3.2.1. Study of varying thickness for PCM29
The decrement factors and total heat absorbed for the combinations were calculated using equations 1 and 2 to assess the performance of the roofs of varying thicknesses at 420 minutes.
\(Decrement factor=\frac{Max temperature at the bottom surface}{Max temperature at the top surface}\) - (1)
Conventional Concrete had a decrement factor of 0.887. In the first case (5 options), PCM29 was placed at the top of the CRC. Simulations showed that PCM1 + RC15 had a decrement factor of 0.77, which can be attributed to the direct heat flux application. PCM2 + RC15 and PCM3 + RC15 showed a decrement factor of 0.75. Similarly, the other cases showed a steady reduction of the decrement factor (0.747 & 0.743 for PCM4 + RC15 & PCM5 + RC15, respectively).
\(Total absorbed heat \left(J\right)=Mass x Heat capacity x Change in temperature\) – (2)
The total heat absorbed for the above simulation cases was found to be 95.47 kJ, 106.79 kJ, 117.28 kJ, 128.40 kJ, and 139.95 kJ for all the options, respectively.
The experimental results for the same cases showed similar behavior. PCM1 + RC15, PCM2 + RC15, and PCM3 + RC15 had a decrement factor of 0.78, 0.77, and 0.758, respectively. The factors were 0.745 and 0.741 for the last two options. The heat absorbed for the cases in practical cases were 69.38 kJ, 79.50 kJ, 90.72 kJ, 103.04 kJ and 114.62 kJ, respectively. The experimental and simulation results for the thermal loading for PCM29 and PCM 37 are tabulated in Tables 3 and 4, respectively.
The second set of cases in which the PCM29 layer was placed in the middle of the component showed a reduction of decrement factors compared to the first set. The usage of RC7.5 + PCM1 + RC7.5 resulted in a decrement factor of 0.65 in the simulation. The other options, RC7.5 + PCM3 + RC7.5, RC7.5 + PCM4 + RC7.5, and RC7.5 + PCM5 + RC7.5 showed decrement factors of 0.623, 0.599, and 0.575, respectively. RC7.5 + PCM2 + RC7.5 was the anomaly and resulted in a decrement factor of 0.537. The absorbed heat values (simulations) for the simulations came out to be 100.45 kJ, 124.84 kJ, 133.51 kJ, 153.46 kJ, and 175.33 kJ.
Experimental results showed decrement factors of 0.658, 0.625, 0.621, and 0.61 for RC7.5 + PCM1 + RC7.5, RC7.5 + PCM3 + RC7.5, RC7.5 + PCM4 + RC7.5, RC7.5 + PCM5 + RC7.5 respectively. The option RC7.5 + PCM2 + RC7.5 obtained a decrement factor of 0.639 and did not show an anomaly. The heat absorbed for the cases in experimental work was 74.52 kJ, 90.51 kJ, 107.24 kJ, 123.92 kJ and 141.19 kJ, respectively.
Table 3
Temperature Values (oC) for experimental and simulation work for different combinations for PCM29
S. No | E − 60 | S − 60 | E − 120 | S − 120 | E − 180 | S − 180 | E − 240 | S − 240 | E − 300 | S − 300 | E − 360 | S − 360 | E − 420 | S − 420 |
RC15 | 29.5 | 29.19 | 30.2 | 29.92 | 31.24 | 30.92 | 32.59 | 32.03 | 33.78 | 33.16 | 35.56 | 34.16 | 36.82 | 35.46 |
