Theoretical and experimental investigation of the thermal performance of a double exposure flat-plate solar collector

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ScienceDirect Solar Energy 119 (2015) 100–113 www.elsevier.com/locate/solener

Theoretical and experimental investigation of the thermal performance of a double exposure flat-plate solar collector N. Nikolic´, N. Lukic´ ⇑ Faculty of Engineering, University of Kragujevac, Sestre Janjic´ 6, 34000 Kragujevac, Serbia Received 24 March 2015; received in revised form 30 May 2015; accepted 2 June 2015

Communicated by: Associate Editor Brian Norton

Abstract This paper presents the results of a theoretical and experimental investigation of a double exposure, flat-plate solar collector with a flat-plate reflective surface. The main role of the reflector, which is placed below and parallel to the collector, is the reflection of solar radiation on the lower absorber surface. To enable absorption from the lower absorber surface, it is necessary for the insulation mounted on the lower part of the collector box to be removed and the lower box surface replaced by a glass cover. In order to determine the feasibility of the proposed concept, theoretical and experimental investigations of a double exposure and conventional flat-plate solar collectors were carried out. The experimental tests verified the developed mathematical models of the thermal behaviour of the mentioned solar collectors. The main advantages of the proposed collector–reflector system in relation to the previously investigated are: parallelism between the reflector and the collector, mirror reflective surface and mobility of the reflector in all three possible orthogonal directions. The proposed system is simpler because it consists of only one reflector. The experimental and theoretical results show that performance of a double exposure, flat-plate solar collector can be significantly higher than a conventional solar collector. The experimentally obtained relative difference of thermal power of these collectors is in the range of 41.79–66.44%, the highest achieved value of this difference in the reviewed literature is 48%. Ó 2015 Elsevier Ltd. All rights reserved.

Keywords: Double exposure solar collector; Flat-plate reflector; Thermal performance; Experiment

1. Introduction The increasing need for renewable energy sources, specifically solar energy, requires more complex research to be conducted to improve the efficiency of systems that transform solar energy. The most common solar systems are flat-plate (water) solar collectors (FPCs). The mentioned collectors transform solar energy into heat energy through an absorber plate with high thermal conductivity (copper, aluminium) placed in an insulated box with a flat glass cover. The main carrier of heat energy is a working ⇑ Corresponding author. Fax: +381 34 357 884.

E-mail address: [email protected] (N. Lukic´). http://dx.doi.org/10.1016/j.solener.2015.06.038 0038-092X/Ó 2015 Elsevier Ltd. All rights reserved.

fluid (water or antifreeze liquid) that passes through the absorber or absorber tubes integrated or attached to the same. Conventional flat-plate collectors receive a relatively low solar flux and have an average efficiency, especially at lower level of solar radiation. Many investigations have been carried out to improve a performance of flat-plate collectors by concentrating solar radiation using reflector. A small part of those investigations has focused on a system of the flat-plate solar collector and flat-plate reflector (McDaniels et al., 1975; Larson, 1979, 1980; Hussein et al., 1999; Taha and Eldighidy, 1980; Tanaka, 2011, 2015; Ekechukwu and Ugwuoke, 2003; Farooqui, 2015; Grassie and Sheridan, 1977; Bollentin and Wilk, 1995;

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Nomenclature A bcon cp D Din F F0 F00 FR Frc G H0 H0 G hc–f hc hr I i Kg Kls Kllow Klup kcon kd ki kt Lv lgeo m Q Ql Qcon T V Vwind W

area (m2) bond width (m) specific heat of collector fluid (J/kg K) diameter of the absorber tube (m) inside diameter of the absorber tube (m) fin efficiency collector efficiency factor collector flow factor collector heat removal factor view factor collector tilt angle (rad) intensity of the instantaneous (hourly) solar radiation on a horizontal surface (W/m2) intensity of the instantaneous (hourly) solar radiation on a tilted surface (W/m2) heat transfer coefficient between the fluid and the tube wall (W/m2 K) convection heat transfer coefficient (W/m2 K) radiation heat transfer coefficient (W/m2 K) total absorbed solar radiation (W/m2) incident angle (rad) collector overall loss coefficient (W/m2 K) collector edge loss coefficient (W/m2 K) collector bottom loss coefficient (W/m2 K) collector top loss coefficient (W/m2 K) bond thermal conductivity (W/m K) diffuse fraction collector insulation thermal conductivity (W/m K) clearness index distance between the absorber and the upper glazing of the collector (m) longitude (°) mass flow rate (kg/s) useful thermal power of the collector (W) collector overall thermal losses (W) energy rate which by conduction enters in the elemental volume of the collector absorber (W) mean temperature (K) flow rate (m3/s) wind speed (m/s) distance between absorber tubes (m)

Hellstrom et al., 2003; Armenta et al., 2011; Kostic´ and Pavlovic´, 2012; Kumar et al., 1995; Pavlovic´ and Kostic´, 2015). Thus, McDaniels et al. (1975) and Larson (1979) determined the optimal tilts of a fixed reflector and collector during the winter period for a collector–reflector system (CRS) in which the reflector was placed in front of the collector. Hussein et al. (1999), Taha and Eldighidy (1980)

Greek symbols b solar altitude (rad) DQ percentage difference of thermal power of the collectors (%) d thickness (m) e emittance g collector efficiency h collector orientation (rad) jcon average bond thickness (m) q coefficient of reflection qw water density (kg/m3) (sa) optical efficiency of the collector u latitude (rad) Subscripts a absorber c conventional solar collector d double exposure solar collector dif diffuse solar radiation dir direct solar radiation e experimental fm fluid i insulation in inlet irr irradiation low lower lowg lower glazing o ambient out outlet r reflector s lateral (side) surface t theoretical up upper upg upper glazing Abbreviations CRS collector–reflector system DEFPC double exposure flat-plate solar collector FPC conventional flat-plate solar collector LAS lower absorber surface

and Tanaka (2011) studied a CRS with the reflector mounted on top of the collector. Ekechukwu and Ugwuoke (2003) and Farooqui (2015) similarly designed and tested a solar cooker with a reflector mounted on top of the collector. Grassie and Sheridan (1977), Larson (1980) and Bollentin and Wilk (1995) investigated various reflector–collector configurations with the reflector placed either in front of or on top of the collector. Hellstrom

