ANALYSIS OF FLAT PLATE PHOTOVOLTAIC-THERMAL (PVT) MODELS

ANALYSIS OF FLAT PLATE PHOTOVOLTAIC-THERMAL (PVT) MODELS J. Bilbao and A. B. Sproul School of Photovoltaic and Renewable Energy Engineering University of New South Wales Kensington, NSW 52, Australia j.bilbao@unsw.edu.au ABSTRACT In this work the performance of four PVT water models were compared: the default TRNSYS PVT model Type50, a modified version of the same model (Type50-C), a new model (Type850) developed using analytical solutions and the empirical relation presented by Akhtar and Mullick [11] to calculate the cover temperature in flat plate collectors, and a double iteration numerical model. A detailed analysis and comparison between all four models was carried out to identify specific errors, and Type50 and Type850 were also compared based on the annual thermal and electrical yields of a PVT residential system using TMY2 data. Results show that errors from some models can be as high as 6 under specific conditions, and close to 1 for annual yield figures. Key words: Photovoltaic-Thermal, PVT, Modeling, 1. INTRODUCTION Within TRNSYS 16, the default model for PVT systems simulations is Type50, which is based on the Florschuetz [1] model to simulate the performance of PVT water systems. In essence, it is an extension of the Hottel-Whillier [2] model for flat plate collectors. Type50 also incorporates the empirical expression for heat losses developed by Klein [3] in conjunction with the convection loss coefficient suggested by McAdams [4]. This is more or less the standard Duffie and Beckman approach [5] which has been widely used for the last 30 years. Today, more accurate models and empirical expressions exist. Charalambous et al [6] was the first to present a review of the literature available for PVT systems, covering existing analytical and numerical models, simulations and experimental work. Later, Zondag presented a complete review [7] of PVT technology, including models developed. In summary, most of the early work on PVTs developed analytical models based on the Hottel-Whillier [2] model for flat plate collectors. According to Charalambous Florschuetz modified the Hottel Willier analytical model for flat plate collectors so all existing expressions and information available in the literature (such as the collector efficiency factor, F and the heat removal factor, F r ) still apply. Bergene and Løvvik [8] found that their model (a more detailed version of the Hottel-Willier model) was able to predict PVT system efficiencies well, but they could not compare their results to experimental data as system parameters were missing in the available literature. Sandnes and Rekstad [9] found a good level of agreement with their experimental results. Zondag et al [10] developed and compared four numerical models, a 3D dynamical model, and 3D, 2D and 1D static models. He found that all the models simulate the PVT system efficiency within 5% error of the experimental data, and that the 1D model, based on Hottel Whillier and Klein equations, was well suited for annual yield studies, mainly for its computational speed. Although, annual yield figures for a domestic PVT system were reported, they were obtained by using the 1D model, and no comparison with the more accurate numerical models was carried out. It could be concluded from the literature that Klein s equation gives a reasonable approximation for steady state models, with an adequate agreement with experimental 1

data. However, Klein s equation has not been tested against annual yield results using experimental data or other models. Moreover, according to Akhtar and Mullick [11], Klein s equation can produce errors of up to 1 in the estimation of the top losses of a flat plate collector for high plate temperatures, and around 5% for low plate temperatures. In the same publication, Akhtar and Mullick propose a new experimental relation to estimate the cover temperature of a flat plate hot water system, in replacement of Klein s equation. The objective of this work was to check the results of different PVT models for collectors with and without a cover. The analysis is focused on heat transfer from the top surfaces of the collector, and therefore is relevant not just for PVT water models but also PVT air. Particular attention was paid to the performance of the