Enhancing the thermal conductivity of ethylene-vinyl acetate (EVA) in a photovoltaic thermal collector

This work was sponsored by ChapmanBDSP, London, UK and the Engineering and Physical Research Council, UK.


BACKGROUND
As the temperature of a PV cell increases, its electrical efficiency decreases.Estimates of the annual losses in performance due to temperature vary from 2.2 to 17.5%. 1 This loss is influenced by installation method; it has been shown that free-standing and ground mounted systems experience less temperature losses than those that are building integrated. 2 EVA is used to encapsulate PV cells and prevent environmental degradation; however these materials have low thermal conductivity.The multiple layers found in a typical PV laminate are shown in Figure 1.
The composite conductivity through the collector can be calculated using (1.1).
Using the values in Figure 1, the calculated conductivity of the composite is 0.82W/(m•K).If the conductivity of the EVA layer on the backside of the PV cell is increased from 0.23W/(m•K) to 2.85W/(m•K), 3 the overall composite conductivity increases by nearly 25% to 1.02W/(m•K).

Enhancing the Thermal Conductivity of EVA
EVA can be mixed with other materials to form composites with intrinsically different properties to the parent material.The mixing of ceramic powders and polymers, to increase thermal conductivity, is used in microelectronics, where heat needs to be efficiently dissipated away from sensitive chips and processors. 4he same concept can be applied to photovoltaic cells.A previous study by Lee et al. 3 revealed that filler materials increase the thermal conductivity of EVA from 0.23 to 2.85W/(m•K) .For a range of different filler materials, a concentration of 20% v/v resulted in a -0.97% to +5.05% change in power output compared to the parent material.. Kemaloglu et al. 5 used Boron Nitride filler with a particle size of approximately 10µm; the conclusion was that conductivity increases with reduced particle size and that nano-sized particles hold promise for the future.

Measuring Thermal Conductivity
Thermal conductivity can be measured using the method outlined in ASTM E1952. 6This method uses modulated differential scanning calorimetery (mDSC) to determine the specific heat capacity, which is then used to calculate the thermal conductivity.Thermal conductivity can also be measured using DSC by placing a 'melting standard' on top of the specimen. 7When heat is supplied from the DSC furnace, the specimen's conductivity is proportional to the melting rate of the standard and can be quantified through comparison with a reference material.[10][11]

METHODOLOGY Sample Preparation
BN powder (Carbotherm, Saint-Gobain, France) was mixed with EVA granules, in concentrations ranging from 10-60% w/w, using twin screw extrusion (HAAKE MiniLab II, Thermo Scientific, US) see Figure 2. The resulting extrusions were compression molded, to form sheets with a thickness of 1 mm.

Measuring Thermal Conductivity
6 mm discs were punched from the compressed sheets and placed into a DSC sample pan.The thermal interface resistance between the pan and the sample was reduced using a thin film of silicone oil, applied directly to the underside of the sample.Crodatherm-25 phase change material (PCM) (Croda, UK) was used as the melting standard because its melting point (25 • C) is well below that of EVA (89 • C).The thermophysical properties of Crodatherm are provided in Table III of the Appenidx.Approximately 2mg of the PCM melting standard was deposited on the surface of the sample disc.This was achieved by gently heating the PCM material above its melting point in a glass pipette, before releasing it and allowing it to recrystallise on the surface of the sample.The method assumes unidirectional heat flow from the DSC furnace, through the sample and into the melting standard.Care had to be taken to ensure that there was no contact between the aluminum pan and the melting standard.The sample pan was then placed, un-crimped, into the sample chamber of the DSC (Perkin Elmer, US), the DSC process is illustrated in Figure 3 (LDPE) with a certified conductivity of 0.33W/m•K (Goodfellow Cambridge Ltd., UK) was used as the reference material and was prepared using the same method detailed above.The melting rate is then calculated as the gradient of a line connecting the melting onset and melting point, see Figure 4. Equation (1.2) is then used to determine the thermal conductivity of the sample. 9 Where the subscripts r and s denote reference and sample respectively, D is disc thickness, A is the disc area, M is the melting rate and λ is the thermal conductivity.

Manufacture of PV laminate
The parent EVA material and doped extrusions were compression molded into 0.5 mm thick sheets measuring 155mm x 155mm.Two cells were laminated independently; one using the parent EVA, the other using the 50% BN/EVA w/w composite.0.12 mm T-type thermocouples (Omega, US) were positioned between the layers shown in Figure 1.The laminate was then placed between a constant heat source (25W ceramic heating mat) and heat sink (chilled absorber plate with inlet set to 21 • C) to generate a one directional heat flux through the laminate.The thermocouples recorded the temperature at each layer as the heat flux passed through the laminate.

Numerical Models
A numerical model based on the finite difference approach was developed to simulate the temperature distribution across the cross section of the PV laminate.The finite difference approach is shown in Figure 5.A system of equations was created to represent the PV laminate shown in Figure 5.A different equation was required for each nodal type.The four nodal types in this model are; exterior interface, layer node, internal interface and heat generation layer.An example of the equations for each type is provided in Table I.The problem was solved iteratively using a program coded in Fortran and the code is supplied in the Appendix.

