Solar Heat Gain Calculator

Collector area (A_c)

Heat-removal factor (F_R)

Absorbed solar radiation (S)

Heat-loss coefficient (U_L)

Fluid inlet temperature (T_i)

Ambient temperature (T_a)

Useful heat gain (Q_u)

Enter the collector area, heat-removal factor, absorbed radiation, loss coefficient, and the two temperatures to get the useful heat gain. Or fill any six fields and leave the unknown blank to solve for it. Switch any field's unit to work in kW, square feet, Fahrenheit, and more.

Estimate energy output and savings

Enter the sun-hours per day, a number of days, and an energy price to turn the instantaneous heat output into energy delivered and the fuel cost it offsets.

Find the fluid outlet temperature

Enter the fluid mass flow rate and its specific heat to see how much the fluid warms as it passes through the collector and the temperature it leaves at.

Please input values into the fields

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Show the energy breakdown

Split the absorbed sunlight into the useful heat delivered to the fluid and the heat lost back to the surroundings.

Show heat gain vs inlet temperature

Plot how the useful heat gain falls as the fluid inlet temperature rises toward the stagnation point where net gain reaches zero.

Show the collector-type comparison

Compare the useful heat of a flat-plate, evacuated-tube, and unglazed collector at your operating point, alongside your own collector.

Solar collectors do not convert all the incident solar radiation into usable heat. Some of the light is reflected by the cover glass, some is lost in heating up the absorber plate and only the remaining heat is transferred to the fluid inside. This calculator uses the Hottel-Whillier-Bliss equation to determine the final amount of heat. It is also possible to work backwards. Leave any field blank and it will be calculated for you.

What is meant by 'usable heat gain'?

The useful heat gain is the actual amount of heat per second that is transferred from the collector to the working fluid. The working fluid typically consists of water or a mixture of ethylene glycol, sometimes air. It is calculated by taking the heat energy absorbed by the absorber and subtracting the heat energy lost through convection and radiation to the surroundings.

When the temperature of the incoming fluid is close to or below ambient, heat losses are small and almost all the heat absorbed by the absorber plate is transferred to the fluid. When the fluid temperature is significantly higher than ambient, losses increase in proportion to this temperature difference. At an equilibrium point, collector inflows and outflows balance and net gain is zero.

To use this calculator:

Enter the total area of collector, heat rejection factor as a percentage, absorbed solar radiation, loss factor, inlet fluid temperature and ambient temperature. The result of calculation is useful gain in watts. You can also convert any field to kilowatts, square feet, Fahrenheit or BTU.

This equation can be fully solved so that you can also leave any field blank and calculate the values backwards. If you enter the desired heat output and five of the remaining values and leave the area field blank, a calculation tool will calculate the required size of the solar collector. In the same way, the heat transfer coefficient, radiation, loss coefficient or limit temperature can be calculated.

Understanding of the Hottel-Whillier-Bliss equation.

The useful heat gain of a flat plate collector or evacuated tube collector is expressed as follows:

Q_u = A_c \, F_R \left[ S - U_L (T_i - T_a) \right]

The values in the square brackets are the net absorption capacity per square meter. The absorbed solar energy S is reduced by the heat quantities given back to the air, i.e. U_L multiplied by the temperature difference. When this is multiplied by the area A_c, you get the value for the entire panel. The additional factor heat transfer coefficient F_R takes into account that in a real heat exchanger not all of the heat from the absorber plate is transferred to the fluid.

Let's take a solar collector with an area of 3 square meters as an example. F_R is 85 percent, S is 800 watts per square meter, U_L is 5 watts per square meter Kelvin, the inlet temperature is 40 degrees Celsius and the ambient air temperature is 20 degrees Celsius.

\begin{aligned} \Delta T &= 40 - 20 = 20\;\text{K} \\ q_{\text{loss}} &= 5 \times 20 = 100\;\text{W/m}^2 \\ q_{\text{net}} &= 800 - 100 = 700\;\text{W/m}^2 \\ Q_u &= 3 \times 0.85 \times 700 = 1785\;\text{W} \end{aligned}

So on a sunny afternoon about 1.79 kilowatts of heat is given to the water. The efficiency is calculated by dividing 1785 by the product of 3 and 800, which is approximately 74 percent of the absorbed sunlight. The table shows the individual input parameters as well as an example value.