standard model included in TRNSYS, Type50 (and therefore Florschuetz and Klein approach), against more accurate models, like the developed Type850. Section two of this paper will describe in detail all the models used in the work. In section three, the results of several simulations between the models are presented, including in-depth comparisons. Finally, in section four, several conclusions and recommendations are provided. The nomenclature is presented in section five. 2. DESCRIPTION OF PVT MODELS USED A total of four PVT models were used in this work: 1) a numerical model using a double iteration solving method of the heat transfer equations; 2) a numerical model, with a single iteration process, where the cover temperature is calculated using the relations developed by Akhtar and Mullick (Type850); 3) Type50 model (part of the standard TRNSYS software package); 4) a modified version of Type50, in which F is calculated for each simulation (called Type50-C). All of the above models were implemented in Excel. These models can generate quick steady state results under particular conditions, and are used for detailed comparison between the models, but are not suited for year long simulations. In order to study the effects of the approximations made in Type50 on an annual yield basis, model number 2, called Type850 from now onwards (work of the authors), was also implemented in TRNSYS, due to its simplicity and good accuracy when compared to the double iteration numerical model (model number 1). 2.1 Double iteration numerical model (implemented in Excel) As its name implies, in this numerical model a double iteration is required to calculate all the heat transfer equations for the case of the PVT collector with cover. First, the initial cover and absorber plate temperatures are set: for the cover temperature the ambient temperature plus one degree is used, and 100 C is used for the plate temperature, which is close to the stagnation temperature. With T p and T c, the Nusselt number of the air in the cavity is estimated using Buchberg [12] relation, in order to calculate the convection losses between both surfaces. Also, from Cooper [13] the relations from the Tables of Thermal Properties of Gases, U.S. Department of Commerce, were used to model the property of the air in the cavity between the plate and cover, according to the average temperature of both surfaces. Then all the convective and radiative losses are calculated and combined as per equation 1, in order to estimate the total losses of the PVT module. (1) [( ) ( ) ] where U rpc and U cpc are the radiative and convective losses between the plate and the cover, U rcs and U w are the radiative and convection losses of the top cover, and U BE is the back and edge losses, constant during the simulation. Then, the thermal efficiency factors are calculated, starting by F, using the equation for collectors with square channels: (2) where h f is the total thermal conductance between the plate and the fluid. F r is calculated using the standard equation in [5]. Then the electrical and thermal useful energy rates per unit of area are calculated using: (3) [ ( )] (4) ( ( )) Notice that for the thermal energy output, the absorbed solar energy is corrected using the electrical energy produced by the PV cells. The mean plate temperature and the cover temperature are calculated using an energy balance approach: (5) In the following sections all the models will be described in more detail. (6) ( ) ( ) ( ) 2

From this point onwards, the new values of T p or T c can be used to recalculate all the equations until the chosen variables converge. Then the same process can be used with the other variable until it converges. This double iteration process will have to be repeated until the error in both variables is small. If done manually it can be a lengthy process, but in excel the solver routine can be used, and solutions are found automatically. For the case of the PVT collector without a cover, there is no need to estimate the cover temperature and a single iteration approach is enough to accurately calculate all the heat losses. The simulation starts with an initial estimation of the plate temperature. Then, the total losses (U L ) are calculated by adding the radiation (U rcs ) and convection (U w ) losses from the top of the panel, plus the back and edge losses (U BE ). Once the losses are calculated, the same equations used for the collector with a cover (Eqs. 2, 3, 4, and 5) are used to calculate F, F r, Q e, Q u, and T p, but the cover temperature is replaced by the plate temperature when required. 