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et al. (2003) and Armenta et al. (2011) studied the effect of placing reflectors in the free space between two collector rows. The possibility of using more flat-plate reflective surfaces was also investigated. Thus, Kostic´ and Pavlovic´ (2012) proposed the use of two reflectors placed on top and in front of the collector. For this CRS, the optimum yearly tilt angle of both of the reflectors for a fixed collector tilt angle of 45° (43°N latitude) was determined. On the other hand, Kumar et al. (1995) and Pavlovic´ and Kostic´ (2015) analysed the effect of the four reflectors on the performance of the solar collector. A reflective surface was attached to each of the four edges of the collector. In all previously mentioned investigations, a reflector was integrated with the solar collector at one or more edges of the solar collector. On the other hand, Tanaka (2015) theoretically analysed a solar collector and flat-plate bottom reflector with a gap between them. The total absorbed solar radiation was calculated for three typical days (spring equinox, summer solstice and winter solstice days) at 30°N latitude. Experimental investigations showed that the maximum heat gains of these CRSs are in the range of 24–80% compared with a conventional solar collector without a reflector. A very interesting approach to improving the performance of this type of FPC is using flat-plate reflectors below a double glazed or double exposure solar collector (DEFPC). The lower absorber surface (LAS) of this collector is also active in the absorption of solar radiation (Souka, 1965; Souka and Safwat, 1966, 1968; Larson, 1979). In Souka (1965), a DEFPC with five reflectors set behind it was experimentally investigated by Souka. The collector was set up at a fixed angle of 40°, the largest reflector at a fixed angle of 60° relative to the horizontal plane, and the other reflectors at an angle of 20° relative to the largest reflector. All the reflectors were fixed during experimental testing conducted in Cairo, Egypt (latitude u = 30.20°N). An aluminium sheet was used as a reflective surface. The results showed that the maximum instantaneous thermal power of this modified solar collector is 48% higher than that of a conventional solar collector. In Souka and Safwat (1966, 1968), the same author presented a theoretical determination of the optimum orientation and tilt angles of the collector and the fixed reflectors, as well as the theoretical determination of the performance of the considered DEFPC, without experimental verification. These investigations were also carried out in Cairo, Egypt. Additionally, they did not discuss the optimal reflector dimensions for which the LAS of the DEFPC is fully irradiated. This modified solar system was later analysed by Larson (1979), who theoretically studied a vertically mounted DEFPC integrated with four reflective surfaces, additionally taking into consideration the impact of diffuse radiation reflected on the LAS by assuming that the reflector is of infinite width. Larson’s CRS consisted of interconnected reflectors that share the dimension of the width with the collector. However, the experimental results obtained from a study conducted at Drexel University,

Philadelphia, PA, USA (latitude u = 39.96°N) show a different relationship between the DEFPC and FPC. The DEFPC had a single glazing and a selective absorber surface, whereas the FPC had a double glazing and a non-selective absorber surface. Although the author determined the optimal tilt angles of the fixed reflectors, he did not determine the optimal dimensions of the reflectors. The CRS analysed in this paper is different from the previously described systems in many ways. First, it is placed in parallel below the collector. In this way, the incident angle of the solar beam falling on the upper absorber surface is the same as the incident angle of the solar beam reflected onto the LAS. The second difference is that reflective surface in this system is a plexiglass mirror with a specular reflection, which means that the incident and reflected angles are the same. The reflector is movable in all three possible orthogonal directions: north–south, east–west and normal to the collector. The reflector dimensions are approximately the same as those of the collector. In practice, these dimensions would be the minimum reflector dimensions relative to the collector for which it is possible to have full irradiation of the LAS of the DEFPC. The proposed CRS is also simpler because it consists of only one reflecting surface. To define the optimum position of the reflector relative to the collector, a theoretical investigation and experimental verification of the proposed mathematical model were carried out (Nikolic´ and Lukic´, 2013). In Nikolic´ and Lukic´ (2013), an original mathematical model for determining the irradiated area of the LAS of the DEFPC for different arbitrary positions; different dimensions of the reflector relative to the collector; different tilt angles, orientations and dimensions of the collector; and for any date and time is presented. The model was used to define the limits for the yearly reflector movement to ensure that the LAS will be fully irradiated at the optimum DEFPC yearly position for Kragujevac, Serbia (latitude u = 44.10°N). Additionally, the optimal reflector dimensions were determined where the reflector can only move in the direction normal to the CRS plane. To compare the thermal behaviour of the DEFPC, a FPC of the same characteristics as the DEFPC was designed. Figs. 1 and 2 show the cross-sections of the FPC and DEFPC, respectively. The both collectors have the identical absorbers (position 1), the absorber tubes (position 2) and the upper glazing (position 3). Instead of the FPC insulation (position 4 (Fig. 1)), the DEFPC has lower glazing (position 4 (Fig. 2)). The absorbers and glazing are placed in the metal housings (position 5). More detailed description of the DEFPC and FPC is given in Sections 2 and 3. This paper presents a mathematical model of the thermal behaviour of the proposed DEFPC. The results of the theoretical and experimental investigation of the DEFPC and FPC with single glazing and identical characteristics are compared and presented. Additionally, the proposed mathematical models of the thermal behaviour of the DEFPC and FPC were experimentally verified.

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Fig. 1. Flows of heat losses of the analysed FPC: 1 – absorber, 2 – absorber tubes, 3 – upper glazing, 4 – insulation, 5 – housing.

Fig. 2. Flows of heat losses of the analysed DEFPC: 1 – absorber, 2 – absorber tubes, 3 – upper glazing, 4 – lower glazing, 5 – housing.

2. Mathematical models of the thermal behaviour of the FPC and DEFPC The thermal behaviour of the solar collector is described by the energy balance equation obtained by applying the law of energy conservation. Assuming that the collector is a black box and the heat transfer within it is stationary, this equation would have the following form for the FPC and DEFPC: Qc ¼ I c  Ac  Qcl ;

ð1Þ

Qd ¼ I d  Ad  Qdl ;

ð2Þ

where Qc (W) is the useful thermal power of the FPC; Ic (W/m2) is the total solar radiation absorbed by the FPC; Ac (m2) is the area of the absorber surface of the FPC; Qcl (W) represents the total thermal losses of the FPC; Qd (W) is the useful thermal power of the DEFPC; Id (W/m2) is the total solar radiation absorbed on the DEFPC; Ad (m2) is the area of the upper (lower) absorber surface of the DEFPC; and Qdl (W) represents the total thermal losses of the DEFPC. 2.1. Absorbed solar radiation The total absorbed solar radiation Ic (W/m2) is defined as the sum of the direct and diffuse radiation absorbed by the upper absorber surface of the FPC (Icupdir, Icupdif): I c ¼ I cupdir þ I cupdif ¼ ðsaÞdir  H 0dir 

cosðiÞ 1 þ cosðGÞ þ ðsaÞdif  H 0dif  ; sinðbÞ 2

ð3Þ

On the other side, the total absorbed solar radiation Id (W/m2) is defined as the sum of the direct and diffuse radiation absorbed by the upper absorber surface (Idup) and the reflected direct and diffuse radiation absorbed by the lower absorber surface of the DEFPC (Idlow) (Nikolic´ and Lukic´, 2013): I d ¼ I dup þ I dlow ; I dup ¼ ðsaÞdir  H 0dir 

