The numerical simulation of free surface evaporation of pure water is confirmed by the experimental and analytical results obtained by Raimundo and those obtained with correlations available in the literature. The evaporation rate from the water surface for pure water has been validated with the experimental and analytical results according to Eq. (11). The results of this numerical work and its differences with the experimental and analytical results are shown in Table Ι, where Va is the mean velocity of air, Ta is average airflow temperature, Pa is the partial pressure of the water vapor contained in the air, Tw is the water temperature at the free surface and Pw is the partial pressure of saturated vapor at water temperature. The achieved results from this study are in good agreement with the experimental and analytical results.
$$J=1\text{*}{10}^{-6}\times (37.17+32.19\text{V}\text{a})(\text{P}\text{w}-\text{P}\text{a})$$
11
The mass flux J corresponds to the evaporation rate from the corresponding surface in grs− 1m− 2. The subscripts fr refers to the formula or analytical results and sim to the numerical simulation.
Table Ι. numerical results and their validation with experimental and analytical results.
Va
|
Ta
|
Tw
|
Pw
|
Pa
|
J-exp.
|
J-fr.
|
J-sim.
|
The difference with exp.
|
The difference with analytical.
|
|
293.3
|
301.9
|
3951.57
|
1900.57
|
0.059
|
0.0831
|
0.0625
|
5.9%
|
24.6%
|
0.101
|
294.6
|
307.9
|
5551.65
|
1525.65
|
0.136
|
0.1631
|
0.125
|
8.08%
|
23.1%
|
|
293.9
|
315.3
|
8274.49
|
1439.49
|
0.27
|
0.2763
|
0.25
|
7.40%
|
9.5%
|
|
293.1
|
317.7
|
9375.17
|
1407.17
|
0.342
|
0.322
|
0.305
|
10.8%
|
5.3%
|
|
295.5
|
301.3
|
3816.25
|
1809.25
|
0.081
|
0.087
|
0.0875
|
8.02%
|
0.42%
|
0.194
|
293.6
|
309.1
|
5931.59
|
1502.59
|
0.182
|
0.192
|
0.1875
|
3.02%
|
2.4%
|
|
294
|
315.2
|
8231.16
|
1445.16
|
0.287
|
0.295
|
0.275
|
4.1%
|
6.6%
|
|
295
|
319
|
10022.4
|
1757.4
|
0.355
|
0.359
|
0.315
|
11.2%
|
12.2%
|
|
295.1
|
301.1
|
3772.04
|
1922.04
|
0.087
|
0.087
|
0.075
|
13.7%
|
13.8%
|
0.308
|
294.9
|
309.8
|
6163.45
|
1962.45
|
0.208
|
0.198
|
0.1875
|
9.8%
|
5.20%
|
|
295.4
|
314.2
|
7808.47
|
1732.47
|
0.294
|
0.286
|
0.262
|
10.8%
|
8.4%
|
|
295.5
|
319.3
|
10177
|
1836
|
0.401
|
0.393
|
0.369
|
7.9%
|
6.04%
|
|
295.1
|
300.8
|
3706.58
|
1730.58
|
0.106
|
0.099
|
0.093
|
12.2%
|
6.3%
|
0.406
|
295.9
|
308.2
|
5644.6
|
1503.6
|
0.206
|
0.208
|
0.2
|
2.9%
|
3.8%
|
|
295.3
|
314.2
|
7808.47
|
1898.47
|
0.301
|
0.297
|
0.325
|
7.9%
|
9.4%
|
|
297.5
|
319.4
|
10229.1
|
1817.1
|
0.4
|
0.423
|
0.393
|
1.75%
|
7.006%
|
|
296.1
|
302.5
|
4091.05
|
1986.05
|
0.114
|
0.112
|
0.1125
|
1.3%
|
0.5%
|
0.497
|
294.9
|
309.9
|
6197.2
|
1959.2
|
0.244
|
0.225
|
0.25
|
2.4%
|
10.9%
|
|
297
|
314.9
|
8102.33
|
1876.33
|
0.332
|
0.331
|
0.312
|
6.02%
|
5.7%
|
|
291.6
|
319.3
|
10177
|
1772
|
0.449
|
0.447
|
0.41
|
8.6%
|
8.2%
|
|
294.4
|
301.7
|
3906.01
|
1759.01
|
0.152
|
0.121
|
0.131
|
13.8%
|
8.2%
|
0.596
|
296.8
|
309.7
|
6129.85
|
1889.85
|
0.257
|
0.239
|
0.23
|
10.5%
|
3.7%
|
|
294
|
313.7
|
7604.25
|
1837.25
|
0.328
|
0.325
|
0.31
|
5.4%
|
4.6%
|
|
296.8
|
319.8
|
10439.4
|
1688.4
|
0.46
|
0.493
|
0.446
|
3.04%
|
9.5%
|
|
296.2
|
301.5
|
3860.9
|
1801.9
|
0.145
|
0.123
|
0.13
|
10.3%
|
5.9%
|
0.697
|
295.9
|
308.7
|
5802.51
|
1936.51
|
0.239
|
0.230
|
0.243
|
1.6%
|
5.4%
|
|
297.7
|
314.7
|
8017.41
|
1956.41
|
0.359
|
0.361
|
0.332
|
7.5%
|
8.1%
|
|
296.6
|
319.1
|
10073.7
|
1778.7
|
0.471
|
0.494
|
0.446
|
5.3%
|
9.7%
|
In which the J-exp. And J-analy. Indicate the experimental and analytical results of the surface evaporation rate (grs− 1m− 2), respectively, obtained by Raimundo.
The effect of adding the Al2O3 and TiO2 nanoparticles to pure water on its surface evaporation rate was investigated. In the cases of Table ΙΙ, a numerical simulation process was done, and apply related nanoparticles to the pure water as the base fluid. These cases have appeared in Table ΙΙ.
Table ΙΙ. the cases that were studied for nanofluids.
Va
|
Ta
|
Tw = Tnf
|
Pw
|
Pa
|
0.101
|
293.9
|
315.3
|
8274.49
|
1439.49
|
0.194
|
294
|
315.2
|
8231.16
|
1445.16
|
0.308
|
295.4
|
314.2
|
7808.47
|
1732.47
|
0.406
|
295.3
|
314.2
|
7808.47
|
1898.47
|
0.497
|
297
|
314.9
|
8102.33
|
1876.33
|
0.596
|
294
|
313.7
|
7604.25
|
1837.25
|
0.697
|
297.7
|
314.7
|
8017.41
|
1956.41
|
Naturally, adding nanoparticles to the base fluid leads to a change in the thermophysical properties of the fluid, which also changes the surface evaporation rate of the base fluid. One of these properties that leads to a change in the surface evaporation rate is the saturated vapor pressure of the fluid. Table ΙΙΙ represents the saturated vapor pressure of the nanofluids with different sizes and concentrations in all nanofluids working temperatures against that of the base fluid (pure water) for the 7 cases selected in Table ΙΙ.