2.2 Single iteration model, TYPE850 (implemented in Excel and TRNSYS) In this model, the empirical relations developed by Akhtar and Mullick [11] to estimate the cover temperature of Flat Plate Solar Collectors were used. One of the strengths of these empirical relations is that they allow for the use of the Sky Temperature, and therefore, the correct calculation of the radiation losses. The algorithm and equations used in this model are exactly the same as in the double iteration model, except for the use of the cover temperature equations. This allows having one less unknown variable and therefore, only a single iteration process can be used. This iteration allows for the selfcorrection of the thermal energy output (eq. 4) and U L, so there is no need to use Florschuetz s proposed adjustment for PVT panels. This also allows the use of Akhtar and Mullick equations without the need of any modifications. For the case of the PVT collector without a cover, the algorithm and equations are the same as for the first model. 2.3 Standard PVT model, Type50 (implemented in Excel, existing in TRNSYS) As explained above, Type50 is a very close implementation of Florschuetz [1] work. Type50 has four modes of operation for flat plate collectors, and other modes for concentrating collectors not reviewed in this paper. In this work, MODE 2 will be used because it proved to be more stable than the others. However, in MODE 2 the angular dependence of the cover transmisivity is considered constant (unlike MODE4 which includes the incident angle modifiers, but was unable to converge), so adjustments were introduced to the solar irradiance data to take into account the angle of incidence to make a fair comparison with the rest of the models. Type 50 also uses a single iteration approach to solve the heat transfer equations, thanks to the use of Klein s equation to estimate the top cover losses. Some key Type50 model details and differences with the original Florschuetz work are: - The algorithm runs for three iterations (controlled by an internal counter) for each time step, after which the program exits the simulation with whatever values are achieved. - Equations for the calculation of F were not implemented in Type50, as F is a given parameter to the model and remains constant through the whole simulation. - The mean fluid temperature is approximated as the average of the inlet and outlet temperature, which is different to the true analytical value. - The cell temperature is calculated at the end of each time step and is used only for output purposes and not as part of the internal calculations. - The thermal losses are calculated using the empirical equation developed by Klein [3], which does not take into account the sky temperature - In the implementation of Klein s equation in Type50, the mean water temperature is used instead of the mean plate temperature. In the Excel implementation of this model, the three iterations limit was not used, and the algorithm runs until the values converge. 2.4 Modified Standard PVT model, Type50-C (implemented in Excel) This type uses the same equations as Type50, but F is calculated using equation 2 for each simulation. This allows an accurate value of the efficiency factor to be calculated depending on the calculated heat losses. Although this is certainly an improvement over Type50, it also makes the model more susceptive to the possible errors introduced in the calculation of the top losses by Klein s equation. 3. RESULTS In the first three parts of this section, all the models using empirical equations (models 2 to 4) are compared in detail against the double iteration numerical model (model 1), studying for example the impact of the simplifications made 3