P1 + RC15 | 29.3 | 29.26 | 29.62 | 29.39 | 29.94 | 29.52 | 30.12 | 29.7 | 30.54 | 29.95 | 30.98 | 30.32 | 31.2 | 30.83 |
P2 + RC15 | 28.2 | 29.23 | 28.68 | 29.35 | 29.01 | 29.46 | 29.56 | 29.6 | 30.07 | 29.78 | 30.53 | 30.02 | 30.8 | 30.05 |
P3 + RC15 | 27.59 | 29.2 | 28.03 | 29.32 | 28.46 | 29.42 | 29.03 | 29.52 | 29.53 | 29.66 | 29.86 | 29.83 | 30.32 | 30.05 |
P4 + RC15 | 27.9 | 29.17 | 28.18 | 29.28 | 28.43 | 29.39 | 28.72 | 29.47 | 29.1 | 29.56 | 29.43 | 29.67 | 29.82 | 29.9 |
P5 + RC15 | 27.7 | 29.18 | 28.03 | 29.3 | 28.21 | 29.39 | 28.43 | 29.46 | 28.87 | 29.54 | 29.13 | 29.62 | 29.66 | 29.73 |
RC7.5 + P1 + RC7.5 | 23.28 | 20.6 | 23.78 | 21.1 | 24.25 | 22.1 | 24.76 | 24 | 25.36 | 24.1 | 25.98 | 25.1 | 26.32 | 26.11 |
RC7.5 + P2 + RC7.5 | 23.32 | 20.25 | 23.21 | 20.37 | 23.76 | 20.49 | 24.23 | 20.65 | 24.78 | 20.83 | 25.01 | 21.13 | 25.58 | 21.49 |
RC7.5 + P3 + RC.5 | 23.29 | 20.13 | 23.51 | 20.49 | 23.81 | 21.2 | 24.01 | 21.94 | 24.53 | 22.88 | 24.89 | 23.88 | 25.10 | 24.92 |
RC7.5 + P4 + RC7.5 | 22.74 | 20.09 | 22.87 | 20.6 | 23.12 | 21.1 | 23.47 | 22.1 | 23.87 | 22.02 | 24.21 | 23.2 | 24.87 | 23.96 |
RC7.5 + P5 + RC7.5 | 22.46 | 20.6 | 22.9 | 20.13 | 23.12 | 20.39 | 23.54 | 20.86 | 23.89 | 20.86 | 24.2 | 22.2 | 24.62 | 23.02 |
RC15 + P1 | 24.06 | 20.2 | 24.43 | 20.55 | 24.86 | 21.3 | 25.29 | 23 | 25.79 | 22.1 | 26.22 | 23.1 | 25.3 | 24.1 |
RC15 + P2 | 23.96 | 20.05 | 24.23 | 20.08 | 24.72 | 20.8 | 25.03 | 21.3 | 25.46 | 21.9 | 25.89 | 22.7 | 24.83 | 23.5 |
RC15 + P3 | 21.53 | 20.03 | 21.78 | 20.6 | 22.06 | 20.5 | 22.54 | 20.8 | 22.84 | 21.2 | 23.04 | 21.8 | 23.54 | 22.4 |
RC15 + P4 | 21.43 | 20.02 | 21.7 | 20.1 | 22.01 | 20.03 | 22.49 | 20.51 | 22.87 | 20.9 | 23.22 | 21.2 | 23.32 | 21.07 |
RC15 + P5 | 20.98 | 20.12 | 21.12 | 20.17 | 21.43 | 20.03 | 21.87 | 20.16 | 22.03 | 20.47 | 22.42 | 20.78 | 22.90 | 21.2 |
E – Experimental result, S – Simulation result
Table 4
Temperature Values (oC) for experimental and simulation work for different combinations for PCM37
S. No | E − 60 | S − 60 | E − 120 | S − 120 | E − 180 | S − 180 | E − 240 | S − 240 | E − 300 | S − 300 | E − 360 | S − 360 | E − 420 | S − 420 |
P1 + RC15 | 29.12 | 29.24 | 29.54 | 29.37 | 29.89 | 29.53 | 30.23 | 29.79 | 30.79 | 30.16 | 31.02 | 30.68 | 31.53 | 31.38 |
P2 + RC15 | 28.89 | 29.22 | 29.01 | 29.33 | 29.53 | 29.46 | 29.87 | 29.63 | 30.1 | 29.87 | 30.42 | 30.2 | 30.9 | 30.66 |
P3 + RC15 | 28.72 | 29.19 | 28.98 | 29.3 | 29.12 | 29.41 | 29.46 | 29.54 | 29.86 | 29.71 | 30.12 | 29.93 | 30.52 | 30.24 |
P4 + RC15 | 28.53 | 29.16 | 28.87 | 29.27 | 29.02 | 29.3 | 29.43 | 29.47 | 29.72 | 29.58 | 29.87 | 29.73 | 30.2 | 29.93 |
P5 + RC15 | 28.43 | 29 | 28.78 | 29.14 | 28.98 | 29.19 | 29.12 | 29.28 | 29.38 | 29.39 | 29.45 | 29.5 | 29.98 | 29.64 |
RC7.5 + P1 + RC7.5 | 23.87 | 20.24 | 24.30 | 20.89 | 24.87 | 21.76 | 25.2 | 22.75 | 25.87 | 23.8 | 26.01 | 24.86 | 26.32 | 25.94 |
RC7.5 + P2 + RC7.5 | 23.13 | 20.22 | 23.54 | 20.33 | 23.87 | 20.42 | 24.53 | 20.54 | 24.89 | 20.67 | 25.12 | 20.85 | 25.58 | 21.07 |
