Solar Hot Water Calculations


What is the collector efficiency of a solar hot water heating system?  For Example: 

Using the flow FLOW RATE METHOD or the TANK TEMPERATURE METHOD we can estimate collector efficiency, but we must know the flow rate of the pump, the intensity of sunlight, the surface area of the collector, and the input and output temperatures to and from the collector when we use the flow rate method. When we use the tank temperature method when we must know the starting and ending temperatures of the storage tank, the heat loss from the tank and of course the sunlight energy available.  A differential controller is used to automate the heat collection process but a controller is not necessary to calculate collector efficiency.



FLOW RATE METHOD

Surface Area of Collector = 8ft2
Flow Rate of Water
.2 gal/min = 12 gal/hr
Temp. collector - Temp. storage = 100 F
Sunlight Energy Available/ft2 = 250 BTU/ft2 = 2,000 BTU/8 ft2 
Heat collected = 12 gal/hr x 8 lbs x 100 F = 960 BTU/hr 
EFFICIENCY = 960/2,000 = 48%
OK. Now that we understand how collector efficiency may be calculated with the flow rate method let's see if we can use the tank temperature change method to estimate collector efficiency. 

TANK TEMPERATURE CHANGE METHOD

From the temperature data collected in the above graph we know that the 7 gallons of water have a temperature rise of 100 F. This means that the heat gain of the tank is: 7 gal x 8 lbs x 100 F = 560 BTUs. However we must take into account the heat loss from the un-insulated tank to calculate collector efficiency. 

If the tank were well insulated the heat loss would be minimal but the tank is not insulated so the heat loss from the tank is an important consideration. I placed 7 gallons of hot tap water in the same tank and let it stand overnight. During this time there was an interval when the differential temps between ambient and tank were the same that they were under the heat gain conditions. This information was used to estimate the heat loss.

Since the temp drop/hr is 7*F the heat loss/hr is 7* x 7 gal x 8 lbs = 392 BTUs and the actual collector heat gain would be: 560 BTU + 392 BTU = 952 BTU and the collector efficiency would be 953/2,000 = 47.6%










 As you can see from this graph the temperature of the water in the storage tank drops about 70 F between the hours of 1 AM and 2AM. There is a 300 F differential in temperature between the inside and the outside of the tank. This is the same differential that existed during the solar heat gain process so this represents the same heat loss that took place during the heat collection process.

The efficiency of heat collection using the flow rate method and the tank temperature method are not always the same. but when the results are similar there is a balance between heat harvest and energy conservation. 





   


The efficiency of solar heat collection is related to many factors such as pitch, orientation, ambient temperature, collector type, flow rate etc… Normally collector efficiency is measured under ideal conditions of maximum sunlight at a given ambient temperature and the flow rate of about .04 gal./min. Unfortunately these ideal conditions are not always available but by measuring the solar flux and flow rate and tank temperatures it is possible to approximate the performance of a collector. 

Efficiencies between 40 and 60% are common. A simplified comparison between flat plate collectors and evacuated tube collectors would go like this. Flat plates harvest more heat per sq. ft. at ambient temperatures above 30* F and evacuated tubes harvest more heat at temperatures below 30*F as long as they are not covered with snow. A side-by-side comparison may be used to evaluate collectors under a variety of conditions.  Remember consistency is the best way to assure accuracy.

Collector Comparison Fixture 
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SOLAR ELECTRONICS
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