Calculating Solar Water Heating Efficiency

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SUMMARY

The discussion focuses on calculating the efficiency of a solar water heating system involving a 1" diameter glass tube filled with water at 250°F and a surrounding 2" diameter tube with water at 40°F. The flow rate is set at 1 gallon per minute, and the goal is to determine how long it will take for the water to reach 80°F in a 100-gallon tank, assuming continuous sunlight. Participants are encouraged to provide solutions or methodologies for this thermal calculation.

PREREQUISITES
  • Understanding of thermodynamics principles related to heat transfer.
  • Familiarity with fluid dynamics, specifically flow rates and temperature gradients.
  • Knowledge of solar water heating systems and their components.
  • Basic mathematical skills for calculating heat exchange and time.
NEXT STEPS
  • Research the principles of heat transfer in cylindrical systems.
  • Learn about the specific heat capacity of water and its implications in heating calculations.
  • Explore solar water heating system designs and efficiency metrics.
  • Investigate software tools for thermal simulation, such as TRNSYS or EnergyPlus.
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Engineers, renewable energy enthusiasts, and anyone involved in designing or optimizing solar water heating systems.

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Is there anyone out there that can help me answer a question I have related to solar heating of water.

- There is a 1" diameter x 4' long glass tube filled with water having an input temperature of 250F.

- There is a 2" diameter tube surrounding it, 4' long, filled with water coming from the opposite direction at a temperature of 40F.

- The Flow rate is 1 gal/min.

- I have 100 gal tank.

How long before the water reaches 80F?

For the sake of simplicity let's assume the sun shinning 24 hours a day.

Any help answering this question would be greatly appreciated.
 
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have you tried some kind of solution?
 
A solution is what I am looking for.

As it has been a while since I am out of engineering school, and have no ready access to the calculations, I was hoping for a little help.
 

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