Tamb ( C) Tamb ( C) in Type50, particularly, the use of the constant F coefficient. For the purpose of these comparisons, the Excel implementations of the models were used, with the parameters at design conditions, shown in Table 1. TABLE 1: PARAMETERS AT DESIGN CONDITIONS FOR THE CALCULATION OF F Value Value Parameter No Cover Cover Description H 800 800 Solar Radiation (W/m 2 ) V w 2 2 Wind velocity (m/s) T in Inlet Temperature ( C) T amb Amb. Temperature ( C) B 30 30 Panel Tilt (degrees) ε p 0.850 0.850 Collector Plate Emissivity ε g - 0.850 Glass cover Emissivity α 0.900 0.900 Effective Absorptance τ 0.9 0.846 Total Transmittance η r 0.144 0.144 Cell Eff. at Ref. Temp. β r 0.0048 0.0048 Cell Temp. Coef. (1/K) ů 0.0 0.011 Mass Flowrate (Kg/s.m 2 ) h f 56.923 43.258 Plate to Fluid (W/m 2.C) U L 18.596 4.622 Total Losses (W/m 2.C) F 0.754 0.903 Collector Eff. Factor In part 3.4 of this section, Type50 and Type850 are compared on an annual basis, using a simulation of a residential hot water system in TRNSYS. 3.1 Effects of F simplification F was calculated at the design conditions (see Table 1) and kept constant in Type50, but it was calculated for each simulation in Type50-C. The value of F r was compared for both models to quantify the errors of the simplification, because is directly proportional to the useful thermal energy Q u. Results for different combinations of ambient temperature, inlet temperature and wind velocity are shown in Figure 1 and Figure 2 respectively, for both type of collectors (with and without a cover). For the panel without a cover, changes in the wind speed have an important impact in the calculation of F r, so the changes in the inlet and ambient temperatures are dwarfed in comparison. This is a logical result, because convection losses are dominant in a coverless panel. When the panel operates close to the design conditions, the errors are small and less than 5%, but at high wind speeds errors can escalate up to 3. The problem of Klein s equation for coverless panels as implemented in Type50, is the use of the mean fluid temperature instead of the correct mean plate temperature. The effects of a constant F are less pronounced in PVT modules with a cover, as the maximum a) F r percentage error (T amb = T sky = C, N = 0) 30 28 5%-1 26-5% 24-5%- 22-1--5% -15%--1 -%--15% 18-25%--% 16-3--25% -35%--3 14 0 1 2 3 4 5 6 7 8 9 10 Wind Velocity (m/s) b) F r percentage error (T amb = T sky = C, N = 1) 55 50 2%-3% 45 1%-2% -1% 40-1%- 35-2%--1% 30-3%--2% 25-4%--3% -5%--4% 15-6%--5% 0 2 4 6 8 10 Wind Velocity (m/s) Fig. 1: F r percentage error for fixed ambient temperature a) F r percentage error (T in = C, N = 0) 30 28 5%-1 26-5% 24-5%- 22-1--5% -15%--1 -%--15% 18-25%--% 16-3--25% -35%--3 14 0 1 2 3 4 5 6 7 8 9 10 Wind Velocity (m/s) b) F r percentage error (T in = C, N = 1) 24 1.5%-2. 22 1.-1.5% 0.5%-1. 0.-0.5% -0.5%-0. 18-1.--0.5% -1.5%--1. -2.--1.5% 16-2.5%--2. -3.--2.5% 14 0 2 4 6 8 10 Wind Velocity (m/s) Fig. 2: F r percentage error for fixed inlet temperature. 4

(W/m2) (W/m2) error is kept below 6%. In this case, the inlet temperature is shown to have an equally important effect to the wind velocity. The results suggest that the effects of using a fixed F are reasonable for a PVT system with a cover. 3.2 Comparison of Type50, 50-C, and 850 against Model 1 Klein s equation is close to the correct calculation of top losses when ambient temperature is similar to sky temperature (cloudy sky), so Type50 should perform well under these conditions. However, PVT panels have high emissivity unlike solar hot water collectors that usually have selective surfaces so it s expected that changes in the sky temperature will produce noticeable effects in the performance of the models even for panels with covers. The model using Akhtar and Mullick equations was also included. Figure 3 shows the errors for q u and Figure 4 for U L, for PVT panels with (N=1) and without (N=0) cover. For this set of simulations all the parameters were kept at the design conditions (best case scenario for Type50), except for the inlet temperature. From Figure 3 and Figure 4 we can conclude that: - The levels of error for Type50-C are close to zero for cloudy sky conditions, and independent of wind velocity and inlet temperature. In clear sky conditions, the errors are limited to 50 W/m 2. - Type50 does not perform well in the calculation of q u, resulting in errors above 150 W/m 2, for clear and cloudy skies. The use of a fixed F has an undesirable large impact in this case. - In the calculation of U L, both models, Type50 and Type50-C, have considerable errors except for the panel without a cover and cloudy