ð4Þ cosðiÞ 1 þ cosðGÞ þ ðsaÞdif  H 0dif  ; sinðbÞ 2 ð5Þ

I dlow ¼ ðsaÞdir  q  H 0dir

cosðir Þ Airr Ar  F rc  þ ðsaÞdif  q  H 0dif  ; sinðbÞ Adlow Adlow ð6Þ

where (sa)dir,dif (–) is the optical efficiency for direct and diffuse radiation; H0 dir (W/m2) is the intensity of the horizontal direct radiation; i (rad) is the incident angle; b (rad) is the solar altitude; H0 dif (W/m2) is the intensity of the horizontal diffuse radiation; G (rad) is the collector tilt angle; q (–) is the coefficient of reflection; ir (rad) is the incident angle of the reflected beam; Airr (m2) is the irradiated area of the lower absorber surface of the DEFPC; Adlow = Adup = Ad (m2) is the area of the upper (lower) absorber surface of the DEFPC; Ar (m2) is the area of the reflector surface; and Frc (–) is the view factor. The parameter H0 dif was calculated according to Erbs’s model (H0 dif = kd  H0 ) (Erbs et al., 1982). The diffuse fraction kd (–) is a function of clearness index kt (–). The total solar radiation incident on a horizontal surface (H0 ) was measured by a pyranometer. The parameter H0 dir was determined as H0 dir = H0  H0 dif. The optical efficiencies (sa)dir

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and (sa)dif were calculated according to the recommendations from Klein (1979), whereas the view factor Frc was calculated according to Ehlert’s model (Ehlert and Smith, 1992). An original mathematical model (Nikolic´ and Lukic´, 2013) was used for calculating the maximum possible irradiation of the LAS of the DEFPC (Airr) for dimensions, tilt angle, orientation and location of the CRS, as in the experiment. When determining the irradiated area of the LAS of the DEFPC, the impact of the lateral edges of the DEFPC on its shape and size was taken into account (Nikolic´ et al., 2013). 2.2. Heat losses A part of the total energy absorbed by the FPC and DEFPC is irreversibly lost to the ambient environment through their boundary areas. The boundary areas of these collectors are the upper collector surface (glazing) (position 3 (Figs. 1 and 2)), the lower collector surface (the lower surface of the collector housing (FPC) (position 5 (Fig. 1)) or glazing (DEFPC) (position 4 (Fig. 2))) and the lateral collector surfaces (the lateral surfaces of the collector housing). If a solar collector is viewed as a heat exchanger, then the amount of heat that is lost per unit of time at FPC (Qcl) and DEFPC (Qdl) could be presented as follows: Qcl ¼ Ac  ðK clup þ K cllow þ K cls Þ  ðT ca  T o Þ ¼ Ac  K cl  ðT ca  T o Þ;

ð7Þ

Qdl ¼ ðAdup  K dlup þ Adlow  K dllow þ Ad  K dls Þ  ðT da  T o Þ ¼ Ad  K dl  ðT da  T o Þ;

ð8Þ

where Kclup (W/m2 K) is the top loss coefficient of the FPC; Kcllow (W/m2 K) is the bottom loss coefficient of the FPC; Kcls (W/m2 K) is the edge (lateral) loss coefficient of the FPC; Tca (K) is the mean absorber temperature of the FPC; To (K) is the ambient (outdoor) temperature; Kcl (W/m2 K) is the overall loss coefficient of the FPC; Kdlup (W/m2 K) is the top loss coefficient of the DEFPC; Kdllow (W/m2 K) is the bottom loss coefficient of the DEFPC; Kdls (W/m2 K) is the edge loss coefficient of the DEFPC; Tda (K) is the mean absorber temperature of the DEFPC; and Kdl (W/m2 K) is the overall loss coefficient of the DEFPC. Figs. 1 and 2 present the flows of the heat losses of the analysed FPC and DEFPC. Assuming stationary and one-dimensional heat transfer in the solar collectors, the equations for Kclup, Kcllow, Kdlup and Kdllow can be easily derived:  1 1 1 K clup ¼ þ ; ð9Þ hcr;a–upg þ hcc;a–upg hcr;upg–o þ hcc;upg–o  1 dci 1 k ci K cllow ¼ þ  : ð10Þ k ci hcr;low–o þ hcc;low–o dci  1 1 1 K dlup ¼ þ : ð11Þ hdr;a–upg þ hdc;a–upg hdr;upg–o þ hdc;upg–o

where hcr,a–upg (W/m2 K) is the radiation heat transfer coefficient between the absorber and the upper glazing of the FPC; hcc,a–upg (W/m2 K) is the convection heat transfer coefficient between the absorber and the upper glazing of the FPC; hcr,upg–o (W/m2 K) is the radiation heat transfer coefficient from the upper glazing of the FPC to the ambient air; hcc,upg–o (W/m2 K) is the convection heat transfer coefficient from the upper glazing of the FPC to the ambient; dci (m) is the insulation thickness of the FPC; kci (W/m K) is the insulation thermal conductivity of the FPC; hcr,low–o (W/m2 K) is the radiation heat transfer coefficient from the lower surface of the FPC to the ambient; hcc,low–o (W/m2 K) is the convection heat transfer coefficient from the lower surface of the FPC to the ambient; hdr,a–upg (W/m2 K) is the radiation heat transfer coefficient between the absorber and the upper glazing of the DEFPC; hdc,a–upg (W/m2 K) is the convection heat transfer coefficient between the absorber and the upper glazing of the DEFPC; hdr,upg–o (W/m2 K) is the radiation heat transfer coefficient from the upper glazing of the DEFPC to the ambient; and hdc,upg–o (W/m2 K) is the convection heat transfer coefficient from the upper glazing of the DEFPC to the ambient. From Fig. 2, it can be seen that the upper part of the DEFPC is the same as the lower part, and thus the DEFPC is symmetrical with respect to its absorber. Because the absorber of the DEFPC is of small thickness, it was assumed that the temperatures of the upper and lower absorber surfaces are the same. Additionally, the lower glazing is assumed to have identical properties to the upper glazing. Based on the above, it was assumed that the heat losses from the LAS are the same as the heat losses from the upper absorber surface. In other words, all parameters that are related to the upper part of the DEFPC are identical with those for the lower part: hdr,a–lowg = hdr,a–upg, hdc,a–lowg = hdc,a–upg, hdr,lowg–o = hdr,upg–o, hdc,lowg–o = hdc,upg–o and Kdllow = Kdlup. The values of these coefficients were obtained by using the equations from Duffie and Beckmann (2006). The theoretical analysis of heat losses from the lateral collector surfaces is a complex process. The heat is lost by convection and radiation through these boundary surfaces. In Figs. 1 and 2, the parameters hcr,s–o, hcc,s–o, hdr,s–o and hdc,s–o (W/m2 K) represent, respectively, the radiation heat transfer coefficient from the lateral surfaces of the FPC to the ambient, the convection heat transfer coefficient from the lateral surfaces of the FPC to the ambient, the radiation heat transfer coefficient from the lateral surfaces of the DEFPC to the ambient and the convection heat transfer coefficient from the lateral surfaces of the DEFPC to the ambient. To reduce heat losses from the lateral surfaces, the edge insulation is mounted along its height or their height of the collector. In that case, it is considered that these losses are constant over time and independent of the ambient and absorber temperatures. On the other hand, when the area of the lateral collector surfaces is negligible relative to the

