Extending the Efficiency of Facade-Integrated PVT through Coupling with Radiant Cooling

Mohannad Bayoumi1

Associate Professor, Department of Architecture, King Abdulaziz University, Jeddah, Saudi Arabia

*Corresponding author: Mohannad Bayoumi, Associate Professor, Department of Architecture, King Abdulaziz University, Jeddah, Saudi Arabia, Department of Architecture, Jeddah, Saudi Arabia. E-mail: mbayoumi@kau.edu.sa

Citation: Mohannad Bayoumi (2020) Extending the Efficiency of Facade-Integrated PVT through Coupling with Radiant Cooling. J Civil Engg ID 1(2): 5-16

Received Date: : 13 July,2020; Accepted Date: 19 July,2020; Published Date: 23 July,2020

Abstract

Hybrid photovoltaic/thermal (PVT) systems combine electric and thermal energy generation and have quiet operation, and space-saving features. Since the efficiency of photovoltaic (PV) panel increases at low surface temperatures, this paper sug-gests combining the PVT panel with the radiant cooling panel in one system called PVTRC. The proposed system joins the return pipe of the radiant panel with the supply pipe of the PVT. The return water of the radiant panel is circulated through the pipes of the PVT system. This work proposes an analytical model to assess the performance of the system. Using the dynamic thermal simulation software IDA-ICE, a set of PVTRC elements is incorporated into the facade of generic typical office space in hot and cold locations, Jeddah and Munich, respectively. In Munich, positive energy balance can be achieved within the framework of this study in every season. In addition, efficient electric and cooling energy generation as well as a surplus amount for other electric usages can be achieved via PVTRC elements for all seasons except for summer. In both locations, the results indicated a substantial impact on the efficiency of PV module with an increase of up to 35% and a remarkable contribution to façade-supported cooling and elec-tricity generation. The obtained results contribute to building-integrated PV, PVT, and radiant cooling elements, suggesting a good application potential for the PVTRC elements. The proposed system has been patented by the US Patent office; US Patent number: US10355154 B1.

Keywords: Photovoltaic-thermal systems; PV thermal, Radiant cooling; Building-integrated photovoltaic; Facade; Solar cooling;

Introduction

Local and decentralized energy generation is important for improved energy efficiency. Compared to the conventional approach of centralized energy generation, decentralized energy generation is associated with reduced losses in transportation and conversion process of energy forms. One form of this approach is building-integrated photovoltaic, which are becoming an essential part of contemporary architecture. In this approach, a significant portion of irradiated energy is absorbed by PV cells, which increases the surface temperature of the panel. This further leads to a substantial deterioration of the efficiency of the panels and, consequently, their output. Generally, under standard test conditions (STC), for each degree increase in temperature, the output performance of the PV is expected to decrease by 0.4-0.5%[1]. However, experiments show that the real operating conditions of PV panels are not represented by STC parameters [2]. In a comparison of different types of PV cells, Radziemska investigated the effect of temperature on energy production and efficiency of a system and found that an increase in cell temperature led to a drop in power at ca. -0.65% per K [3]. In hot climates, PVs are more likely to be affected by increasing surface temperature due to the elevated ambient temperatures (Tamb) and the associated incident solar irradiance (G). Even in cold climates, despite low ambient temperatures, substantial losses occur due to increased surface temperatures caused by the absorbed solar irradiance [4]. This is particularly evident in façade-integrated PV panels (e.g. south facade in the northern hemisphere). The study by Huld and Amillo claims that although wind velocity plays a significant role in module efficiency, ambient temperature and irradiance are the most decisive factors in crystalline silicon-based cells. Moreover, depending on the geographical location, the impact of these factors results in -15% to +5% variation in the conversion efficiency of PV cells [4].

The surface temperature of PV can be reduced by attaching pipes that circulate a fluid at the back of the PV absorber. This combination of two systems is called hybrid photovoltaic/thermal (PVT) [5]. This technology was proposed in 1978 by Kern and Russel [6]. The water in the pipes (or ducts in the case of air) absorbs the thermal energy from the heated-up surface and delivers it to be used at another point for potable water for instance. Depending on the design of the system, water is usually used as a refrigerant due to its higher thermal capacity.

One of the main advantages of hybrid PVT systems is that it combines the functions of both a PV panel and a solar collector. This means more space efficiency, fewer installation requirements, and more cost saving. Charalambous et al. asserted that a PVT can generate more energy per unit area than a pair of PV panel and a solar collector located next to each other [7]. Another advantage of PVT is that it cools the surface of PV cells, thus, enhancing the efficiency of electric energy generation.

In recent years, there has been an increasing research interest on PVT technology and the possible usage of the generated thermal energy [8]. Essential remarks on the performance of PVT panels have been investigated and described in previous works [9]. In the realm of domestic hot water production, several studies have dealt with methods improving the efficiency of performance [10-12]. An experimental study by Zondag et al. showed thermal efficiency and electrical efficiency of around 58% and 9.7%, respectively [13]. Furthermore, Prieto et al. [14] discussed the potential of facade-integrated PVT that can be used for solar-assisted cooling using the principles of solar cooling addressed by Henning [15]. However, these approaches are limited by the outlet temperature (Tf,out) of the fluid, which flows out of PVT. Here, it should be noted that associating cooling with facade-integrated energy generation is an interesting topic as high cooling loads often occur during times of high solar irradiation. Some solutions include coupling the PVT to water-to-water heat pumps that use the thermal output to maximize the system’s COP [16].

Basically, in the field of thermal energy generation using PVT, the challenge lies in the quality of the generated thermal energy, which essentially impacts its efficiency. According to a previous study [17], the cooling of the PV back surface via the attached pipes helps to improve the electrical performance. Moreover, the cooling can be counter-productive as it also affects the thermal energy generation process. This is because the heat exchanger underperforms comparably to a typical solar thermal collector. In other words, maximizing the electrical output prevents the system from being optimized. This is why many PVT domestic hot water generation systems are equipped with auxiliary heaters connected to the heat exchanger in the top of the hot water storage tank to compensate for the thermal energy deficit [18].