RC7.5 + P3 + RC.5 | 23.09 | 20.09 | 23.47 | 20.44 | 23.96 | 21.08 | 24.23 | 21.94 | 24.76 | 22.89 | 25.01 | 23.91 | 25.31 | 24.96 |
RC7.5 + P4 + RC7.5 | 23 | 20.14 | 23.38 | 20.47 | 23.87 | 21.02 | 24.1 | 21.75 | 24.46 | 22.59 | 24.89 | 23.51 | 25.01 | 24.48 |
RC7.5 + P5 + RC7.5 | 22.9 | 20.06 | 23.21 | 20.17 | 23.49 | 20.49 | 23.72 | 21.03 | 24.02 | 21.7 | 24.52 | 22.48 | 24.82 | 23.35 |
RC15 + P1 | 23.82 | 20.11 | 24.24 | 20.57 | 24.74 | 21.3 | 25.12 | 22.1 | 25.49 | 23 | 25.87 | 24 | 26.2 | 25.1 |
RC15 + P2 | 23.9 | 20.19 | 24.13 | 20.84 | 24.42 | 21.68 | 24.78 | 22.63 | 25.19 | 23.6 | 25.51 | 24.59 | 25.8 | 25.59 |
RC15 + P3 | 24.12 | 20.02 | 24.34 | 20.17 | 24.76 | 20.04 | 24.94 | 20.8 | 25.21 | 21.3 | 25.4 | 21.9 | 25.6 | 22.5 |
RC15 + P4 | 24.24 | 20.01 | 24.32 | 20.1 | 24.51 | 20.3 | 24.74 | 20.5 | 24.89 | 20.8 | 25.1 | 21.3 | 25.23 | 21.8 |
RC15 + P5 | 24.17 | 20 | 24.29 | 20.05 | 24.47 | 20.1 | 24.62 | 20.3 | 24.73 | 20.5 | 24.85 | 20.8 | 25 | 21.2 |
E – Experimental result, S – Simulation result
The PCM29 layer kept at the bottom of the CRC layer constituted the last set of options. RC15 + PCM1 had a decrement factor of 0.602, while RC15 + PCM2 had an incremental factor of 0.587 resulting from the simulations. The other cases had reduced decremental factors with the increase in thickness. Simulations for RC15 + PCM3, RC15 + PCM4, and RC15 + PCM5 resulted in decremental factors of 0.56, 0.52, and 0.53, respectively. The total heat absorbed (simulations) for the above options were 102.57 kJ, 120.6 kJ, 141.48 kJ, 165.65 kJ and 184.93 kJ respectively.
The experimental results for the cases resulted in decremental values of 0.63, 0.62, and 0.588 for the cases RC15 + PCM1, RC15 + PCM2, and RC15 + PCM3, respectively. The last two cases increased the values to 0.58 and 0.57. The simulation and experimental work show that PCM-integrated roofs performed better (decrement factor reduces) as the thickness increases, as illustrated in Figs. 4a, b, and c. The heat absorbed from the experimentation resulted in 75.60 kJ, 92.09 kJ, 112.17 kJ, 130.46 kJ, and 150.26 kJ respectively.
3.2.2. Study of varying thickness for PCM37
The second type of PCM used was PCM37, and the same set of cases was used for simulations and experiments. Simulations showed that PCM1 + RC15 had a decrement factor of 0.785, while PCM2 + RC15 and PCM3 + RC15 showed decrement factors of 0.766 and 0.756. The other two cases, PCM4 + RC15 & PCM5 + RC15 resulted in decrement factors of 0.748 & 0.74. The heat absorbed was 94.5 kJ, 104.64 kJ, 115.34 kJ, 126.43 kJ and 138.05 kJ respectively. The experimental results for the same cases showed similar behaviour. PCM1 + RC15, PCM2 + RC15, and PCM3 + RC15 had a decrement factor of 0.787, 0.772 and 0.763, respectively. The factors were 0.755 and 0.749 for the last two options. The values are graphically represented using Fig. 5a. The total heat absorbed was 94.34 kJ, 104.164 kJ, 114.48 kJ, 125.34 kJ and 136.34 kJ respectively.