skies. In all other cases, the errors are significant - Because the thermal losses are underestimated, the useful thermal energy for both models, Type50 and Type50-C, were overestimated, although the corrected model has consistently smaller errors. - The model using Akhtar and Mullick equations does remarkably well, with errors well below 5% for U L and under 1 to 2 W/m 2 for q u, which is a big improvement over Type50. The correction factor proposed by Florschuetz [1] can account for up to 5% of difference in the calculation of U L. When using iterative methods, the extra correction leads to a under prediction of U L and over prediction of the useful thermal output. The results show that the biggest limitation of Type50 is the implementation of Klein s equation, as even Type50-C, using correct F values can produce errors as high as 7% at the design conditions, and up to 17% in the worst cases. 3.3 Performance under stagnation It s important to study no flow conditions in a PVT system, more than in a normal flat plate collector, because the temperatures reached in the plate affect the electric performance. Therefore, it is imperative for a PVT model to estimate as accurately as possible the stagnation temperatures. -1-15% -% -25% -3-35% -4-45% -5-55% 0 180 160 140 1 100 80 60 40 a) q u absolute error (Wv=2m/s, Ta= C, N=0) 0 15 25 30 35 40 0 180 160 140 1 100 80 60 40 Type50-C, Ts=Ta Type50, Ts=Ta Type50-C, Ts=Ta-18 Type50, Ts=Ta-18 b) q u absolute error (Wv=2m/s, Ta= C, N=1) 0 15 25 30 35 40 45 50 55 A&M, Ts=Ta Type50-C, Ts=Ta Type50, Ts=Ta A&M, Ts=Ta-18 Type50-C, Ts=Ta-18 Type50, Ts=Ta-18 Fig. 3: q u absolute error compared to numerical model. 5% -5% a) U L percentage error (Wv=2m/s, Ta= C, N=0) -6 15 25 30 35 40 45 50 55 Type50-C, Ts=Ta Type50, Ts=Ta Type50-C, Ts=Ta-18 Type50, Ts=Ta-18 b) U L percentage error (Wv=2m/s, Ta= C, N=1) 5% -5% -1-15% -% -25% -3-35% -4-45% -5-55% -6 15 25 30 35 40 45 50 55 A&M, Ts=Ta Type50-C, Ts=Ta Type50, Ts=Ta A&M, Ts=Ta-18 Type50-C, Ts=Ta-18 Type50, Ts=Ta-18 Fig. 4: U L percentage error compared to numerical model. 5

(W/m2) (W/m2) 1 0-1 -2-3 -4-5 -6-7 a) q e absolut error (Wv=2m/s, Ta= C, N=0) connected to a 300 liter electric boosted hot water tank, with a set point of 60 C. The electric output of the PV array is assumed to be always at the maximum power point, and no losses in the inverter or cables have been incorporated. For both models a PVT panel of 1.28m 2 was used, with an electrical efficiency of 14% at STC. The size and the electrical efficiency of the PVT panel are similar to commercially available PV panels. -8 15 25 30 35 40 45 50 55 Type50, Ts=Ta Type50, Ts=Ta-18 1 0-1 -2-3 -4 b) q e absolute error (Wv=2m/s, Ta= C, N=1) -5% -1-15% -% -25% -3 a) Q aux percentage error (18 panels) -5-6 -7-8 15 25 30 35 40 45 50 55 A&M, Ts=Ta Type50, Ts=Ta A&M, Ts=Ta-18 Type50, Ts=Ta-18 Fig. 5: q e absolute error compared to numerical model in stagnation conditions. Depending on the size of the system, and its operation and controls, it is probable that a PVT system will spend several hours in stagnation during summer. Figure 5 shows the results for the error in the calculation of the electric output per unit of area, for different wind, inlet temperature (needed for the calculation T mf and of U L in Klein s equation), and sky temperature under stagnation. As can be seen, Type50 tends to underestimate the electrical output under stagnation conditions; which will suggest an overestimation in the plate temperatures. This agrees with the results reported by the ECN [14]. Errors in the collector without a cover are generally small. For the collector with a cover, errors are more important and close to 1 under design conditions or around 7 (W/m2). The model using Akhtar and Mullick equations again performs well. 3.4 Annual Yields Comparison in TRNSYS In this section, the thermal and electrical annual yield of a residential PVT system located in Sydney, Australia, are presented. The system was simulated using TRNSYS, with two different PVT models: Type50, and Type 850. The simulation models the energy requirements of a standard four person residence in the Sydney climate. The annual hot water energy consumption is estimated to be 2,709 kwh, or 7.4 kwh/day, and the annual electric energy usage is estimated as 8,249 kwh, or 22.6 kwh/day (total daily energy