## Example

A fully mixed water storage tank contains 500 kg of water, has a UA product equal to 12 W/°C, and is located in a room that is at a constant temperature of 20°C. The tank is examined in a 10 h period starting from 5 am where the Qu is equal to 0, 0, 0, 10, 21, 30, 40, 55, 65, 55 MJ. The load is constant and equal to 12 MJ in the first 3 h, 15 MJ in the next 3 h, and 25 MJ the rest of time. Find the final storage tank temperature if the initial temperature is 45°C.

Solution

The estimation time interval is 1 h. Using Eq. (5.34) and inserting the appropriate constants, we get

By inserting the initial storage tank temperature (45°C), Qu, and Ql according to the problem, Table 5.3 can be obtained.

 Hour Qu (MJ) Qi (MJ) Ts (0C) Qtl (MJ) 45 5 0 12 38.7 1.1 6 0 12 32.6 0.8 7 0 12 26.6 0.5 8 10 15 24.1 0.3 9 21 15 26.9 0.2 10 30 15 33.9 0.3 11 40 25 40.8 0.6 12 55 25 54.7 0.9 13 65 25 73.1 1.5 14 55 25 86.4 2.3

Therefore, the final storage tank temperature is 86.4°C. For these calculations, the use of a spreadsheet program is recommended.

The collector performance equations in Chapter 4 can also be used with the more detailed determination of inlet fluid temperature to estimate the daily energy output from the collector. This is illustrated by the following example.