A number of parameters influence the performance of PVT such as mass flow rate, inlet temperature, packing factor and type of PV module [19]. The present research suggests a combination of facade-integrated radiant cooling and PVT with a focus on the inlet temperature to improve the overall efficiency of the system. While the PVT is located on the external side, the radiant cooling surface faces the interior space. The objective is to investigate the impact of the proposed system on module efficiency and associated surface temperature of the PV absorber as well as its application practicality in an indoor space such as office environment. Within the scope of this paper, the suggested system will be named as PVTRC. As suggested by Jayasuriya et al., at the current stage, such proposed improvement and optimization is best made in the design stage using available simulation tools and cannot be conducted using experimental techniques as many design parameters need to be optimized and tested in the design simultaneously [9,20].

Methods

Description of the proposed system

Figure 1 outlines the basic components of the PVTRC wall element. The system comprises a PVT and radiant cooling panel, installed to the back of each other. Cooling pipes are attached to the back of either part. A chiller fluidly connects the inlet of the radiant cooling panel and the outlet of the PVT. Further, a frame is configured to separate the PVT panel and the radiant cooling panel and form an enclosed space.

Figure 1: Left: Conceptual wall section of the PVTRC. Right: Basic components of the PVTRC

After introducing the proposed PVTRC, the sizing process of the radiant cooling part is described. Next, a demonstration of the PVT analytical model is presented. To evaluate the impact of the proposed system in different climate conditions where cooling is required, a generic model for office space is selected. Certain PVTRC elements are integrated into a part of the facade. The cooling capacity of the radiant cooling elements facing the room is integrated into a dynamic simulation model using IDA-ICE to determine its impact on room temperature and user comfort at different times of the year. One more advantage of the dynamic simulation is depicting the cooling load that is covered using the radiant cooling elements. This information is then linked to the electric energy output by the PVT part, which is mainly used to compensate the power requirement of the chiller. It also indicates an excess of energy production for other purposes such as covering the demand for air conditioning that is supposed to be mainly utilized for hygienic purposes, i.e., maintaining a healthy level of CO2 concentration in the room.

Sizing of the radiant cooling part

Understanding the effect of the radiant cooling part and its impact on the total energy balance is essential to size the radiant cooling panels according to the designed configurations. After that, the cooling capacity of the radiant cooling panel should be used in dynamic simulation software IDA-ICE for further assessment with respect to the cooling load in the room. This also helps to observe the resulting room temperature with the aid of the used system. Within the scope of this paper, for the cooling energy generation using PV cells, a DC chiller has been considered with a COP of 3.0.

The following equation Eq. (1) describes the total sensible heat flux of the panel, where, U0, Tr, and Tpm are the total heat transfer coefficient, room temperature, and mean panel surface temperature, respectively. Eq. (2) is recommended by a previous study for practical applications that include vertical radiant cooling and heating surfaces [21,22].

Q ˙ c,rc = A rc F R U o T r T cw,in                   (1)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiqadgfapaGbaiaadaWgaaWcbaWdbiaadogacaGGSaGaamOC aiaadogaa8aabeaak8qacqGH9aqpcaWGbbWdamaaBaaaleaapeGaam OCaiaadogaa8aabeaak8qacaWGgbWdamaaBaaaleaapeGaamOuaaWd aeqaaOWdbiaadwfapaWaaSbaaSqaa8qacaWGVbaapaqabaGcpeWaae Waa8aabaWdbiaadsfapaWaaSbaaSqaa8qacaWGYbaapaqabaGcpeGa eyOeI0Iaamiva8aadaWgaaWcbaWdbiaadogacaWG3bGaaiilaiaadM gacaWGUbaapaqabaaak8qacaGLOaGaayzkaaGaaeiiaiaabccacaqG GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeik aiaabgdacaqGPaGaaiiOaaaa@5CC4@
Q ˙ c,rc,room = Q ˙ c,rc N rc                   (2)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiqadgfapaGbaiaadaWgaaWcbaWdbiaadogacaGGSaGaamOC aiaadogacaGGSaGaamOCaiaad+gacaWGVbGaamyBaaWdaeqaaOWdbi abg2da9iqadgfapaGbaiaadaWgaaWcbaWdbiaadogacaGGSaGaamOC aiaadogaa8aabeaak8qacqGHflY1caWGobWdamaaBaaaleaapeGaam OCaiaadogaa8aabeaak8qacaqGGaGaaeiiaiaabccacaqGGaGaaeii aiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGa GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeOmaiaabMca caGGGcaaaa@5974@

According to a previous study one of the methods to determine U0 is by dividing qo by the temperature difference between Tr and Tpm[21]. It is also recommended to use a trial value for Tpm, which is still unknown. Therefore, a value of 0.5 K higher than the inlet temperature of the chilled water into the radiant cooling system Tcw, inlet is to be used. Tcw, inlet and Tpm have been set to 17 and 17.5°C, respectively. Accordingly, the resulting value of U0 is 8 W/m2.K for a desired Tr of 24°C.

The cooling energy output of a single radiant cooling panel (Q̇c,rc) is calculated using Eq. (3).