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area of the absorber surface, then the mentioned losses are usually neglected. In the case of the tested FPC and DEFPC, these heat losses could not be neglected. The first reason is that it is not possible to neglect the area of the lateral surfaces relative to the area of the absorber surface, as the absorber is relatively small in size (0.840  0.460 m). The second reason is that there is no insulation on the lateral collector surfaces. For these reasons, these losses were not constant over time and were dependent on the ambient temperature and the absorber (fluid) temperature. The values of the coefficients Kcls and Kdls were determined from the obtained experimental data on the total collector heat losses. First, the values of the coefficients Kclup (Kdlup) and Kcllow (Kdllow) were determined using a theoretical model. Then, using the same model, the values of the coefficients Kcl and Kdl were determined for which the theoretical total heat losses approximately correspond to the experimental total heat losses. It was noted that the values of the coefficients Kcl and Kdl and therefore of the coefficients Kcls and Kdls increase with the increase of the difference between the mean fluid temperature (Tc,fm (Td,fm)) and the ambient temperature (To). Based on the obtained values of the parameters Kcls and Kdls for all testing days of the solar collectors, general equations for their calculation were determined: K cls ¼ 0:551724  ðT c;fm  T o Þ  3:2541;

ð12Þ

K dls ¼ 0:511644  ðT d;fm  T o Þ  3:6312:

ð13Þ

absorber was analysed first. Because the absorber tubes usually divide the absorber into several equal units and the temperature gradient within each of them is the same, only one unit is considered in the analysis. Due to the symmetry of the temperature distribution between the absorber tubes, only half of a tube-absorber unit was considered below (Fig. 3). Fig. 3 shows a half of the FPC absorber, whereas Fig. 4 shows an elemental volume of the FPC absorber with energy flows. Applying the law of energy conservation to an elemental volume of the FPC absorber, the equation of energy balance will have the form:    @Qc;con Qc;con þ I c  dAc ¼ Qc;con þ ð16Þ dx þ QclðdAc Þ ; @x where Qc,con (W) is the amount of heat per unit of time that enters the elemental volume of the FPC absorber by conduction, Qcl(dAc) (W) is the amount of heat per unit of time that leaves the elemental volume of the FPC absorber and dAc (m2) is the elemental area of the absorber surface of the FPC. When compared with the FPC, the DEFPC differs in that the lower absorber surface absorbs the solar radiation. Both analysed solar collectors have an absorber with the same properties. The absorbers have the same thickness, distance between the tubes and tube diameter. Therefore,

Both of these equations were included in the mathematical models of the thermal behaviour of the FPC and DEFPC. If the temperature difference (Tc,fm  To) was less than or equal to 5.9 K, a value for coefficient Kcls of 0.5 W/m2 K would be adopted. On the other hand, if the temperature difference (Td,fm  To) was less than or equal to 7.1 K, a value for coefficient Kdls of 0.5 W/m2 K would be adopted. 2.3. Thermal power The equations for the thermal power of solar collectors (Eqs. (1) and (2)) are rarely used in practice in this form because it is difficult to measure the absorber temperature (Tca or Tda). That is why it is necessary to express Qc and Qd as functions of other more easily measurable temperatures. It is common for the useful thermal power of the collector to be expressed by the mean fluid temperature (Tc,fm or Td,fm) or fluid inlet temperature (Tc,in or Td,in) instead of the mean absorber temperature (Tca or Tda). Qc ¼ F R;c  Ac  ½I c  K cl  ðT c;in  T o Þ;

ð14Þ

Qd ¼ F R;d  Ad  ½I d  K dl  ðT d;in  T o Þ;

ð15Þ

where FR,c (–) is the heat removal factor of the FPC, and FR,d (–) is the heat removal factor of the DEFPC. To derive the above equations, an elemental volume of the collector absorber was analysed. In this analysis, it was assumed that the gradient of the absorber temperature along the absorber tube is negligible. The elemental volume of the FPC

105

Fig. 3. Analysed part of FPC absorber.

Fig. 4. Elemental volume of the FPC absorber.

106

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dda = dca, Wd = Wc, Dd = Dc and Dd,in = Dc,in. Because of the ability of the DEFPC to absorb solar radiation from its LAS, the scheme of energy flows differs in that there is a flow of energy in an elemental volume of the absorber from its lower side (Fig. 5). From Fig. 5, Qd,con (W) is the amount of heat per unit of time that enters the elemental volume of the DEFPC absorber by conduction, Qdl(dAd) (W) is the amount of heat per unit of time that leaves the elemental volume of the DEFPC absorber and dAd (m2) is the elemental area of the absorber surface of the DEFPC. Applying the law of energy conservation to an elemental volume of the DEFPC absorber, the equation of energy balance will be:    @Qd;con Qd;con þ ðI dup þ I dlow Þ  dAd ¼ Qd;con þ dx @x þ QdlðdAd Þ ¼ Qd;con þ I d  dAd : ð17Þ Because the upper and lower absorber surfaces are the same, the parameters of the radiation absorbed from both surfaces can be summed. Additionally, as analysed collectors have absorbers of the same size, it follows that dAc = dAd. This is significant because Eq. (17) is essentially identical to Eq. (16) for the FPC. In other words, solving these equations and the derivation of parameters F0c , FR,c, F00c , Tc,fm, Tca, and Tcupg for the FPC and F0d , FR,d, F00d , Td,fm, Tda, Tdupg, and Tdlowg for DEFPC are identical. The parameters F0c , F00c , Tcupg, F0d , F00d , Tdupg and Tdlowg represent, respectively, the efficiency factor of the FPC (–), the flow factor of the FPC (–), the mean temperature of the upper glazing of the FPC (K), the efficiency factor of the DEFPC (–), the flow factor of the DEFPC (–), the mean temperature of the upper glazing of the DEFPC (K) and the mean temperature of the lower glazing of the DEFPC (K). The procedure of derivation of the above parameters is the same as the procedure proposed in Duffie and Beckmann (2006). The only difference between the equations for F0c , FR,c, F00c , Tc,fm, Tca, and Tcupg and the equations for F0d , FR,d, F00d , Td,fm, Tda, Tdupg and Tdlowg is that the respective parameters are related to either the FPC or the DEFPC. For this reason, only the equations related to the DEFPC are shown below:

Fig. 5. Elemental volume of the DEFPC absorber.

