## Example

For the industrial process heat system in Example 11.12, estimate the storage tank losses for the month of June by considering the ambient temperature where the tank is located to be at 18°C and the tank (UA)s = 6.5 W/°C.

### Solution

To solve this problem, we have to assume an average tank temperature. For June, we assume a value of 72°C. The tank losses are estimated with Eq. (11.51):

Qst = (UA)s (Ts - Tenv)At = 6.5(72 - 18) X 30 X 24 X 3600 = 0.91GJ

The total load would then be = 16.20 + 0.91 = 17.11 GJ. Because the load is indirectly proportional to the dimensionless parameters, the new values are 16.20/17.11 times the values given in Example 11.12. Therefore,

16.20 17.11

4.49

From Eq. (11.48), we get fTL = 0.61. From Eq. (11.46), we can estimate Y:

AcFr (to)NHR L

17.11 X 109

1.517

0.61 1.511

0.402

The Kt in June is 0.70; therefore, the coefficients are A = —1.5715, B = 0.0871, and C = 1.0544. Now, from Eq. (11.34a) by trial and error, the new value of Xc = 0.43_from the original of 0.39.

As in Eq. (11.45) Xc is directly proportional to temperature difference, then the original difference of (70 — 25.8) = 44.2°C must be increased by the ratio 0.43/0.39. Therefore,

0.43

0.39

0.43

14.50C

The average tank temperature is then equal to (74.5 + 70)/2 = 72.3°C. This is very near the original assumption, so no iterations are required. The solar fraction is then obtained from Eq. (11.53):

0.91

16.2

0.59

Therefore, the consideration of tank losses reduces the fraction for June from 64% to 59%.

### 11.3.2 Heat Exchanger Correction

The heat exchanger increases the storage tank temperature by adding a thermal resistance between the tank and the load. This results in a reduction in the useful energy collection by having higher collector inlet temperatures and an increase in the storage tank losses. The average increase in tank temperature that is necessary to supply the required energy load is given by (Klein and Beckman, 1979):

£ LCmin where

AtL = number of seconds during a month the load is required (s). eL = effectiveness of load heat exchanger.

Cmin = minimum capacitance of the two fluid streams in the heat exchanger (W/°C).

The temperature difference found by Eq. (11.55) is added to the Tmin to find the monthly average critical radiation from Eq. (11.45). 