Q ˙ c, rc = A rc F R U o T r T cw,in                 (3) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qaceWGrbWdayaacaWaaSbaaSqaa8qacaWGJbGaaiilaiaacckacaWG YbGaam4yaaWdaeqaaOWdbiabg2da9iaadgeapaWaaSbaaSqaa8qaca WGYbGaam4yaaWdaeqaaOWdbiaadAeapaWaaSbaaSqaa8qacaWGsbaa paqabaGcpeGaamyva8aadaWgaaWcbaWdbiaad+gaa8aabeaak8qada qadaWdaeaapeGaaiikaiaadsfapaWaaSbaaSqaa8qacaWGYbaapaqa baGcpeGaeyOeI0Iaamiva8aadaWgaaWcbaWdbiaadogacaWG3bGaai ilaiaadMgacaWGUbaapaqabaGccaGGPaaapeGaayjkaiaawMcaaiaa bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae iiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqG OaGaae4maiaabMcaaaa@5CAA@
Q ˙ c, rc,room = Q ˙ c,rc N rc                   (4) MathType@MTEF@5@5@+= feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaaeaaaaaaaaa8 qaceWGrbWdayaacaWaaSbaaSqaa8qacaWGJbGaaiilaiaacckacaWG YbGaam4yaiaacYcacaWGYbGaam4Baiaad+gacaWGTbaapaqabaGcpe Gaeyypa0Jabmyua8aagaGaamaaBaaaleaapeGaam4yaiaacYcacaWG YbGaam4yaaWdaeqaaOWdbiabgwSixlaad6eapaWaaSbaaSqaa8qaca WGYbGaam4yaaWdaeqaaOWdbiaabccacaqGGaGaaeiiaiaabccacaqG GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabIcacaqG0aGaaeyk aaaa@5947@

The number of radiant cooling panels in the room (Nrc) is 6. Therefore, while Qc,rc is around 80 W/panel, the total cooling energy capacity in the room Q̇ c,rc is 480 W. Table 1 lists the input values for the sizing of the radiant cooling system.

Table 1: Input values for the sizing of the radiant cooling system

Parameter

Unit

Value

Arc

[m2]

1.64

Cp

[Wh/kg.K]

1.163023

CL

[m]

30

Din

[m]

0.00635

hf

[W/m2.K]

400

Krc

[W/m.K]

240

Ksil

[W/m.K]

98.9

Kw

[W/m.K]

0.6

Lrc

[m]

0.001

m'

[kg/s]

0.04

Tpm, assumed

[°C]

17.5

Tcw,in

[°C]

17

Wrc

[m]

0.99

Wgp

[m]

0.045

αcell

[mA/K]

0.85

αTedlar

[mA/K]

0.5

βc

[V/K]

0.9

ηcell

[%]

0.09

τG

[-]

0.95

(ατ)eff

[mA/K]

0.6973

μfl

[mPa.s]

0.00108

ρ

[kg/m3]

1000

The heat removal factor (FR) is calculated using the following method in Eq. (5). FR represents the ratio of the actual cooling capacity of the panel if the whole panel surface is at the temperature of the inlet Tcw,inlet. F’ is the efficiency factor calculated according to Eq. (6). It is the ratio of the actual heat transfer at a particular location to the heat transfer that would result if the panel surface had been at the temperature of the inlet Tcw,inlet. Eq. (7) describes the fin efficiency factor (F), which is calculated for straight fins with a rectangular profile. Therefore, it is important to determine the forced convection heat transfer coefficient (hi) for turbulent flow inside the tube. This value is calculated in Eq. (8).

