Solar thermal
Solar thermal collector output (ISO 9806 / EN 12975 efficiency curve)
- where
- mean fluid to ambient temperature difference (K)
- mean fluid temperature (°C)
- ambient air temperature (°C)
- collector efficiency
- zero-loss efficiency
- first-order heat loss coefficient (W/m²K)
- irradiance on the collector (W/m²)
- second-order heat loss coefficient (W/m²K²)
- heat output (W)
- collector area (m²)
Explain this equation
Works out how efficiently a solar thermal collector turns sunlight into heat, and its output, at given conditions. Use it to compare collectors or estimate output on a sunny day.
η₀ is the efficiency when the fluid is at air temperature, so nothing is lost to the surroundings. As the fluid gets hotter than the air, heat leaks out: a₁ covers losses that rise in proportion to ΔT, and a₂ the extra that grows faster at high temperatures. Losses are divided by G because they are compared with the sunlight received. Output is area times sunlight times efficiency.
This is the standard test-curve model from the collector test standards; the coefficients come from the collector's test report.
Sense check: a flat plate with η₀ = 0.78 at 30 K above ambient and 800 W/m² runs at about 63% efficiency; 2.35 m² gives about 1.2 kW.
Watch out: use the area the coefficients were measured on (usually aperture). Efficiency falls sharply on dull days and when the fluid is hot.
Instantaneous heat output of a glazed solar thermal collector from its tested efficiency coefficients, irradiance and temperatures.
Enter your values to see the result.
Good to know
η0, a1 and a2 come from the collector's Solar Keymark or test certificate, stated on aperture or gross area; use the matching area. Flat plates have high η0 but larger a1; evacuated tubes lose less heat and do better at high temperature differences. Tm is the average of inlet and outlet temperatures.
Common mistake
Using gross area with coefficients stated on aperture area (or the reverse), or putting the tank temperature in place of the collector mean fluid temperature.
Limits
Steady-state model at near-normal incidence. Ignores incidence-angle effects, wind and thermal capacity. Annual yield needs a simulation such as the SAP Appendix H or MCS solar thermal methods.
Sources
- BS EN ISO 9806:2017 Solar energy – Solar thermal collectors – Test methods (replaces EN 12975-2); steady-state efficiency η = η0 − a1(Tm − Ta)/G − a2(Tm − Ta)²/G
- nPro: Solar thermal calculation (ISO 9806 steady-state model q = Gη0 − a1(Tm − Ta) − a2(Tm − Ta)²; example flat plate η0 0.784, a1 3.69, a2 0.012)
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow MCS standards, manufacturer data, BS 7671, the ENA connection rules and Building Regulations. System design and DNO applications need a competent, certified installer.