# Calculating the output temperature of a Solar Thermal system

• I
So say I have a PV-Thermal array and assuming standard test conditions.
How would I calculate the temperature of the water coming out of the system?

The thermal output of the system is 67.5kWp with a maximum flow rate of 65L/h. Approximately 500m of 3/4" pipes.

## Answers and Replies

Andrew Mason
Science Advisor
Homework Helper
If you know the specific heat of the fluid substance in the pipes and the initial temperature, use: ##\dot{Q}t = mc\Delta T## where ##\dot{Q}## is the rate of heat flow out of the fluid (67.5kW), t is the time during which heat flow occurs (one hour), m is the mass of the fluid from which the heat flow occurs (the mass of 65 L of fluid) , and c is the specific heat of the fluid (heat flow/unit mass).

AM

Khashishi
Science Advisor
What is a kWp? Is that a typo?

Andrew Mason
Science Advisor
Homework Helper
What is a kWp? Is that a typo?
Not a typo. It is a term used for solar panels to denote the power output under optimal conditions with maximum solar radiation.

AM

Is there way to take into account a continuous input of 20 degrees Celsius water at the given flow rate?

Andrew Mason
Science Advisor
Homework Helper
Is there way to take into account a continuous input of 20 degrees Celsius water at the given flow rate?
##\dot{Q}t = mc(T-T_i)## where ##T_i## = 20C. Work out from the pipe volume the volume of the fluid in the pipe. Then divide by the flow rate to determine the length of time (t) that the fluid will be absorbing heat flow at the stated rate. According to my calculations, fluid will be in the pipe for a bit more than 2 hours. During that time, figure out how much heat a unit of fluid absorbs. From that you can work out the temperature difference.

AM

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I understand the equation, but it doesn't take into account the constant flow of water in. After doing the math with the equation you provided I get delta T to be 235 degrees celsius which seems like a ridiculous value.

Andrew Mason
Science Advisor
Homework Helper
I can't really comment much unles you show your calculation and provide the values for m and c.

But just looking at your values there is something wrong here. Maximum solar insolation is 1.3 kw per m2 and the area of 500 m. of pipe would be just under 10m2, so it can't be putting out 65.7 kw. Maximuum would be 13 kw.

AM

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