Thermal Conductivity
EVA:BN composite was prepared with varying concentration of BN filler (10,20,30 and 60%) weight %.The thermal conductivity was measured for each sample and the results are shown in Figure 6.
Figure 6 shows that, by increasing the BN concentration from 0% to 60% w/w, thermal conductivity increases from 0.23 W/m•K to 0.83 W/m•K, with a linear regression value of 0.9956.To compare the results with the findings of the study by Lee 3 the mass fraction must be converted to volume fraction, ϕ, using (1.3).Where W , V and ρ are the weight, volume and density respectively; and subscripts, E and B denote EVA and BN respectively.For 60% w/w Boron Nitride to EVA, the corresponding volume fraction is approximately 40% v/v as shown in Table II.For 40% v/v BN concentration Lee et al. reported a thermal conductivity of approximately 0.75 W/m•K 3 which is agreement with the 0.83W/ m•K measured in this study.Lee et al. continued to increase the BN concentration up to 60% v/v; however it was found that increased filler increased the stiffness of the material, which could cause problems for manufacture and durability.The same issue was experienced in this study.

Interface Temperature
The thermocouples did not embed seamlessly between the layers; instead air bubbles formed around each thermocouple.An attempt was made to reduce the thickness of the thermocouple wire to 0.12 mm; however air bubbles were still present.To compensate for this variation, an average laminate temperature was calculated.A comparison of the doped vs standard EVA case is shown in Figure 7.The doped laminate was consistently around 6% cooler than the standard laminate, under the same conditions.

Numerical Models
The temperature profile across the external, interior and interface nodes were plotted for two cases and three conductivities of backing-EVA.In Case 1 the rear surface temperature of the laminate, T10, was fixed at a 25 • C.This case resembles the temperature controlled absorber plate of a PVT collector.The top surface was assigned an overall loss coefficient of 11W/m 2 • • C In Case 1, shown in Figure 8, the temperature of the PV cell, T5, is highest for the un-doped EVA.As the thermal conductivity of the backing-EVA increases, the PV cell temperature reduces.A temperature reduction of 0.7 • C in PV cell temperature is seen when thermal conductivity of the backing-EVA is increased from 0.23W/m•K to 0.83W/m•K.Using the power temperature coefficient for a crystalline cell, as supplied by the manufacturer (-0.42%/K), this would enhance the performance by 0.3%.Further increasing the thermal conductivity to 2.85 W/m•K, the PV cell temperature is reduced by an additional 0.2 • C indicating a non-linear relationship between the conductivity of the backing-EVA and PV cell temperature.The increased conductivity of the backing also reduces the overall temperature of laminate.The front surface of the panel is hottest for the 0.23W/m•K and coldest for the 2.85W/m•K backing-EVA.
In Case 2, a heat loss coefficient was applied to both the top surface and the rear surface of laminate; resembling a PV module that is evenly ventilated on each surface.The temperature was kept at 20 • C.
Case 2, shown in Figure 9, temperature of the PV cell highest for the standard EVA; when the thermal conductivity is increased from 0.23 W/m•K to 0.83 W/m•K, the temperature difference is much smaller than Case 1 at 0.1 • C, equating to a power improvement of 0.04%.The temperature difference between 0.83 W/m•K and 2.85 W/m•K is negligible.The rear surface temperature, T10, is lowest for the 0.23 W/m•K backing-EVA and highest for the 2.85 W/m•K .This is due to the low thermal conductivity of the backing material reducing heat flow and insulating the PV cell.This results in a higher PV cell temperature and lower surface temperature.
The PV cell temperature for Case 2 is higher (49.6The Carbotherm filler costs 240e/kg; it is believed that the improvements in both Case 1 and 2 do not justify the additional material and manufacturing costs.

CONCLUSION
Doping EVA with boron nitride increased the thermal conductivity by a factor of 4; which is in agreement with previous studies.However it was noticed that the material became stiffer and more brittle with increasing filler content.Further work is required to determine how this will influence the manufacture and lifetime of the PV module.A numerical model showed improvement in performance was 0.3% for a PVT collector.Considering the high price of thermal fillers, further research should focus on whether they are worth the cost for such a small increase in performance.Perhaps their use would be more suited to concentrator systems where higher temperatures are experienced.

AFIG. 1 .
FIG. 1.The layers of a PV laminate and their respective thicknesses and thermal conductivities.Thickness and thermal conductivity from Ref. 3.
FIG. 3. Illustration of the DSC melting standard method.

TABLE I .
Example of the equations used to represent the heat transfer through the laminate cross section.

TABLE II .
Calculation of volume fraction.FIG. 7. A comparison of the average laminate temperature for the enhanced and standard material.
• C) than that of Case 1 (26.7 • C); which is a 10% improvement in power output from the PV cell; thus showing the ability of a PVT collector to maintain the operating efficiency of the PV cell.