degradation and Lifetime

Typical lifetimes:

Degradation mechanisms:

Maintenance requirements:

Solar thermal systems have excellent reliability when properly installed. The main failure modes are freeze damage (if glycol not maintained), overheating (inadequate load), and component wear.

Geographic and Resource Constraints

Solar heating is viable across a wide range of climates:

Excellent resources (>1800 kWh/m²/year GHI):

  • Mediterranean, Middle East, Australia, Southwest US
  • Solar fractions of 70-90% for hot water achievable

Good resources (1200-1800 kWh/m²/year):

  • Central Europe, Northern US, Japan, China
  • Solar fractions of 50-70% for hot water typical

Marginal resources (<1200 kWh/m²/year):

  • Northern Europe, Canada, Northern Russia
  • Solar fractions of 30-50%; larger collector areas needed; seasonal storage may help

Unlike CSP, solar heating collectors can use diffuse radiation, making them effective even in cloudy climates. However, seasonal mismatch is a challenge: solar availability peaks in summer when heating demand is lowest.

Site requirements:

Power and Energy Density

Instantaneous flux:

Annual energy density:

Land use:

System sizing (domestic hot water):

Temporal Characteristics

Diurnal variation:

  • Output follows solar irradiance with thermal lag
  • Storage tanks (typically 50-100 L per m² of collector) buffer daily variations
  • Hot water available morning and evening from previous day's collection

Weather variation:

  • Cloudy days reduce output significantly (50-80% reduction)
  • 1-2 days of storage sufficient for most weather patterns
  • Backup heating (gas, electric, heat pump) covers extended cloudy periods

Seasonal variation:

  • Summer output 2-5× winter output depending on latitude
  • Space heating demand inversely correlated with solar availability
  • Seasonal storage (large water tanks, underground thermal storage) can shift summer excess to winter, but is expensive and primarily used in district heating

Predictability:

System Role and Integration

Applications:

  1. Domestic hot water (DHW): Primary application globally. Solar preheats water, backup system boosts to delivery temperature. Solar fraction typically 50-70%.

  2. Space heating (combi-systems): Combined DHW and space heating. Requires larger collector area and storage. Solar fraction for heating load typically 20-40%.

  3. Pool heating: Unglazed collectors operate near ambient temperature with high efficiency. Can provide 100% of heating load in summer.

  4. District heating: Large collector fields (>1000 m²) feed into district heating networks. Seasonal storage enables high solar fractions (>50%). Growing market in Denmark, Germany, Austria.

  5. Industrial process heat: Solar heat for processes requiring temperatures up to 150°C (washing, drying, preheating). Emerging market with large potential.

Integration with other systems:

Complementary infrastructure:

Scaling Characteristics

Output Scaling Behaviour

Solar thermal collectors are modular. Output scales linearly with area from residential (4-10 m²) to district heating (10,000-100,000 m²+). No minimum efficient scale exists; no maximum scale has been reached.

Economies of scale are modest:

Diseconomies can emerge from:

Viable Scale Range

Minimum: Single-collector systems (2 m²) for individual households. Even smaller systems exist for remote applications.

Maximum: The largest solar district heating plants exceed 150,000 m² (>100 MW_th):

No fundamental limit to scaling. District heating networks can aggregate multiple large solar fields with seasonal storage.

Land/Area Requirements

Rooftop systems:

  • 4-8 m² per person for DHW
  • 10-20 m² per person for DHW + space heating
  • Zero additional land use

Ground-mounted systems:

  • Collector spacing required to avoid shading (varies with latitude)
  • Typical ground coverage ratio: 30-50%
  • 2-3 m² land per m² collector

District heating scale:

  • 100 MW_th solar field: ~200,000-300,000 m² land
  • Can co-locate with other land uses (parking lots, agricultural land, industrial sites)

Current Status

Technology Readiness Level

Technology TRL Status
Flat-plate collectors (glazed) 9 Mature, mass-produced
Evacuated tube collectors 9 Mature, dominated by Chinese manufacturing
Unglazed collectors 9 Mature, simple technology
Large-scale district heating 9 Commercial, especially in Denmark/Germany
Evacuated flat-plate 7-8 Commercial but limited deployment
PVT (hybrid PV-thermal) 8 Growing market, ~30 manufacturers globally

Solar thermal heating is a mature technology with over 100 years of development and 40+ years of mass deployment. Manufacturing processes are well-established and reliable performance is demonstrated over multi-decade timescales.

Installed Capacity and Market

Global capacity (end of 2024):

Market trends:

Leading countries by installed capacity:

  1. China: ~392 GW_th
  2. European Union: ~41 GW_th (led by Germany, Austria, Greece, Spain)
  3. Brazil: ~18 GW_th
  4. India: ~11 GW_th
  5. United States: ~8 GW_th
  6. Turkey: ~7 GW_th
  7. Australia: ~6 GW_th

Annual installations (2024):

Levelised Cost of Heat

Cost varies significantly by application, scale, and location:

Application Installed Cost LCOH
Residential DHW (small system) 500−1500/m2∣500-1500/m² 0.05-0.15/kWh
Residential DHW (larger system) 300−800/m2∣300-800/m² 0.03-0.10/kWh
Commercial/industrial 200−500/m2∣200-500/m² 0.02-0.06/kWh
District heating (large scale) 150−350/m2∣150-350/m² 0.02-0.05/kWh

For comparison:

Solar thermal is competitive with gas in high-irradiance regions and expensive gas markets. It struggles against cheap natural gas and modern heat pumps in many markets.

Major Deployments

Large-scale solar district heating:

Plant Location Capacity Storage
Silkeborg Denmark 110 MW_th (157,000 m²) Pit storage
Vojens Denmark 50 MW_th (70,000 m²) 200,000 m³ pit
Groningen Netherlands 34 MW_th (48,800 m²) 2024
Graz Austria 5.6 MW_th District heating

Denmark leads with >100 large solar district heating systems, enabled by district heating infrastructure and carbon taxes on fossil fuels.

Industrial process heat:

Research Frontiers

Advanced collectors:

Hybrid PVT systems:

Seasonal thermal storage:

Solar cooling:

Process heat integration:

Cost reduction: