3.1. Aspect Ratio Effect
Figure 2a shows the streamlines (red dashed lines) and isotherms (black solid lines) for the case with a PCM melting point of 26 °C and aspect ratio (
Am) of 0.277 for practical weather conditions. The melted region has a fast temperature increase compared to the part that has not yet melted because the solid phase still has to go through the melting process, which keeps the MEPCM temperature almost constant.
Figure 2b shows the case with
Am = 1, where the temperature gradient slowly increases to a maximum and decreases afterwards.
Figure 3a shows that the minimum average efficiencies of the PV cell without the MEPCM layer and with
Am = 0.277 and
Am = 1 MEPCM layers are 18.80%, 18.91%, and 18.65%, respectively. The stable average efficiencies for the PV cell without the MEPCM layer and with
Am = 0.277 and
Am = 1 MEPCM layers are 18.84%, 18.94%, and 18.7%, respectively. Use of the MEPCM layer with
Am = 0.277 increases the stable average efficiency by approximately 0.1%. Use of the MEPCM layer with A
m = 1 decreases the stable average efficiency by approximately 0.14%.
Figure 3b shows that at both the left (
Qm,o) and right walls (
Qm,i), the heat transfer quantities for the case of
Am = 0.277 are higher than those for A
m = 1. The maximum heat transfer on the left and right for
Am = 0.277 is 241.2 kJ/m and 177.72 kJ/m, respectively. The maximum heat transfer on the left and right for
Am = 1 is 68.56 kJ/m and 68.93 kJ/m, respectively. For
Am = 0.277, the heat transfer on the left is much higher than that on the right, but for
Am = 1, it is the same on both sides.
Figure 2.
Streamlines (red) and isotherms (black) in the MEPCM layer. (a) Am = 0.277 (TM = 26 oC) and (b) Am = 1 (TM = 26 oC).
Figure 2.
Streamlines (red) and isotherms (black) in the MEPCM layer. (a) Am = 0.277 (TM = 26 oC) and (b) Am = 1 (TM = 26 oC).
Figure 3c has an initial displacement curve, which occurs because the increasing rate of heat input from the left side is much higher than the heat transfer on the right side. When these two heat transfer amounts are approximately equal, the energy fraction becomes zero (the
Am = 1 results); however, for
Am = 0.277, the heat transfer quantities are never equal, and the energy fraction is approximately 0.26.
Figure 3d shows that the amount of heat transferred to the interior of the cell (
Qm,i) with the MEPCM (for both
Am = 0.277 and
Am = 1) is less than that of the PV cell without the MEPCM. The amount of heat transferred to the exterior of the cell with the
Am = 1 MEPCM layer is larger than that of the PV cell without the MEPCM layer, but the cell with the
Am = 0.277 MEPCM layer has a smaller amount of heat transferred than the PV cell without the MEPCM. The total electrical gain, heat transfer to the exterior, and heat transfer to the interior of the PV cell without the MEPCM layer are 559.94 kJ/m, 628.06 kJ/m, and 313.53 kJ/m, respectively. The total electrical gain, heat transfer to the exterior, and heat transfer to the interior of the PV cell with the
Am = 0.277 MEPCM layer are 562.98 kJ/m, 534.71 kJ/m, and 177.72 kJ/m, respectively. The total electrical gain, heat transfer to the exterior, and heat transfer to the interior of the PV cell with the
Am = 1 MEPCM layer are 555.67 kJ/m, 700.45 kJ/m, and 68.93 kJ/m, respectively.
Figure 3.
Thermal and electrical performance of PV module with and without MEPCM layer of different aspect ratios of Am = 0.277 and 1. (a) Average temperature and efficiency of PV cell; (b) Total heat transfer rate across the MEPCM layer; (c) Fraction of energy stored inside the MEPCM layer; and (d) Total heat transfer rate across the PV cell.
Figure 3.
Thermal and electrical performance of PV module with and without MEPCM layer of different aspect ratios of Am = 0.277 and 1. (a) Average temperature and efficiency of PV cell; (b) Total heat transfer rate across the MEPCM layer; (c) Fraction of energy stored inside the MEPCM layer; and (d) Total heat transfer rate across the PV cell.