Table ΙΙΙ. saturated vapor pressure of nanofluids with different sizes and concentrations in all working temperatures (unit: Pa)
|
Temp. (k)
|
313.7
|
314.2
|
314.7
|
314.9
|
315.2
|
315.3
|
Pure water
|
|
7604.25
|
7808.47
|
8017.41
|
8102.33
|
8231.16
|
8274 .49
|
Al2O3 13 nm
|
0.5%
|
7628.129
|
7868.063
|
8107.999
|
8203.972
|
8347.934
|
8395.92
|
|
1%
|
7535.773
|
7775.203
|
8014.633
|
8110.405
|
8254.063
|
8301.949
|
|
2%
|
7502.615
|
7742.265
|
7981.915
|
8077.775
|
8221.565
|
8269.495
|
Al2O3 20 nm
|
0.5%
|
7598.956
|
7840.46
|
8081.966
|
8178.568
|
8323.471
|
8371.771
|
|
1%
|
7568.686
|
7798.49
|
8028.296
|
8120.218
|
8258.101
|
8304.061
|
|
2%
|
7480.824
|
7717.208
|
7953.594
|
8048.148
|
8189.979
|
8237.255
|
Al2O3 80 nm
|
0.5%
|
7525.935
|
7768.33
|
8010.725
|
8107.683
|
8253.12
|
8301.598
|
|
1%
|
7444.445
|
7685.395
|
7926.345
|
8022.725
|
8167.295
|
8215.485
|
|
2%
|
7369.233
|
7606.263
|
7843.293
|
7938.105
|
8080.323
|
8127.729
|
TiO2 21 nm
|
0.5%
|
7744.158
|
7994.938
|
8245.718
|
8346.03
|
8496.498
|
8546.654
|
|
1%
|
7656.768
|
7904.648
|
8152.528
|
8251.68
|
8400.408
|
8449.984
|
|
2%
|
7570.747
|
7817.517
|
8064.287
|
8162.995
|
8311.057
|
8360.411
|
After numerical investigating of mentioned cases for nanofluids, these cases were also investigated by some correlation in the literature. Both methods showed that adding the nanoparticles to the base fluids leads to the decreasing and increasing effects on the surface evaporation rate of the fluid, dependent on the size and the concentration of the nanoparticles. The results of all nanofluids with all sizes and concentrations have been presented in Fig. 2.
As shown in Fig. 2, nanofluids' amount surface evaporation rate with different sizes and concentrations has been compared with pure water in numerical and formula methods. In all cases, by increasing the concentration of the nanoparticles, the surface evaporation rate of the nanofluids takes a declining trend. The TiO2 nanofluid, in most cases and concentrations, has a higher surface evaporation rate than pure water. Also, for Al2O3 nanofluid, with increasing sizes and concentrations of nanoparticles, nanofluid takes decreasing trend. In almost all cases and concentrations, 80 nanometers lower surface evaporation rate than water.
From Fig. 2, it's also clear that the Al2O3 nanofluid in the concentration of 0.5 percent and size of 13 nanometers has a higher evaporation rate than the base fluid in both numerical and formula methods. In 0.5 percent concentration and with a nanoparticle size of 20 nanometers, this nanofluid also has higher evaporation than the water. Still, it shows a less additive effect on the evaporation rate than the 13 nanometers size. When in 0.5 percent concentration, the size of the nanoparticle increases to 80 nanometers, the increasing trend of the surface evaporation rate will be changed so that in some cases, it's clear that the surface evaporation rate of the nanofluid is lower than that of the pure water.
In Al2O3 nanofluid with nanoparticle concentration of 1 percent, in size of 13 nanometers, the surface evaporation has been increased but lower than that of 0.5 percent concentration. In the concentration of 1 percent and size of 13 nanometers, some cases have a slower evaporation rate than the base fluid. This demonstrates that in the concentration of 1 percent, other governing parameters on the evaporation rate, such as air velocity, nanofluids temperature, etc., are also involved in reducing or increasing the surface evaporation rate. Increment the size to 20 and 80 nanometers indicates a more subtractive effect on the evaporation of the nanofluid. This decreasing effect is different in different cases.
The Al2O3 nanofluid with a 2 percent concentration has an evaporation rate lower than the base fluid in sizes of 13, 20, and 80 nanometers. With an increment in the size of the nanoparticle, this subtractive effect will be increased. It is concluded that in the 2 percent concentration of the nanofluid, the evaporation rate is less than that of the base fluid in all cases, therefore in high concentrations, the evaporation rate can be reduced.
For TiO2 nanofluids, with looking at Fig. 2, it can be seen that in 0.5 percent concentration, the surface evaporation rate of all cases is higher than that of the base fluid, and even in this concentration, the cumulative effect on the evaporation is more than the Al2O3 nanofluid with the same concentration. With increasing the concentration of this nanofluid to 1 percent, it was observed that the TiO2 nanofluid still has an accumulative effect on the surface evaporation but is lower than the 0.5 percent concentration. In the 2 percent concentration of this nanofluid, it can be seen that the increasing effect on surface evaporation is lower than the 0.5 and 1 percent concentrations, which indicates that with increasing the nanoparticle concentration, the surface evaporation takes a declining trend.