1=K dl

F 0d ¼ ( 1 K dl ½Dd þðW d Dd ÞF d 

F R;d

md  cp;d ¼  Ad  K dl

F 00d ¼

)

1

þ kd;con bd;con þ jd;con



1e

Ad F 0 K dl d md cp;d

1 hd;cf Dd;in p

ð18Þ

Wd

! ;

F R;d ; F 0d

ð19Þ ð20Þ

  Qd  1  F 00d ; Ad  F R;d  K dl

ð21Þ

Qd  ð1  F R;d Þ; Ad  F R;d  K dl

ð22Þ

T d;fm ¼ T d;in þ T da ¼ T d;in þ

;

T dupg ¼ T da 

K dlup  ðT da  T o Þ ; hdr;a–upg þ hdc;a–upg

ð23Þ

K dllow  ðT da  T o Þ ; hdr;a–lowg þ hdc;a–lowg

ð24Þ

T dlowg ¼ T da 

where kd,con (W/m K) is the bond thermal conductivity of the DEFPC, bd,con (m) is the bond width of the DEFPC, jd,con (m) is the average bond thickness of the DEFPC and hd,c–f (W/m2 K) is the heat transfer coefficient between the fluid and the tube wall of the DEFPC. It should be noted that the coefficient hd,c–f was calculated according to the procedure proposed in Duffie and Beckmann (2006). In order to calculate parameters Qc and Qd, parameters FR,c (FR,d), Ic (Id), Kcl and Kdl have to be calculated first. The temperatures Tc,in (Td,in) and To were considered to be known. The procedure of determining parameters Ic and Id has been explained in Section 2.1 and (Nikolic´ and Lukic´, 2013). The calculation of temperatures Tca (Tda), Tcupg (Tdupg) and Tdlowg precedes the calculation of coefficients Kcl and Kdl. Because the experimental measurements of these temperatures are complex, the same temperatures were assumed at the beginning of the calculation. For the assumed temperatures, coefficients Kcl and Kdl were calculated. The new values for Tcupg, Tdupg and Tdlowg were calculated and compared with the assumed values by an iterative procedure. If the deviation between the obtained and the assumed values was minimal (<0.01 K) then parameters hc,c–f (hd,c–f), F0c (F0d ), FR,c (FR,d), F00c (F00d ) and Qc (Qd) were calculated. After obtaining the values of these parameters, the new values for Tc,fm (Td,fm) and Tca (Tda) were determined by an iterative procedure. Additionally, if the deviation between the obtained and the assumed values of the temperatures Tc,fm (Td,fm) and Tca (Tda) is within the limits of tolerance (<0.01 K) then the calculation is finished and the results of parameters FR,c (FR,d), Kcl (Kdl) and Qc (Qd) are printed. During the testing of the solar collectors on the basis of the measured values of the fluid mass flow rate mc (md), the fluid output temperature Tc,out (Td,out) and the fluid inlet temperature Tc,in (Td,in), for the calculation of the experimental useful thermal powers (Qc,e and Qd,e), the following equations were used:

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Qc;e ¼ mc  cp;c  ðT c;out  T c;in Þ;

ð25Þ

Qd;e ¼ md  cp;d  ðT d;out  T d;in Þ:

ð26Þ

107

2.4. Efficiency Beside the parameter Qc (Qd) for the evaluation of the thermal behaviour of the solar collector, the parameter gc (gd) that represents the collector efficiency is also used. In general, the efficiency of an energy system is defined as the ratio of the obtained (useful) and inputted (maximum available) energies. In a solar collector, the useful energy is the energy transferred to the working fluid (Qc (Qd)), whereas the inputted energy is the total solar energy received by the surface of the collector glazing H0 cG  Ac (H0 dG  Ad) (W). The equations used to calculate parameters gc and gd are given as: gc ¼ ¼ gd ¼ ¼

Qc F R;c  Ac  ½I c  K cl  ðT c;in  T o Þ ¼ H 0cG  Ac H 0cG  Ac F R;c  I c F R;c  K cl  ðT c;in  T o Þ  ; H 0cG H 0cG

ð27Þ

Qd F R;d  Ad  ½I d  K dl  ðT d;in  T o Þ ¼ H 0dG  Ad  Ad

H 0dG

F R;d  I d F R;d  K dl  ðT d;in  T o Þ  ; H 0dG H 0dG

ð28Þ

where H0 cG (W/m2) is the total incident solar radiation on the glazing surface of the FPC, and H0 dG (W/m2) is the total incident solar radiation on the glazing surface of the DEFPC. The equations used to calculate parameters H0 cG and H0 dG are similar to Eqs. (3)–(6). The only difference here is that they do not include parameters (sa)dir and (sa)dif. The experimental collector efficiencies gc,e and gd,e were calculated in the following way: gc;e ¼

Qc;e mc  cp;c  ðT c;out  T c;in Þ ¼ ; H 0cG  Ac H 0cG  Ac

ð29Þ

gd;e ¼

Qd;e 0 H dG  Ad

ð30Þ

¼

md  cp;d  ðT d;out  T d;in Þ : H 0dG  Ad

Fig. 6. The experimental setup of the collector–reflector system: 1 – metal support frame, 2 – DEFPC, 3 – reflector and 4 – tracking system.

The chosen reflector is a plexiglass mirror with dimensions of 1000  500  2 mm and a coefficient of reflection of 0.9. It was placed in parallel below the DEFPC and was able to move by a tracking system in all three possible orthogonal directions: normal to the collector, east–west and north–south. The limits on the reflector movement in all three directions defined by the maximum distances between the absorber and reflector central points are 0.80 m (toward east), 0.70 m (toward west), 0.22 m (toward north), 0.58 m (toward south) and 0.60 m (normal to the collector). To compare the thermal behaviour of the DEFPC, a FPC of the same characteristics as the DEFPC was designed. Figs. 1 and 2 show the cross-sections of the FPC and DEFPC, respectively. The technical characteristics of the DEFPC and FPC are given in Table 1. Both solar collectors were developed, installed and tested in the open area of the Thermodynamics and Thermotechnics Laboratory of the Faculty of Engineering, University of Kragujevac, Serbia (longitude lgeo = 20.54°, latitude u = 44.10°N). They are tilted at an angle G = 36° and are oriented at an angle h = 147°. The tilt angle of these collectors is approximately same as the

3. Experiment 3.1. DEFPC and FPC

Table 1 Technical characteristics of the DEFPC and FPC.