The aspect ratio seems to affect whether the MEPCM layer is advantageous or disadvantageous for the electrical energy gain or electrical efficiency. For example,
Am = 0.277 gives a better electrical energy gain and better PV cell efficiency, but
Am = 1 reduces the electrical energy gain and electrical efficiency. The results in
Figure 3b imply that the interior wall temperature for
Am = 1 is lower than that for
Am = 0.277, but the
Am = 1 layer cannot maintain the outer temperature,
i.e., the PV cell temperature below the outer temperature of the
Am = 0.277 layer. Thus, we can conclude that
Am = 1 reduces the heat transferred through the interior wall but is not good for improving the electrical efficiency of the PV cell, while
Am = 0.277 can somewhat improve the efficiency because the temperature, compared to that of only the PV cell, is too small.
3.2. Melting Temperature Effect
Figure 4a shows that the minimum average efficiencies for the PV cell without the MEPCM layer and with the
TM = 26 °C and
TM = 34 °C MEPCM layers are 18.80%, 18.91%, and 18.9%, respectively. The stable average efficiencies for the PV cell without the MEPCM layer and with the
TM = 26 °C and
TM = 34 °C MEPCM layers are 18.84%, 18.94%, and 18.94%, respectively. Use of the
TM = 26 °C MEPCM layer increases the minimum average efficiency by approximately 0.11%. Inclusion of the
TM = 34 °C MEPCM layer decreases the minimum average efficiency by approximately 0.1%.
Figure 4b shows that the maximum heat transfers on the left (
Qm,o) and right walls (
Qm,i) for
TM = 26 °C are 241.2 kJ/m and 177.72 kJ/m, respectively. The maximum heat transfers on the left and right for
TM = 34 °C are 225.8 kJ/m and 191.45 kJ/m, respectively. For
TM = 26 °C, the heat transfer on the left is much higher than that for
TM = 34 °C, but the heat transfer on the right wall for
TM = 34 °C is higher than that for
TM = 26 °C.
Figure 4c shows an initial displacement curve, which occurs because the increasing rate of heat input from the left side is much higher than the heat transfer on the right side due to increasing solar irradiation. The energy fraction for
TM = 34 °C starts to increase later than when
TM = 26 °C because its melting point is higher. Neither of these stored energy fractions reaches zero. In the end, the
TM = 26 °C and
TM = 34 °C layers have a stored energy fraction of approximately 0.26 and 0.152, respectively.
Figure 4d shows that the heat transferred to the interior and exterior using the MEPCM (both
TM = 26 °C and
TM = 34 °C) is less than that of the PV cell without the MEPCM layer. The total electrical gain, heat transfer to the exterior, and heat transfer to the interior of the PV cell without the MEPCM layer are 559.94 kJ/m, 628.06 kJ/m, and 313.53 kJ/m, respectively. The total electrical gain, heat transfer to the exterior, and heat transfer to the interior for the PV cell with the
TM = 34 °C MEPCM layer are 562.98 kJ/m, 534.71 kJ/m, and 177.72 kJ/m, respectively. The total electrical gain, heat transfer to the exterior, and heat transfer to the interior for the PV cell with the
TM = 26 °C MEPCM layer are 562.86 kJ/m, 549.12 kJ/m, and 191.45 kJ/m, respectively.
Figure 4.
Thermal and electrical performance of PV module with and without MEPCM layer (Am = 0.277) with different melting points of TM = 26 and 34 °C. (a) Average temperature and efficiency of PV cell; (b) Total heat transfer rate across the MEPCM layer; (c) Fraction of energy stored inside the MEPCM layer; and (d) Total heat transfer rate across the PV cell.
Figure 4.
Thermal and electrical performance of PV module with and without MEPCM layer (Am = 0.277) with different melting points of TM = 26 and 34 °C. (a) Average temperature and efficiency of PV cell; (b) Total heat transfer rate across the MEPCM layer; (c) Fraction of energy stored inside the MEPCM layer; and (d) Total heat transfer rate across the PV cell.