F R = m ˙ C p A rc U o 1exp A U o F' m' C p                            (5)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadAeapaWaaSbaaSqaa8qacaWGsbaapaqabaGcpeGaeyyp a0ZaaSaaa8aabaWdbiqad2gapaGbaiaapeGaam4qa8aadaWgaaWcba Wdbiaadchaa8aabeaaaOqaa8qacaWGbbWdamaaBaaaleaapeGaamOC aiaadogaa8aabeaak8qacaWGvbWdamaaBaaaleaapeGaam4BaaWdae qaaaaak8qadaWadaWdaeaapeGaaGymaiabgkHiTiaadwgacaWG4bGa amiCamaabmaapaqaa8qadaWcaaWdaeaapeGaamyqaiaadwfapaWaaS baaSqaa8qacaWGVbaapaqabaGcpeGaamOraiaacEcaa8aabaWdbiaa d2gacaGGNaGaam4qa8aadaWgaaWcbaWdbiaadchaa8aabeaaaaaak8 qacaGLOaGaayzkaaaacaGLBbGaayzxaaGaaeiiaiaabccacaqGGaGa aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae ikaiaabwdacaqGPaGaaiiOaaaa@676F@
F'= 1/ U o W rc 1 U 0 D o + W rc D o F + 1 h i π K w ln D o D in + γ k b bw + L rc K rc                             (6)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadAeacaGGNaGaeyypa0ZaaSaaa8aabaWdbiaaigdacaGG VaGaamyva8aadaWgaaWcbaWdbiaad+gaa8aabeaaaOqaa8qacaWGxb WdamaaBaaaleaapeGaamOCaiaadogaa8aabeaak8qadaWadaWdaeaa peWaaSaaa8aabaWdbiaaigdaa8aabaWdbiaadwfapaWaaSbaaSqaa8 qacaaIWaaapaqabaGcpeWaamWaa8aabaWdbiaadseapaWaaSbaaSqa a8qacaWGVbaapaqabaGcpeGaey4kaSYaaeWaa8aabaWdbiaadEfapa WaaSbaaSqaa8qacaWGYbGaam4yaaWdaeqaaOWdbiabgkHiTiaadsea paWaaSbaaSqaa8qacaWGVbaapaqabaaak8qacaGLOaGaayzkaaGaam OraaGaay5waiaaw2faaaaacqGHRaWkdaWcaaWdaeaapeGaaGymaaWd aeaapeGaamiAa8aadaWgaaWcbaWdbiaadMgaa8aabeaak8qacqaHap aCcaWGlbWdamaaBaaaleaapeGaam4DaaWdaeqaaaaak8qacaWGSbGa amOBamaabmaapaqaa8qadaWcaaWdaeaapeGaamira8aadaWgaaWcba Wdbiaad+gaa8aabeaaaOqaa8qacaWGebWdamaaBaaaleaapeGaamyA aiaad6gaa8aabeaaaaaak8qacaGLOaGaayzkaaGaey4kaSYaaSaaa8 aabaWdbiabeo7aNbWdaeaapeGaam4Aa8aadaWgaaWcbaWdbiaadkga a8aabeaak8qacaWGIbGaam4DaaaacqGHRaWkdaWcaaWdaeaapeGaam ita8aadaWgaaWcbaWdbiaadkhacaWGJbaapaqabaaakeaapeGaam4s a8aadaWgaaWcbaWdbiaadkhacaWGJbaapaqabaaaaaGcpeGaay5wai aaw2faaaaacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqG GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeii aiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeikaiaabAdacaqGPa GaaiiOaaaa@8779@
F= tanh m ˙ W D out /2 m ˙ W D out /2 ,m= U o / K b L rc                        (7)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadAeacqGH9aqpdaWcaaWdaeaapeGaamiDaiaadggacaWG UbGaamiAamaadmaapaqaa8qaceWGTbWdayaacaWdbmaabmaapaqaa8 qacaWGxbGaeyOeI0Iaamira8aadaWgaaWcbaWdbiaad+gacaWG1bGa amiDaaWdaeqaaaGcpeGaayjkaiaawMcaaiaac+cacaaIYaaacaGLBb Gaayzxaaaapaqaa8qaceWGTbWdayaacaWdbmaabmaapaqaa8qacaWG xbGaeyOeI0Iaamira8aadaWgaaWcbaWdbiaad+gacaWG1bGaamiDaa WdaeqaaaGcpeGaayjkaiaawMcaaiaac+cacaaIYaaaaiaacYcacaWG TbGaeyypa0ZaaOaaa8aabaWdbiaadwfapaWaaSbaaSqaa8qacaWGVb aapaqabaGcpeGaai4laiaadUeapaWaaSbaaSqaa8qacaWGIbaapaqa baGcpeGaamita8aadaWgaaWcbaWdbiaadkhacaWGJbaapaqabaaape qabaGccaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa bIcacaqG3aGaaeykaiaacckaaaa@6F63@
h tu = Nu K f D in ,Nu=0.023R e 2/3 P r 0.4                       (8)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadIgapaWaaSbaaSqaa8qacaWG0bGaamyDaaWdaeqaaOWd biabg2da9maalaaapaqaa8qacaWGobGaamyDaiaadUeapaWaaSbaaS qaa8qacaWGMbaapaqabaaakeaapeGaamira8aadaWgaaWcbaWdbiaa dMgacaWGUbaapaqabaaaaOWdbiaacYcacaWGobGaamyDaiabg2da9i aaicdacaGGUaGaaGimaiaaikdacaaIZaGaamOuaiaadwgapaWaaWba aSqabeaapeGaaGOmaiaac+cacaaIZaaaaOGaamiuaiaadkhapaWaaW baaSqabeaapeGaaGimaiaac6cacaaI0aaaaOGaaeiiaiaabccacaqG GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeii aiaabccacaqGGaGaaeiiaiaabIcacaqG4aGaaeykaiaacckaaaa@62CF@
Nu= fr 8 Re1000 P r w 1+12.7 fr 8 2/3 1                      (9)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaad6eacaWG1bGaeyypa0ZaaSaaa8aabaWdbmaalaaapaqa a8qacaWGMbGaamOCaaWdaeaapeGaaGioaaaadaqadaWdaeaapeGaam OuaiaadwgacqGHsislcaaIXaGaaGimaiaaicdacaaIWaaacaGLOaGa ayzkaaGaamiuaiaadkhapaWaaSbaaSqaa8qacaWG3baapaqabaaake aapeGaaGymaiabgUcaRiaaigdacaaIYaGaaiOlaiaaiEdadaWadaWd aeaapeWaaSaaa8aabaWdbiaadAgacaWGYbaapaqaa8qacaaI4aaaaa Gaay5waiaaw2faa8aadaahaaWcbeqaa8qadaqadaWdaeaapeGaaGOm aiaac+cacaaIZaaacaGLOaGaayzkaaaaaOGaeyOeI0IaaGymaaaaca qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae iiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeyoaiaabMcacaGG Gcaaaa@66A4@
fr= 1.82log Re 1.64 2                     (10)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadAgacaWGYbGaeyypa0ZaaeWaa8aabaWdbiaaigdacaGG UaGaaGioaiaaikdacaWGSbGaam4BaiaadEgadaqadaWdaeaapeGaam OuaiaadwgaaiaawIcacaGLPaaacqGHsislcaaIXaGaaiOlaiaaiAda caaI0aaacaGLOaGaayzkaaWdamaaCaaaleqabaWdbiabgkHiTiaaik daaaGccaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabIcacaqGXaGaaeimaiaa bMcacaGGGcaaaa@5A6D@
Re= vρ D i μ                   (11)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadkfacaWGLbGaeyypa0ZaaSaaa8aabaWdbiaadAhacqaH bpGCcaWGebWdamaaBaaaleaapeGaamyAaaWdaeqaaaGcbaWdbiabeY 7aTbaacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGOaGaaeymaiaabgdacaqGPaGaaiiOaaaa @4F2E@

Eq. (9) is used to calculate the Nusselt number for forced convection inside tubes in transition or turbulent flow according to with the aid of Eq. (10) to estimate the Froude number. Moreover, the calculated Reynolds number (Re) 5240 lies within the range that was validated experimentally for copper tubes by a previous study [23,24]. The values of Tpm and Tcw, out are obtained from the following equations Eqs. (12) and (13), respectively:

