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.

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