The CRS was designed to verify the mathematical models of the optimal reflector position and the thermal behaviour of the DEFPC (Fig. 6). It consists of a metal support frame (position 1), DEFPC (position 2), reflector (position 3) and tracking system (construction for the reflector movement) (position 4). The DEFPC has dimensions of 945  483  105 mm. The housing and absorber are made from aluminium, whereas the absorber tubes and the mixer and splitter tubes as well as the connecting tubes are made from copper.

Absorber length (m) Absorber width (m) da (m) Lcv (m) (FPC) Ldv (m) (DEFPC) ea (–) (Aluminium) a (–) (Aluminium) eupg, elowg (–) (Glass) ka (W/m K) (Aluminium) ki (W/m K) (Hard pressed mineral wool) di (m) W (m) Din (m) (Copper)

0.840 0.460 0.002 0.035 0.048 0.9 0.9 0.95 203 0.041 0.032 0.092 0.015

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capacity of 10 l and a power of 2 kW (position 3). Solar radiation was measured by a pyranometer (position 9) and the ambient temperature by a mercury thermometer. The wind speed was not experimentally measured, but its values were taken from the meteorological station in Kragujevac. The specifications of the experimental testing and monitoring devices are provided in Table 2. 3.3. Measurement procedure Fig. 7. Schema of the experimental installation with measuring equipment: 1 – DEFPC, 2 – FPC, 3 – electrical water heater, 4 – regulating valves, 5 – stop valve, 6 – tanks, 7 – Pt-100 probes at collector water inlet, 8 – Pt-100 probes at collector water outlet, 9 – pyranometer and 10 – mercury thermometer.

yearly optimal tilt angle of the collector for Kragujevac, Serbia. According to Skerlic´ and Bojic´ (2010), the yearly optimal collector position for Kragujevac is determined by the tilt angle of 37.5° and the orientation of 180°. The orientation of these collectors was defined by the position of the object on which they were mounted. In any case, the basic requirement of measurement included the same conditions for the FPC and DEFPC. 3.2. Apparatus The main goal of the experimental tests of the solar collectors was to obtain data on their thermal behaviour. The thermal behaviour of the solar collector is defined by its thermal power and efficiency. To calculate the experimental values of these parameters, Eqs. (25), (26), (29) and (30) were used. The values of the temperatures and flow rates were determined experimentally (the value for Airr was calculated using a mathematical model given in Nikolic´ and Lukic´ (2013)) using the measuring chain shown in Fig. 7. The working fluid was water. The water inlet and outlet temperatures of the DEFPC and FPC were measured by using Pt-100 temperature probes (position 7) connected to a TESTO digital thermometer. The flow rate, V (m3/s) was measured volumetrically by recording the time and reading the level of the water in the tanks (position 6). The mass flow rate was calculated as m = qw  V, where qw is the water density. Before measuring, the tanks with a capacity of 50 l were scaled. The flow rate was controlled by using the regulating valves (position 4). Control of the water inlet temperature was performed by adjusting the output of the electrical heater in the water heater with a

Experimental testing of the DEFPC and FPC was performed for different values of the volume flow rate and the water inlet temperature from the 5th of August to the 19th of October 2012. Because the experimental installation is open air and the used working fluid was water, the solar collectors were tested only when the lowest ambient temperature was above zero. Measurements of the thermal properties of the solar collectors started at 10:00 am and finished at 5:00 pm. During the testing period, which included the end of September and the beginning of October, the measurements would be finished before 5:00 pm because of the presence of the shadow from neighbouring objects on the CRS. During the testing period both solar systems were inclined at the angle of G = 36° and oriented at the angle of h = 147°. The reflector of the CRS was moved manually every hour during the testing period to its optimal position in the middle of the one-hour testing period. Data on the instantaneous horizontal solar radiation, the water inlet and outlet temperatures, the mass flow rates, the ambient temperature and the wind speed were recorded simultaneously. Data on the horizontal solar radiation were recorded every 30 s, the water inlet and outlet temperatures every 5 min, the ambient temperature every 15 min and the wind speed every hour during the testing. Because the tested models of the DEFPC and FPC had relatively small receiving areas (absorber area is 0.39 m2), high water inlet temperatures would cause low values of the collector thermal power and significantly increase the relative measurement errors. For this reason, the control of the water inlet temperature was adjusted so that the mean fluid temperature of the collectors was approximately ten degrees higher than the ambient temperature. 4. Results and discussion In this paper, the experimental results for four selected dates, the 8th of August, 4th of September, 9th of

Table 2 Specifications of the used experimental testing and monitoring devices. Device Pyranometer CMP 6 Kipp & Zonen Data logger METEON Kipp & Zonen Temperature probes Pt100 0609 1273 Digital thermometer TESTO 735

Measured physical parameter

Accuracy 2

Global horizontal irradiance (W/m ) Global horizontal irradiance (W/m2) Temperature (°C) Temperature (°C)

<5% <0.1% ±0.2 °C ±0.2 °C

N. Nikolic´, N. Lukic´ / Solar Energy 119 (2015) 100–113

September and 4th of October 2012 are presented. For each of these dates, the ambient conditions, the values of the collector fluid inlet temperature, mass flow rate and irradiated area of the LAS of the DEFPC were different. Daily operation conditions during the experimental tests for the mentioned days are presented in Tables 3–6. Figs. 8 and 9 show the experimental and theoretical thermal power of the DEFPC and FPC for the 4th of September and 4th of October 2012, respectively. From the above figures, relatively good agreement between the theoretical model and experiment can be seen. Depending on the testing day, the average error of the mathematical model ranged from 3% to 7% compared with the experimental data. Among the all factors that influenced the size of this error, the transient effects in the last testing hour due

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to the water temperature decrease in the system and its heat capacity which the simulation model did not take into account should be mentioned. Particularly interesting was the effect of the double reflected radiation from the CRS reflector, from the lower glass surface and the LAS, which was more or less expressed depending on the testing date and hour. In fact, at some points in the testing, the mutual positions of the DEFPC and the reflector allowed a part of the radiation specularly reflected from the lower glass surface (and absorber) and the reflector to fall again on the DEFPC absorber. Due to the complexity of this phenomenon, the double reflected radiation was not taken into consideration in the mathematical model of the DEFPC. Fig. 10 shows the experimental thermal power of the DEFPC and FPC, as well as their relative (percentage)

Table 3 Operation conditions during the experimental tests for the 8th of August 2012. Time (h) Tc,fm (°C) Td,fm (°C) To (°C) m (kg/s) H0 (W/m2) Vwind (m/s)