T pm = T cw,in + m ˙ ' C p T cw,out T cw,in A U o F R 1 F R                    (12)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadsfapaWaaSbaaSqaa8qacaWGWbGaamyBaaWdaeqaaOWd biabg2da9iaadsfapaWaaSbaaSqaa8qacaWGJbGaam4DaiaacYcaca WGPbGaamOBaaWdaeqaaOWdbiabgUcaRmaalaaapaqaa8qaceWGTbWd ayaacaWdbiaacEcacaWGdbWdamaaBaaaleaapeGaamiCaaWdaeqaaO Wdbmaabmaapaqaa8qacaWGubWdamaaBaaaleaapeGaam4yaiaadEha caGGSaGaam4BaiaadwhacaWG0baapaqabaGcpeGaeyOeI0Iaamiva8 aadaWgaaWcbaWdbiaadogacaWG3bGaaiilaiaadMgacaWGUbaapaqa baaak8qacaGLOaGaayzkaaaapaqaa8qacaWGbbGaamyva8aadaWgaa WcbaWdbiaad+gaa8aabeaak8qacaWGgbWdamaaBaaaleaapeGaamOu aaWdaeqaaaaak8qadaqadaWdaeaapeGaaGymaiabgkHiTiaadAeapa WaaSbaaSqaa8qacaWGsbaapaqabaaak8qacaGLOaGaayzkaaGaaeii aiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGa GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca caqGGaGaaeiiaiaabIcacaqGXaGaaeOmaiaabMcacaGGGcaaaa@6F05@
T cw, out = T r + T cw,in T r ex p A U o F' m ˙                     (13)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadsfapaWaaSbaaSqaa8qacaWGJbGaam4DaiaacYcacaGG GcGaam4BaiaadwhacaWG0baapaqabaGcpeGaeyypa0Jaamiva8aada WgaaWcbaWdbiaadkhaa8aabeaak8qacqGHRaWkdaqadaWdaeaapeGa amiva8aadaWgaaWcbaWdbiaadogacaWG3bGaaiilaiaadMgacaWGUb aapaqabaGcpeGaeyOeI0Iaamiva8aadaWgaaWcbaWdbiaadkhaa8aa beaaaOWdbiaawIcacaGLPaaacaWGLbGaamiEaiaadchapaWaaWbaaS qabeaapeGaeyOeI0IaamyqaiaadwfapaWaaSbaaWqaa8qacaWGVbaa paqabaWcpeGaamOraiaacEcaceWGTbWdayaacaaaaOWdbiaabccaca qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae iiaiaabccacaqGGaGaaeikaiaabgdacaqGZaGaaeykaiaacckaaaa@6750@

Performance calculation of the PV part

The level of Tc substantially affects the efficiency of the silicon-based photovoltaic cells [25]. It has a significant effect on photovoltaic parameters and controls the quality and performance of the solar cell. The open circuit voltage, maximum power, fill factor and efficiency are found to be decreased with cell temperature [26].

According to a previous study [27], the module temperature rise beyond STC at Tc = 50°C causes a drop of around 7.5-10% efficiency.

As the ambient temperature Tamb and the global irradiance are among the main factors affecting the efficiency of the PV module, it is imperative to model the Tc and observe the impact of the flowing water on the backside temperature (Tbs) via attached copper tubes. Eqs. (14) and (15) demonstrate the calculation formulas for Tc and Tbs, respectively. In Eq. (25), for the sake of simplicity, the wind velocity (V) is set to 1 m/s as the precise calculation of the wind velocity over the plate is complex and beyond the scope of this paper.

T c = ατ eff Gk+ U t T amb + U T T bs U t + U T                       (14)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadsfapaWaaSbaaSqaa8qacaWGJbaapaqabaGcpeGaeyyp a0ZaaSaaa8aabaWdbmaabmaapaqaa8qacqaHXoqycqaHepaDaiaawI cacaGLPaaapaWaaSbaaSqaa8qacaWGLbGaamOzaiaadAgaa8aabeaa k8qacaWGhbGaam4AaiabgUcaRiaadwfapaWaaSbaaSqaa8qacaWG0b aapaqabaGcpeGaamiva8aadaWgaaWcbaWdbiaadggacaWGTbGaamOy aaWdaeqaaOWdbiabgUcaRiaadwfapaWaaSbaaSqaa8qacaWGubaapa qabaGcpeGaamiva8aadaWgaaWcbaWdbiaadkgacaWGZbaapaqabaaa keaapeGaamyva8aadaWgaaWcbaWdbiaadshaa8aabeaak8qacqGHRa WkcaWGvbWdamaaBaaaleaapeGaamivaaWdaeqaaaaak8qacaqGGaGa aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa bccacaqGGaGaaeiiaiaabccacaqGGaGaaeikaiaabgdacaqG0aGaae ykaiaacckaaaa@684B@
T bs = h p1 ατ eff Gk+ U tT T amb + h f T f U tT + h f                     (15)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadsfapaWaaSbaaSqaa8qacaWGIbGaam4CaaWdaeqaaOWd biabg2da9maalaaapaqaa8qacaWGObWdamaaBaaaleaapeGaamiCai aaigdaa8aabeaak8qadaqadaWdaeaapeGaeqySdeMaeqiXdqhacaGL OaGaayzkaaWdamaaBaaaleaapeGaamyzaiaadAgacaWGMbaapaqaba GcpeGaam4raiaadUgacqGHRaWkcaWGvbWdamaaBaaaleaapeGaamiD aiaadsfaa8aabeaak8qacaWGubWdamaaBaaaleaapeGaamyyaiaad2 gacaWGIbaapaqabaGcpeGaey4kaSIaamiAa8aadaWgaaWcbaWdbiaa dAgaa8aabeaak8qacaWGubWdamaaBaaaleaapeGaamOzaaWdaeqaaa GcbaWdbiaadwfapaWaaSbaaSqaa8qacaWG0bGaamivaaWdaeqaaOWd biabgUcaRiaadIgapaWaaSbaaSqaa8qacaWGMbaapaqabaaaaOWdbi aabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGGaGaaeikaiaabgdacaqG1aGaaeykaiaa cckaaaa@6C16@

The following expressions in Eqs. (16) to (26) outline the calculation methods of the factors in Eqs. (14) and (15). Table 2 overviews the design parameters.