In the second set of cases, RC7.5 + PCM1 + RC7.5 and RC7.5 + PCM2 + RC7.5 resulted in a decrement factor of 0.648 & 0.56 in the simulation. The options RC7.5 + PCM3 + RC7.5, RC7.5 + PCM4 + RC7.5, and RC7.5 + PCM5 + RC7.5 displayed decrement factors of 0.624, 0.612 and 0.583, respectively. The heat absorbed was 99.9 kJ, 123.9 kJ, 131.31 kJ, 148.42 kJ and 169.78 kJ, respectively. Experimental results showed decrement factors of 0.658, 0.639, 0.632, 0.612 and 0.583 for RC7.5 + PCM1 + RC7.5, RC7.5 + PCM2 + RC7.5, RC7.5 + PCM3 + RC7.5, RC7.5 + PCM4 + RC7.5, RC7.5 + PCM5 + RC7.5 respectively as shown in Fig. 5b. The total heat absorbed was 99.6 kJ, 114.89 kJ, 130.25 kJ, 146.28 kJ and 162.36 kJ respectively.
Lastly, RC15 + PCM1, RC15 + PCM2, and RC15 + PCM1 and RC15 + PCM2 have decrement factors of 0.627 and 0.639, respectively. Simulations for RC15 + PCM3, RC15 + PCM4, and RC15 + PCM5 resulted in decremental factors of 0.562, 0.545, and 0.53, respectively. The total heat absorbed was 100.83 kJ, 114.87 kJ, 138.76 kJ, 159.23 kJ and 180.62 kJ respectively. The experimental results for the cases resulted in decremental values of 0.655, 0.645, and 0.64 for RC15 + PCM1, RC15 + PCM2, and RC15 + PCM3, respectively. The last two cases’ values were 0.631 and 0.625. The decrement factor values are illustrated in Fig. 5c. The total heat absorbed was 99.72 kJ, 114.45 kJ, 129.38 kJ, 145.4 kJ and 161.45 kJ respectively.
The thickness and the performance are directly proportional for all the cases of PCM roofs. The PCM roof thickness of 5 cm seemed to be the best option for both PCM29 and PCM37.
A closer look at the rate of reduction of decrement factors suggested PCM roofs with thicknesses of 4 and 5 cm did not perform to the expected levels. The values were reduced by an average of 12.06%, 13.64%, and 14.44% for the options PCM1 + RC15, PCM2 + RC15, and PCM3 + RC15, respectively, compared to CRC. PCM4 + RC15 and PCM5 + RC15 resulted in an average of 14.67% and 15.5%, respectively. Similarly, RC7.5 + PCM1 + RC7.5, RC7.5 + PCM2 + RC7.5, and RC7.5 + PCM3 + RC7.5 reduced the decrement factors by an average of 25.8%, 29.09%, and 29.6% respectively, while the other last two cases had reductions of 29.9% and 30.22%.
RC15 + PCM3 had average values of 28.9%, 30.2%, and 32.7%, respectively. RC15 + PCM4 and RC15 + PCM5 had average values of 33.4% and 33.89%. The performance was appreciable for PCM roofs of 2 cm thickness for all cases. The thickness was also better from an economic standpoint compared to the other thicknesses. The saturation in the thermal performance could be related to the percentage of the PCM layer that changes its phase. The upper part of the PCM layer changes its phase and begins to store the applied thermal energy. The heat flux could not penetrate the whole layer of PCM and saturates after two centimetres. The average values were calculated using the experimental and simulation decrement values for both PCM types. The quantity of heat absorbed also showed that a thickness of 2 cm absorbed substantial amount compared to the thicker counterparts. The thicker sections will be costlier in an economic standpoint.
An extended study on optimal PCM thickness for three tropical climates (Coimbatore, Hyderabad, Mumbai) in India was also done using COMSOL Multiphysics. The above locations were selected as they were diversified in climatic conditions compared to the others. The data for the study was taken from epw (Energy Plus Weather) files for the corresponding locations and the same combinations were examined. The hottest day in the year was provided as the input interpolation function for the study for the simulations. The same interpolation function was applied on physical specimens as surface temperature using same setup as discussed earlier. The study indicated that a thickness of 2 to 3 cm was adequate to enhance the energy savings for both PCM types. Thicker sections of PCM increased construction costs, but the benefits were limited.