10:00 37.55 39.05 29.4 0.00654 724 2.8

11:00 40.2 41.85 30.7 0.00654 812 3.7

12:00 41.35 42.6 31.7 0.00647 853 2.5

13:00 42.3 42.55 32.5 0.00647 848 2

14:00 42.95 43.45 33.6 0.00651 797 3.2

15:00 43.35 44.65 33.1 0.00651 699 5

16:00 43 44.6 33.1 0.00653 556 5

17:00 42.9 43.75 32 0.00653 366 3.1

Table 4 Operation conditions during the experimental tests for the 4th of September 2012. Time (h) Tc,fm (°C) Td,fm (°C) To (°C) m (kg/s) H0 (W/m2) Vwind (m/s)

10:00 36.55 37.7 26.8 0.00616 608 1.9

11:00 38.6 39.85 28.3 0.00616 698 2

12:00 40.15 41.15 30.2 0.00582 739 2

13:00 41.75 42.05 31.4 0.00582 732 2.2

14:00 42.25 43.9 32.8 0.00569 676 2.4

15:00 42.6 44.65 32.7 0.00569 571 2.6

16:00 42.75 44.5 32.9 0.00569 417 2.7

17:00 42.75 43.25 32.1 0.0055 214 2.1

Table 5 Operation conditions during the experimental tests for the 9th of September 2012. Time (h) Tc,fm (°C) Td,fm (°C) To (°C) m (kg/s) H0 (W/m2) Vwind (m/s)

10:00 35.7 36.9 26 0.00497 639 1

11:00 38.55 40.25 28 0.00497 730 2

12:00 40.6 41.9 29.2 0.00472 770 2.9

13:00 41.5 42.6 29.8 0.00472 760 3.2

14:00 42.25 44.1 30.8 0.00472 701 3.4

15:00 42.65 45.05 31.3 0.00453 591 3.5

16:00 43.3 45.15 30.4 0.00453 432 3.5

17:00 42.15 42.6 29.3 0.00453 222 2.6

Table 6 Operation conditions during the experimental tests for the 4th of October 2012. Time (h) Tc,fm (°C) Td,fm (°C) To (°C) m (kg/s) H0 (W/m2) Vwind (m/s)

10:00 33.9 34.85 19.4 0.00622 522 1.6

11:00 36.65 38.05 22.1 0.00622 639 1.9

12:00 37.65 39.35 23.3 0.00586 688 1.9

13:00 39.4 41 24.8 0.00586 668 2

14:00 40.65 42.65 25.2 0.00586 581 2

15:00 41.5 43.15 25.8 0.00569 426 1.8

N. Nikolic´, N. Lukic´ / Solar Energy 119 (2015) 100–113

Q c,e , Q c,t, Q d,e , Q d,t (W)

350 300 250 200 150 100

Qc,e (W) Qc,t (W) Q d,e (W) Qd,t (W)

50 0 10:00

11:00

12:00

13:00

14:00

15:00

16:00

17:00

Time (h)

Fig. 8. Theoretical and experimental thermal power of the DEFPC (Qd,t, Qd,e) and FPC (Qc,t, Qc,e) for the 4th of September 2012 (m = 0.005796 kg/ s).

Q c,e , Q c,t, Q d,e , Q d,t (W)

350 300 250 200 150 100

Qc,e (W) Qc,t (W) Q d,e (W) Qd,t (W)

50 0 10:00

11:00

12:00

13:00

14:00

15:00

Time (h)

Fig. 9. Theoretical and experimental thermal power of the DEFPC (Qd,t, Qd,e) and FPC (Qc,t, Qc,e) for the 4th of October 2012 (m = 0.00595 kg/s).

350

100 90

Q c,e, Q d,e (W)

300

80

250

70

200

60 50

150

40

100

Qc,e (W)(L) Q d,e (W)(L) Airr (%)(R) ∆Q (%)(R)

50 0 10:00

11:00

12:00

13:00

14:00

15:00

16:00

30 20 10 0 17:00

Time (h)

Fig. 10. Thermal power of the DEFPC (Qd,e) and FPC (Qc,e), their relative difference (DQ) and irradiated area of the LAS of the DEFPC (Airr) for the 8th of August 2012 (m = 0.006506 kg/s).

differences, expressed as DQ (%) = 100  (Qd,e  Qc,e)/Qc,e for the 8th of August 2012. Fig. 10 also presents the theoretically calculated irradiated area of the LAS of the DEFPC Airr (%) (according to Nikolic´ and Lukic´ (2013) and Nikolic´ et al. (2013)). The operating values of the Tc,fm, Td,fm, To, m, H0 and Vwind for the same day are given in Table 3. The central “drop down” in the curve of thermal power of the DEFPC is characterised for the summer and temperate northern (southern) latitudes when the optimal reflector position requires a larger normal distance from the DEFPC and the real CRS has its own constructive limitations (Nikolic´ and Lukic´, 2013). Specifically, on the tested

CRS, the maximum normal distance of the reflector from the DEFPC was 0.6 m. Maximum DQ was achieved in the late morning and mid-afternoon hours. The average value of the DQ for the entire testing date was 41.79%. From the figure, it can be seen that the change of the irradiated area, Airr well follows the change of the DQ. Although the value of the Airr right after 1:00 pm is equal to zero due to the inertia of the system and the higher temperature of the DEFPC absorber, the corresponding DQ is not equal to zero. For the most part, the value of Airr (%) is higher than DQ (%) as a consequence of heat losses from the DEFPC. In the last 30 min of testing, the sun rapidly changed its position in relation to the frequency of the change of the optimal reflector position (1 h), so that Airr had significant leaps and falls, and with it DQ, although this was mitigated by the system inertia. This phenomenon would certainly be avoided by shortening the intervals of changing the reflector position or, in the best case, by its continual movement towards the optimal position. Fig. 11 shows the experimental thermal power of the DEFPC and FPC, DQ and Airr for the 9th of September 2012. The operating values of the Tc,fm, Td,fm, To, m, H0 and Vwind for the 4th and 9th of September 2012 are given in Tables 4 and 5. The central “drop down” in the curve of the thermal power of the DEFPC is reduced, and at the most critical period, it is not equal to zero, but a small part of the LAS of the DEFPC is still irradiated. Maximum DQ was achieved in the late morning and early and mid-afternoon hours. The average value of the DQ for the entire testing date was 52.16%. From the figure, it can be seen that the change of the irradiated area, Airr, well follows the change of DQ. The explanation for the sudden leaps and falls of the Airr and DQ is the same as in the previous case. Fig. 12 shows the experimental thermal power of the DEFPC and FPC, DQ and Airr for the 4th of October 2012. The operating values of the Tc,fm, Td,fm, To, m, H0 and Vwind for the same day are given in Table 6. The central “drop down” is significantly shallower, and the minimal irradiation of the LAS of the DEFPC is approximately 60%. Maximum DQ was achieved in the late morning and early and mid-afternoon hours. The average

350

100 90

300

Q c,e, Q d,e (W)

110

80

250

70

200

60 50

150

40

100

0 10:00

30

Qc,e (W)(L) Q d,e (W)(L) А irr (%)(R) ∆Q (%)(R)

50 11:00

12:00

13:00

14:00

15:00

20 10 16:00

0 17:00

Time (h)

Fig. 11. Thermal power of the DEFPC (Qd,e) and FPC (Qc,e), their relative difference (DQ) and irradiated area of the LAS of the DEFPC (Airr) for the 9th of September 2012 (m = 0.004727 kg/s).