ατ eff = τ g α c β c + α T 1 β c β c η el U tT + h f                        (16)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbmaabmaapaqaa8qacqaHXoqycqaHepaDaiaawIcacaGLPaaa paWaaSbaaSqaa8qacaWGLbGaamOzaiaadAgaa8aabeaak8qacqGH9a qpdaWcaaWdaeaapeGaeqiXdq3damaaBaaaleaapeGaam4zaaWdaeqa aOWdbmaadmaapaqaa8qacqaHXoqypaWaaSbaaSqaa8qacaWGJbaapa qabaGcpeGaeqOSdi2damaaBaaaleaapeGaam4yaaWdaeqaaOWdbiab gUcaRiabeg7aH9aadaWgaaWcbaWdbiaadsfaa8aabeaak8qadaqada WdaeaapeGaaGymaiabgkHiTiabek7aI9aadaWgaaWcbaWdbiaadoga a8aabeaaaOWdbiaawIcacaGLPaaacqGHsislcqaHYoGypaWaaSbaaS qaa8qacaWGJbaapaqabaGcpeGaeq4TdG2damaaBaaaleaapeGaamyz aiaadYgaa8aabeaaaOWdbiaawUfacaGLDbaaa8aabaWdbiaadwfapa WaaSbaaSqaa8qacaWG0bGaamivaaWdaeqaaOWdbiabgUcaRiaadIga paWaaSbaaSqaa8qacaWGMbaapaqabaaaaOWdbiaabccacaqGGaGaae iiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqG GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc cacaqGGaGaaeiiaiaabccacaqGGaGaaeikaiaabgdacaqG2aGaaeyk aiaacckaaaa@75E0@
h p1 = U T U T + U t                        (17)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadIgapaWaaSbaaSqaa8qacaWGWbGaaGymaaWdaeqaaOWd biabg2da9maalaaapaqaa8qacaWGvbWdamaaBaaaleaapeGaamivaa WdaeqaaaGcbaWdbiaadwfapaWaaSbaaSqaa8qacaWGubaapaqabaGc peGaey4kaSIaamyva8aadaWgaaWcbaWdbiaadshaa8aabeaaaaGcpe GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca caqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiai aabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGa aeymaiaabEdacaqGPaGaaiiOaaaa@548E@
h p2 = h fT U fT + h f                        (18)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadIgapaWaaSbaaSqaa8qacaWGWbGaaGOmaaWdaeqaaOWd biabg2da9maalaaapaqaa8qacaWGObWdamaaBaaaleaapeGaamOzai aadsfaa8aabeaaaOqaa8qacaWGvbWdamaaBaaaleaapeGaamOzaiaa dsfaa8aabeaak8qacqGHRaWkcaWGObWdamaaBaaaleaapeGaamOzaa Wdaeqaaaaak8qacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca caqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiai aabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa aeiiaiaabIcacaqGXaGaaeioaiaabMcacaGGGcaaaa@567E@
U tT = 1 U t + 1 U T 1                       (19)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadwfapaWaaSbaaSqaa8qacaWG0bGaamivaaWdaeqaaOWd biabg2da9maadmaapaqaa8qadaWcaaWdaeaapeGaaGymaaWdaeaape Gaamyva8aadaWgaaWcbaWdbiaadshaa8aabeaaaaGcpeGaey4kaSYa aSaaa8aabaWdbiaaigdaa8aabaWdbiaadwfapaWaaSbaaSqaa8qaca WGubaapaqabaaaaaGcpeGaay5waiaaw2faa8aadaahaaWcbeqaa8qa cqGHsislcaaIXaaaaOGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae iiaiaabIcacaqGXaGaaeyoaiaabMcacaGGGcaaaa@57C7@
U fT = 1 h f + 1 U T 1                       (20)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadwfapaWaaSbaaSqaa8qacaWGMbGaamivaaWdaeqaaOWd biabg2da9maadmaapaqaa8qadaWcaaWdaeaapeGaaGymaaWdaeaape GaamiAa8aadaWgaaWcbaWdbiaadAgaa8aabeaaaaGcpeGaey4kaSYa aSaaa8aabaWdbiaaigdaa8aabaWdbiaadwfapaWaaSbaaSqaa8qaca WGubaapaqabaaaaaGcpeGaay5waiaaw2faa8aadaahaaWcbeqaa8qa cqGHsislcaaIXaaaaOGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae iiaiaabIcacaqGYaGaaeimaiaabMcacaGGGcaaaa@57B6@
U L = U b + U tf                     (21)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadwfapaWaaSbaaSqaa8qacaWGmbaapaqabaGcpeGaeyyp a0Jaamyva8aadaWgaaWcbaWdbiaadkgaa8aabeaak8qacqGHRaWkca WGvbWdamaaBaaaleaapeGaamiDaiaadAgaa8aabeaak8qacaqGGaGa aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa bccacaqGGaGaaeiiaiaabIcacaqGYaGaaeymaiaabMcacaGGGcaaaa@5051@
U tf = 1 h f + 1 U tT 1                     (22)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadwfapaWaaSbaaSqaa8qacaWG0bGaamOzaaWdaeqaaOWd biabg2da9maadmaapaqaa8qadaWcaaWdaeaapeGaaGymaaWdaeaape GaamiAa8aadaWgaaWcbaWdbiaadAgaa8aabeaaaaGcpeGaey4kaSYa aSaaa8aabaWdbiaaigdaa8aabaWdbiaadwfapaWaaSbaaSqaa8qaca WG0bGaamivaaWdaeqaaaaaaOWdbiaawUfacaGLDbaapaWaaWbaaSqa beaapeGaeyOeI0IaaGymaaaakiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaa bccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae ikaiaabkdacaqGYaGaaeykaiaacckaaaa@578B@
U T = L c K c + L T K T 1                     (23)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadwfapaWaaSbaaSqaa8qacaWGubaapaqabaGcpeGaeyyp a0ZaamWaa8aabaWdbmaalaaapaqaa8qacaWGmbWdamaaBaaaleaape Gaam4yaaWdaeqaaaGcbaWdbiaadUeapaWaaSbaaSqaa8qacaWGJbaa paqabaaaaOWdbiabgUcaRmaalaaapaqaa8qacaWGmbWdamaaBaaale aapeGaamivaaWdaeqaaaGcbaWdbiaadUeapaWaaSbaaSqaa8qacaWG ubaapaqabaaaaaGcpeGaay5waiaaw2faa8aadaahaaWcbeqaa8qacq GHsislcaaIXaaaaOGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqG GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOaGaaeOm aiaabodacaqGPaGaaiiOaaaa@57F5@
U t = L gl K gl + 1 h 0 1                     (24)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadwfapaWaaSbaaSqaa8qacaWG0baapaqabaGcpeGaeyyp a0ZaamWaa8aabaWdbmaalaaapaqaa8qacaWGmbWdamaaBaaaleaape Gaam4zaiaadYgaa8aabeaaaOqaa8qacaWGlbWdamaaBaaaleaapeGa am4zaiaadYgaa8aabeaaaaGcpeGaey4kaSYaaSaaa8aabaWdbiaaig daa8aabaWdbiaadIgapaWaaSbaaSqaa8qacaaIWaaapaqabaaaaaGc peGaay5waiaaw2faa8aadaahaaWcbeqaa8qacqGHsislcaaIXaaaaO GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca caqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiai aabccacaqGGaGaaeiiaiaabccacaqGOaGaaeOmaiaabsdacaqGPaGa aiiOaaaa@58BA@
h o =5.7+3.8V V=1m/s                            (25)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsafaqabe Gabaaabaaeaaaaaaaaa8qacaWGObWdamaaBaaaleaapeGaam4BaaWd aeqaaOWdbiabg2da9iaaiwdacaGGUaGaaG4naiabgUcaRiaaiodaca GGUaGaaGioaiaadAfaa8aabaWdbiaadAfacqGH9aqpcaaIXaGaamyB aiaac+cacaWGZbaaaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaae iiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqG GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabIcacaqGYaGaaeyn aiaabMcacaGGGcaaaa@5A3C@
U b = L i K i + 1 h i 1                            (26)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadwfapaWaaSbaaSqaa8qacaWGIbaapaqabaGcpeGaeyyp a0ZaamWaa8aabaWdbmaalaaapaqaa8qacaWGmbWdamaaBaaaleaape GaamyAaaWdaeqaaaGcbaWdbiaadUeapaWaaSbaaSqaa8qacaWGPbaa paqabaaaaOWdbiabgUcaRmaalaaapaqaa8qacaaIXaaapaqaa8qaca WGObWdamaaBaaaleaapeGaamyAaaWdaeqaaaaaaOWdbiaawUfacaGL DbaapaWaaWbaaSqabeaapeGaeyOeI0IaaGymaaaakiaabccacaqGGa GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca caqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiai aabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa aeiiaiaabIcacaqGYaGaaeOnaiaabMcacaGGGcaaaa@5B75@