Symbol	Meaning	Example
A_c	Collector area	3 square meters
F_R	Heat-removal factor	85 percent
S	Absorbed solar radiation	800 W per square meter
U_L	Heat-loss coefficient	5 W per square meter per K
T_i	Fluid inlet temperature	40 degrees Celsius
T_a	Ambient temperature	20 degrees Celsius
Q_u	Useful heat gain	1785 watts

The selection of solar thermal collector is based on loss factor.

As there are losses, the choice of collector is critical. At low temperatures and high inlet temperature the value of the temperature difference times the U-value can consume a large part of the gain (S) before heat is transferred to the fluid. Vacuum tube collectors are one solution for this problem and have very low loss factors of about 1 to 2 watts per square meter kelvin.

Flat plate collectors offer average performance with a loss factor of about 4 to 8 and are the most common choice for domestic hot water systems. Cheap non-glass fiber reinforced pool collectors have values over 15, but they only pay off if inlet temperature is slightly above ambient air temperature. This is the operating condition for swimming pool heating. In a comparison table of different collector types you can see how the three kinds of collectors perform under your own operating conditions.

Fields of application for this equation:

Engineers use the Hottel-Whillier-Bliss equation to determine the size of domestic hot water systems, pool heaters, air conditioning heat loops, industrial process heat sources and agricultural product dryers. This equation allows for comparison between different collector types under specific conditions, prediction of daily heat output based on local solar radiation and ensures that the equipment selected will achieve the desired target temperature.

Pool installers work mainly with non-GLV collectors where the temperature difference is small. Hot water system designers deal mostly with the mid-range of temperatures where flat plate collectors are most commonly used. Processes requiring temperatures above 100 °C use vacuum tube and concentrating collectors.

Tips to maximize thermal gain:

Keep the inlet temperature at the lowest value acceptable for your application. For every degree increase of inlet temperature above ambient, you will lose U_L Watts per square meter. Insulate piping between the storage tank and collector. Heat losses in the piping can affect performance.

Choose a collector with good thermal contact between the absorber plate and the fluid channels, and run the pump at sufficient speed to keep the temperature difference between the absorber plate and the fluid small. Also clean the cover glass regularly; dust or pollen deposits can reduce absorbed radiation by 5 to 15 percent without your noticing it.

Frequently asked questions

What is the actual heat extraction factor?

For absorber plates with properly attached copper tubes the heat removal factor F_R for high quality flat plate collectors is typically in the range of 85 to 92 percent. For evacuated tube collectors this value can be as much as 95 percent, since the inner glass envelope maintains the absorber plate at a temperature close to that of the fluid.

Why can the usable heat gain be negative?

If the value resulting from multiplying the loss term U_L by the difference between T_i and T_a is greater than the absorbed radiation S, then the panel gives off more heat to the air than it receives from the sun. A negative value means that the collector actively cools the liquid. This is a situation which an efficient control system can recognize before sunrise and after sunset.

What is the difference between radiation intensity I and absorbed radiation S?

The radiation intensity is the energy that reaches the glazing. S is the actual energy remaining on the absorber, after the glass has passed most of the light and the absorber reflects a small part of it. Since I and S are connected by the product of transmittance and absorptance, S equals I multiplied by this product. For high-quality glass, this product typically ranges from 0.7 to 0.9.

How can you determine a collector's loss coefficient, UL?

This value is either directly stated in the manufacturer's technical data sheets or is represented as the slope of the efficiency curve. The efficiency curve is plotted with (T_i - T_a) / S on the horizontal axis. As a rough guide, flat plate collectors have values from 4 to 8 watts per square meter Kelvin, vacuum tube collectors have values from 1 to 2 watts and non-glass based pool collectors have values of 15 to 25 watts.

Is this formula also applicable to concentrating solar thermal plants?

Although the form is similar, in this case the area refers to aperture area and not absorber area, and the loss coefficient must also be calculated on the basis of this aperture area. For high temperature systems a fourth power radiation loss term is usually added as it becomes dominant at higher absorber temperatures.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Solar thermal collector
Collector types, the useful-heat-gain relation, and the roles of the heat-removal factor and loss coefficient.
Duffie and Beckman, Solar Engineering of Thermal Processes
The standard reference for the Hottel-Whillier-Bliss equation and collector performance modeling.
NREL: Solar water heating
Background on solar thermal systems and their real-world performance.