N. Nikolic´, N. Lukic´ / Solar Energy 119 (2015) 100–113 350

Q c,e, Q d,e (W)

300

100

0.70

100

90

0.65

90

80

0.60

80

0.55

70

250

70

200

60 50

150

40

100

30

Qc,e (W)(L) Q d,e (W)(L) A irr (%)(R) ∆Q (%)(R)

50 0 10:00

11:00

12:00

13:00

14:00

15:00

111

60

0.50

50

0.45

40

0.40

20

0.35

10

0.30

0

0.25 10:00

30 20

η c,e (-)(L) η d,e (-)(L) Airr (%)(R)

11:00

12:00

Time (h)

10

13:00

14:00

0 15:00

Time (h)

Fig. 12. Thermal power of the DEFPC (Qd,e) and FPC (Qc,e), their relative difference (DQ) and irradiated area of the LAS of the DEFPC (Airr) for the 4th of October 2012 (m = 0.00595 kg/s).

value of DQ for the entire testing date was 66.44%. The values for DQ are slightly higher, which can be explained by the lower ambient temperature. Due to the lower ambient (absorber) temperature, the percentage difference of the heat loss coefficients and total heat losses will be less due to the lower values of coefficients Kclup, Kdlup and Kdllow. The values of coefficients Kcls and Kdls are always approximately the same regardless of the ambient temperature. Coefficient Kcllow also has the same value regardless of the value of the ambient temperature. Fig. 13 shows the thermal efficiency of the DEFPC and FPC calculated according to Eqs. (29) and (30), as well as the theoretically calculated irradiated area of the LAS of the DEFPC, Airr for the 8th of August 2012. From the figure, it can be seen that there is no significant difference between the thermal efficiency of the DEFPC and FPC during the testing day and that they were not significantly influenced by the change of Airr. Differences in the mean water temperatures in the collectors did not exceed 2.5 °C, so they did not significantly affect the difference in the heat losses of the DEFPC and FPC. Additionally, increased radiation heat losses from the lower glass surface of the DEFPC did not come to the fore. One of the reasons for this is the reflection of the longwave infrared radiation of the heat losses from the reflector to the lower glass surface of the DEFPC. However, at the

Fig. 14. Thermal efficiency of the DEFPC (gd,e) and FPC (gc,e) and irradiated area of the LAS of the DEFPC (Airr) for the 4th of October 2012 (m = 0.00595 kg/s).

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

Fig. 15. Thermal efficiency of the DEFPC (gd,e) as a function of (Td,in  To)/H0 dG operating values for the 4th of October 2012.

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

Fig. 16. Thermal efficiency of the FPC (gc,e) as a function of (Tc,in  To)/H0 cG operating values for the 4th of October 2012.

0.70

100

0.65

90

0.60

80 70

0.55

60

0.50

50

0.45

40

0.40

30

0.35

η c,e (-)(L) η d,e (-)(L) A irr (%)(R)

0.30 0.25 10:00

11:00

12:00

13:00

14:00

15:00

16:00

20 10 0 17:00

Time (h)

Fig. 13. Thermal efficiency of the DEFPC (gd,e) and FPC (gc,e) and irradiated area of the LAS of the DEFPC (Airr) for the 8th of August 2012 (m = 0.006506 kg/s).

time of the maximum difference of the mean fluid temperatures (maximum DQ), it can be noted that the efficiency of the FPC is slightly higher than the efficiency of the DEFPC. The average thermal efficiency of the DEFPC and FPC during the testing day was identical, 0.575 and 0.576, respectively. Fig. 14 shows the thermal efficiency of the DEFPC and FPC as well as the irradiated area of the LAS of the DEFPC Airr for the 4th of October 2012. From the figure, it can be seen that there is no significant difference between the thermal efficiency of the DEFPC and FPC during the testing day and that they were not significantly influenced

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by the change of Airr. Differences of the mean water temperatures in the collectors did not exceed 2 °C, so they did not significantly affect the difference of heat losses of the DEFPC and FPC. The average thermal efficiencies of the DEFPC and FPC during the testing day were 0.521 and 0.508, respectively. Thermal efficiencies gc,e and gd,e as a function of (Tc,in  To)/H0 cG and (Td,in  To)/H0 dG operating values for the same day (4th of October 2012) are shown in Fig. 15 and 16. Because of the different values of the H0 cG and H0 dG points (markers) of the thermal efficiency gc,e are shifted to the right relative to the points of the thermal efficiency gd,e. 5. Conclusions In this paper, the results of the theoretical and experimental investigation of the double exposure flat-plate water solar collector with parallel reflector of the same dimensions placed below the collector box are presented. Simultaneously with the experiment, mathematical models of the thermal behaviour of the DEFPC and FPC were developed. A comparison of the theoretical and experimental results showed that the error of the mathematical models for all testing days ranged from 3% to 7%. The main goal of this investigation was to compare the performance (thermal power (thermal energy production) and efficiency) of the identical conventional solar collector with the double exposure solar collector. The results showed that the useful thermal energy (thermal power) generated by the CRS (DEFPC) of moderate size (maximum distance of the collector box and the reflector of 0.6 m), for the northern latitude of 44°, was significantly higher (41.79–66.44%) than useful thermal energy generated by the FPC. The highest obtained daily relative difference DQ (66.44%) is 18.44% higher than the maximum achieved difference of 48% in the previous investigation of the DEFPC (Souka, 1965). The thermal efficiency of the DEFPC was the similar to that of the FPC and the irradiated area of the LAS of the DEFPC does not significantly affect its value. The main advantages of the proposed CRS in relation to the previously investigated are: parallelism between the reflector and the collector, mirror reflective surface and mobility of the reflector in all three possible orthogonal directions. The proposed system is also simpler because it consists of only one reflecting surface. In terms of the lack of space, the CRS of the moderate dimensions can provide significant increase of the obtained thermal power in relation to the conventional construction of the flat-plate water solar collector. According to Nikolic´ and Lukic´ (2013), there are two ways to optimise the design of the CRS construction. The first is for the reflector to have the same dimensions as the collector and move in all three possible orthogonal directions (as in experiment), whereas the second solution implies that the optimal reflector dimensions can be determined where the reflector can only move in the direction normal to the CRS plane. Both solutions must be analysed in detail regarding the available space

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