Table 2: Design parameters of the PV system

Parameter

Unit

Value

APV

[m2]

1.64

Cp

[Wh/kg.K]

1.163

CL

[m]

30

Dins

[m]

0.00635

Hm

[m]

1.66

hf

[W/m2.K]

400

hi

[W/m2.K]

5.8

h0

[W/m2.K]

9.5

hp1

[-]

0.8772

hp2

[-]

0.9841

Kc

[W/m.K]

204

Kgl

[W/m.K]

0.95

Ki

[W/m.K]

0.035

KT

[W/m.K]

0.033

Lc

[m]

0.0006

Lgl

[m]

0.003

LT

[m]

0.0005

m'

[kg/s]

0

Ub

[W/m2.K]

0.62

Ut

[W/m2.K]

9.24

UT

[W/m2.K]

66

UtT

[W/m2.K]

8.1

UL

[W/m2.K]

8.57

Utf

[W/m2.K]

7.93

V

[m/s]

1

Wm

[m]

0.99

Wgp

[m]

0.045

αcell

[mA/K]

0.85

αTedlar

[mA/K]

0.5

βc

[V/K]

0.9

ηcell

[%]

0.09

τG

[-]

0.95

(ατ)eff

[mA/K]

0.697

The average fluid temperature (Tf) over the length of the tube or cooling circuit (CL) below the PV is obtained as follows from Eq. (27). To determine the temperature output of the fluid from the module, the outlet temperature of the PVT (Tf, out) is calculated according to Eq. (28). The penalty factors in both equations hp1 and hp2 reduce the efficiency of PVT through considering the losses in heat transfer from the glass of the PV until it reaches the working fluid.