consumption of 30kWh); figures derived from DEWHA and IPART reports [15-16]. The PVT system is -35% 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Flow Rate (Kg/s.m2) Sydney - No Cover Melbourne - No Cover Sydney - With Cover Melbourne - With Cover 6% 4% 2% -2% -4% -6% -8% b) Q pv percentage error (18 panels) -1 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Flow Rate (Kg/s.m2) Sydney - No Cover Melbourne - No Cover Sydney - With Cover Melbourne - With Cover 6% 4% 2% -2% -4% -6% -8% c) Q net percenatge error (18 panels) -1 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Flow Rate (Kg/s.m2) Sydney - No Cover Melbourne - No Cover Sydney - With Cover Melbourne - With Cover Fig. 6: annual yield percentage error for different parameters and climates, Type50 against Type850. A system of 3,240Wp comprised of 18 panels was chosen to simulate a typical system, similar to what would be installed on a house rooftop. Two scenarios were used, systems with and without a cover. All the parameters are kept equal between both models and scenarios. Results of the errors between Type 50 and Type 850 are presented in Figure 6: auxiliary energy (Q aux ), the electrical energy (Q pv ), pump energy (Q pump ), and the net energy (Q net ) defined as Q net = (Q load - Q aux ) + Q pv - Q pump. 6

The results show that Type50 is consistently over predicting the thermal output, and therefore, the auxiliary energy required is under predicted with respect to Type 850. Errors for the annual amount of required auxiliary energy are around 15% for panels with cover and 6% for panels without a cover. On the electrical output, Type50 with a cover under predicts the annual yield by 7% and over predicts the panel without a cover by 3%, i.e., Type50 with cover runs hotter than Type850, and Type50 without a cover runs cooler. The energy required by the pump is in direct relation of the amount of hours that the thermal system was working. In this scenario, Type50 with and without a cover runs the pump 7% and % longer time frames, respectively. Some findings might seem contradictory, but in reality, they reflect how a PVT system performance changes depending on the size of the system, its operation, and in particular, if it was carried out as an individual unit or as part of a system. This reaffirms the point that PVT systems performance and design should be always analyzed in the context of an application. 4. CONCLUSIONS From the specific analysis of Type50, we can summarize the shortcomings of the model as: - The value of F is assumed as a constant parameter, independent of the changes in the total losses U L which depends on ambient conditions (wind speed, ambient temperature) and fluid temperature. Errors of up to 1 are expected when maintaining F constant. - Sky temperature is not used for the calculation of radiation losses. This is particularly important in PVT systems, compared to hot water collectors, because PV panels have high emissivity. - The model implements the original equation of Klein [3] using T mf instead of T p. This leads to more errors and instabilities when T mf < T amb. For PVT systems with small areas, this is not an uncommon scenario (Akhtar and Mullick equation has the same problem when T p < T amb, less often). - The model uses Florschuetz s correction factor for U L to account for the electrical output of the system. However, it is considered that this correction factor should not be used. - As a result, Type50 calculation of U L can produce errors of up to 6 in the worst cases. - Although 3 iterations should be enough for the model to converge most of the times, there is no guarantee that moderate errors could not be happening in some time steps. From the annual yield analysis we can conclude that: - Even though the errors are in general smaller than in the specific analysis, some serious differences are still present, specifically regarding the thermal output and its effect in the auxiliary power, with maximum errors of 16% for Sydney climate and 32% for Melbourne climate. - Type50 underestimates the thermal losses of the panel and therefore the model overestimates the thermal output. This results in the controller running the pump more hours during the year, which leads to large errors in the calculations of the annual energy required by the pump system. - PV electric