10.07.2015   BACKGROUND

Comparison between numerical and experimental values

To verify the mathematical model, the experimental results reported by [Flores and Alvarez, 2002] were used. The verification consisted in comparing interior air temperatures measured with the same ones calculated by the theoretical model. Table 2 presents twelve experimental temperatures, the numbers in the parenthesis are the coordinates of each measured point. Table 3 shows their corresponding theoretical air temperatures and Table 4 presents their corresponding percentage differences. From this table, we can see that the maximum percentage difference was 6.04% (30.34°C experimental, 28.51 °C calculated, maximum difference 1.83°C,) and the minimum percentage was 0.11%. The average percentage difference was 1.87%, which corresponds to an average difference of

0. 66°C. The uncertainty of the experiment was ±0.5°C, thus the theoretical model can represent very closely the experimental air measurements in the interior of the cavity.

Table 2. Experimental air temperatures and its x, y, z-coordinate

31.75 (0.2,9,5)

40.63 (2.5,9,5)

42.35 (7.5,9,5)

49.29 (9.8,9,5)

30.34 (0.2,5,5)

35.55 (2.5,5,5)

35.72 (7.5,5,5)

43.69 (9.8,5,5)

26.50 (0.2,1,5)

30.49 (2.5,1,5)

31.71 (7.5,1,5)

41.76 (9.8,1,5)

Table 3. Theoretical air temperatures calculated and its x, y, z-coordinate

31.14 (0.2,9,5)

40.59 (2.5,9,5)

41.81 (7.5,9,5)

49.01 (9.8,9,5)

28.51 (0.2,5,5)

34.71 (2.5,5,5)

34.77 (7.5,5,5)

44.71 (9.8,5,5)

26.42 (0.2,1,5)

30.04 (2.5,1,5)

32.01 (7.5,1,5)

41.08 (9.8,1,5)

Table 4. Percentage differences between the experimental and theoretical interior air ________________________________ temperatures in the cavity._______________________________

1.93%

0.11%

2.05%

0.57%

6.04%

2.35%

2.65%

2.34%

0.29%

1.48%

0.95%

1.63%

Knowing the air temperatures distribution from the numerical solution of the governing equations, the interior convective, radiative and total Nusselt numbers were calculated for an irradiation of 1000 W/m2. From the results, assuming that the absorption of energy of the glass is zero, the absorbed thermal energy by the solar control coating was 500 W/m2, in which, 81.1 W/m2 is transferred to the interior by thermal radiation; 72.4 W/m2 is by convection to the interior. Thus the energy that is transferred to the interior is 653.5 W/m2 and 346.5 W/m2 is going to the exterior. Therefore, we can see that percentage of radiative energy that goes to the interior is 12.41% and the percentage convective energy is 11.01%.

Using equations (17) and (18) the convective and radiative numbers were calculated. The convective Nusselt number was 11.48 and the radiative one was 12.8. Thus, the order of magnitude of the contribution of the radiative energy is almost the same as the convective one, meaning that the radiative exchange between surfaces plays and important role in the heat transfer process for this cavity. The solar heat gain coefficient calculated by using equation (19) was 0.65 and imply that 65% of the energy goes into the interior.