A small pool of water, with dimensions of 3 meters
in width, 2 meters in depth, and indefinite length, is subjected to energy
transfer from several sources produced by energy input and solar radiation. The
aim of this project is to determine the time required for this pool of water to
reach a prescribed average temperature of 30 degrees C.
The
pool is subject to the following conditions:
- The sides of the pool are lined with heating elements which produce a constant heat flux of 250 W/m 2into the pool.
- The surface of the pool is exposed to the air, the temperature of which varies sinusoidally throughout a 24hr cycle from 0 to 30 degrees C, the air can be considered to have a constant convection coefficient of 150 W/m 2K.
- Solar radiation incoming on the pool also varies sinusoidally but from sunrise, at 6AM to sunset at 6PM, the flux as a result of solar radiation varies from 0 to 1000 W/m 2.
- The heat flux at a particular depth z of the pool is given by: I(z)=I o exp (-z/0.3)
- nitially at the start of the process, the entire pool is filled with water at a constant temperature of 10 degrees C.
The following assumptions are made:- The walls and floor of the pool are perfectly insulated and thus no heat loss occurs through them.
- No water evaporates from the pool.
The following are to be determined:- The variation of the average temperature in the pool as a function of time.
- The net energy gain of the pool as a function of time.
- The time required at the specified conditions to reach an average temperature of 30 degrees C throughout the volume of the pool.
- Several cross sections illustrating local temperature distribution.
This is to be accomplished using a finite element analysis method.
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