energy output errors are of the order of ±5%, which can be considered acceptable. - As for any summary of data, the annual yield gives an average of the errors, possibly masking large differences in the operation of the system in a day to day basis. In conclusion, it appears clear that Type50 offers several limitations where high levels of accuracy are required. Although the electrical output accuracy is worrying at a model level, the errors in the annual yield case are acceptable. The errors on the thermal output can be above 1, which introduces a higher level of uncertainty in the design of a system. On the other hand, the work proposed by Akhtar and Mullick [7] proved to be exceptionally accurate when compared to the complete numerical solution. Finally, it is recommended that system analyses with whole year simulations (using TMY2 data or similar) should be used to study the performance of PVT systems and to compare different models. 5. NOMENCLATURE B tilt angle of panel F collector efficiency factor F r collector heat removal factor H total solar radiation incident on collector N number of covers q u useful thermal energy collection rate per unit area q e useful electrical energy collection rate per unit area S absorbed solar radiation per unit area T a ambient temperature T c cover temperature T in inlet temperature T p mean plate temperature T r PV reference temperature T s sky temperature h f thermal conductance between absorber and fluid U BE bottom and edges heat loss coefficient U L overall heat loss coefficient U cpc convection heat loss coefficient among plate and cover U rcs radiation heat loss coefficient between cover and sky U rpc radiation heat loss coefficient between plate and cover U w convection heat loss coefficient due to wind speed ů mass flow rate V w wind velocity α effective absorptance of collector absorber 7

β r σ ε g ε p η r τ temperature coefficient of solar cell Stefan Boltzmann constant glass emissivity absorber plate emissivity cell efficiency at reference temperature transmittance of collector glass cover (16) IPART, Residential energy and water use in Sydney, the Blue Mountains and Illawarra Results from the 06 household survey, Independent Pricing and Regulatory Tribunal of New South Wales, 07 6. REFERENCES (1) Florschuetz, L. W., Extension of the Hottel-Whillier model to the analysis of combined photovoltaic/thermal flat plate collectors, Solar Energy 22(4): 361-6, 1979 (2) Hottel, H. C., Whillier, W., Evaluation of flat-plate solar collector performance, Proceedings Of the Conference on the use of Solar Energy, University of Arizona, Vol II: 74-104, 1958 (3) Klein, S.A., Calculation of flat-plate collector loss coefficients, Solar Energy 17: 79-80, 1975 (4) McAdams, W.C., Heat Transmission (3 rd Edn), McGraw-Hill, 1954 (5) Duffie, J.A. and Beckman W.A., Solar Engineering of Thermal Processes (3 rd Edn), Wiley, 06 (6) Charalambous, et al., Photovoltaic thermal (PV/T) collectors: A review, Applied Thermal Engineering 27(2-3): 275-286, 07 (7) Zondag, H. A., Flat-plate PV-Thermal collectors and systems: A review, Renewable and Sustainable Energy Reviews 12(4): 891-959, 08 (8) Bergene, T. and O. M. Løvvik., Model calculations on a flat-plate solar heat collector with integrated solar cells, Solar Energy 55(6): 453-462, 1995 (9) Sandnes, B. and J. Rekstad., A photovoltaic/thermal (PV/T) collector with a polymer absorber plate. Experimental study and analytical model, Solar Energy 72(1): 63-73, 02 (10) Zondag, H. A., de Vries, D. W., et al., The thermal and electrical yield of a PV-thermal collector, Solar Energy 72(2): 113-128, 02 (11) Akhtar, N. and Mullick, S. C., Approximate Method For Computation of Glass Cover Temperature and Top Heat-Loss Coefficient of Solar Collectors with Single Glazing, Solar Energy 66(5):349 354, 1999 (12) Buchberg, H., Catton, I., Edwards, D.K., Natural Convection in Enclosed Spaces - A Review of Application to Solar Energy Collection, Journal of Heat Transfer 98(2): 182-189, 1976 (13) Cooper, P.I., The Effect of Inclination on the Heat Loss From Flat-Plate Solar Collectors, Solar Energy 27(5):413-4, 1981 (14) PVT performance measurement guidelines, PV Catapult, ECN and ISFH, 05 (15) DEWHA, Energy Use in the Australian Residential Sector 1986, Department of the Environment, Water, Heritage and the Arts, 09 8