T ¯ f,average = T amb + h p1 h p2 ατ eff G U L 1 1exp W m U L CL m ˙ Cp W m U L CL m ˙ Cp + T f,inlet 1exp W m U L CL m ˙ Cp W m U L CL m ˙ Cp                                  (27)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsafaqabe Gabaaabaaeaaaaaaaaa8qaceWGubWdayaaraWaaSbaaSqaa8qacaWG MbGaaiilaiaadggacaWG2bGaamyzaiaadkhacaWGHbGaam4zaiaadw gaa8aabeaak8qacqGH9aqpdaWadaWdaeaapeGaamiva8aadaWgaaWc baWdbiaadggacaWGTbGaamOyaaWdaeqaaOWdbiabgUcaRmaalaaapa qaa8qacaWGObWdamaaBaaaleaapeGaamiCaiaaigdaa8aabeaak8qa caWGObWdamaaBaaaleaapeGaamiCaiaaikdaa8aabeaak8qadaqada WdaeaapeGaeqySdeMaeqiXdqhacaGLOaGaayzkaaWdamaaBaaaleaa peGaamyzaiaadAgacaWGMbaapaqabaGcpeGaam4raaWdaeaapeGaam yva8aadaWgaaWcbaWdbiaadYeaa8aabeaaaaaak8qacaGLBbGaayzx aaWaamWaa8aabaWdbiaaigdacqGHsisldaWcaaWdaeaapeWaaeWaa8 aabaWdbiaaigdacqGHsislcaWGLbGaamiEaiaadchadaqadaWdaeaa peWaaSaaa8aabaWdbiabgkHiTiaadEfapaWaaSbaaSqaa8qacaWGTb aapaqabaGcpeGaamyva8aadaWgaaWcbaWdbiaadYeaa8aabeaak8qa caWGdbGaamitaaWdaeaapeGabmyBa8aagaGaa8qacaWGdbGaamiCaa aaaiaawIcacaGLPaaaaiaawIcacaGLPaaaa8aabaWdbmaalaaapaqa a8qacqGHsislcaWGxbWdamaaBaaaleaapeGaamyBaaWdaeqaaOWdbi aadwfapaWaaSbaaSqaa8qacaWGmbaapaqabaGcpeGaam4qaiaadYea a8aabaWdbiqad2gapaGbaiaapeGaam4qaiaadchaaaaaaaGaay5wai aaw2faaaWdaeaapeGaey4kaSYaaSaaa8aabaWdbiaadsfapaWaaSba aSqaa8qacaWGMbGaaiilaiaadMgacaWGUbGaamiBaiaadwgacaWG0b aapaqabaGcpeWaaeWaa8aabaWdbiaaigdacqGHsislcaWGLbGaamiE aiaadchadaqadaWdaeaapeWaaSaaa8aabaWdbiabgkHiTiaadEfapa WaaSbaaSqaa8qacaWGTbaapaqabaGcpeGaamyva8aadaWgaaWcbaWd biaadYeaa8aabeaak8qacaWGdbGaamitaaWdaeaapeGabmyBa8aaga Gaa8qacaWGdbGaamiCaaaaaiaawIcacaGLPaaaaiaawIcacaGLPaaa a8aabaWdbmaalaaapaqaa8qacqGHsislcaWGxbWdamaaBaaaleaape GaamyBaaWdaeqaaOWdbiaadwfapaWaaSbaaSqaa8qacaWGmbaapaqa baGcpeGaam4qaiaadYeaa8aabaWdbiqad2gapaGbaiaapeGaam4qai aadchaaaaaaaaacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca caqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiai aabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGa aeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccaca qGGaGaaeiiaiaabccacaqGOaGaaeOmaiaabEdacaqGPaGaaiiOaaaa @B727@
T f,out = T amb + h p1 h p2 ατ eff G U L 1exp W m U L CL m ˙ Cp + T f,inlet exp W m U L CL m ˙ Cp                      (28)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiaadsfapaWaaSbaaSqaa8qacaWGMbGaaiilaiaad+gacaWG 1bGaamiDaaWdaeqaaOWdbiabg2da9maadmaapaqaa8qacaWGubWdam aaBaaaleaapeGaamyyaiaad2gacaWGIbaapaqabaGcpeGaey4kaSYa aSaaa8aabaWdbiaadIgapaWaaSbaaSqaa8qacaWGWbGaaGymaaWdae qaaOWdbiaadIgapaWaaSbaaSqaa8qacaWGWbGaaGOmaaWdaeqaaOWd bmaabmaapaqaa8qacqaHXoqycqaHepaDaiaawIcacaGLPaaapaWaaS baaSqaa8qacaWGLbGaamOzaiaadAgaa8aabeaak8qacaWGhbaapaqa a8qacaWGvbWdamaaBaaaleaapeGaamitaaWdaeqaaaaaaOWdbiaawU facaGLDbaadaWadaWdaeaapeGaaGymaiabgkHiTiaadwgacaWG4bGa amiCamaabmaapaqaa8qadaWcaaWdaeaapeGaeyOeI0Iaam4va8aada WgaaWcbaWdbiaad2gaa8aabeaak8qacaWGvbWdamaaBaaaleaapeGa amitaaWdaeqaaOWdbiaadoeacaWGmbaapaqaa8qaceWGTbWdayaaca WdbiaadoeacaWGWbaaaaGaayjkaiaawMcaaaGaay5waiaaw2faaiab gUcaRiaadsfapaWaaSbaaSqaa8qacaWGMbGaaiilaiaadMgacaWGUb GaamiBaiaadwgacaWG0baapaqabaGcpeGaamyzaiaadIhacaWGWbWa aeWaa8aabaWdbmaalaaapaqaa8qacqGHsislcaWGxbWdamaaBaaale aapeGaamyBaaWdaeqaaOWdbiaadwfapaWaaSbaaSqaa8qacaWGmbaa paqabaGcpeGaam4qaiaadYeaa8aabaWdbiqad2gapaGbaiaapeGaam 4qaiaadchaaaaacaGLOaGaayzkaaGaaeiiaiaabccacaqGGaGaaeii aiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGa GaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabcca caqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiai aabccacaqGGaGaaeikaiaabkdacaqG4aGaaeykaiaacckaaaa@9610@

The selected PV module is a monocrystalline silicon panel with an electric power capacity of 260 W, i.e., ηref =26% under STC. The following Eq. (29) is used to determine the module efficiency with respect to Tc. The parameter βcoef = 0.0045 °C-1 is a coefficient that represents the temperature effect that is usually provided by the manufacturer according to previous studies [28,29]. The output of the module is obtained by multiplying the total irradiance with the module efficiency ηPV and the area of the module.

η PV = η ref 10.0045 T cell T ref                           (29)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiabeE7aO9aadaWgaaWcbaWdbiaadcfacaWGwbaapaqabaGc peGaeyypa0Jaeq4TdG2damaaBaaaleaapeGaamOCaiaadwgacaWGMb aapaqabaGcpeWaamWaa8aabaWdbiaaigdacqGHsislcaaIWaGaaiOl aiaaicdacaaIWaGaaGinaiaaiwdadaqadaWdaeaapeGaamiva8aada WgaaWcbaWdbiaadogacaWGLbGaamiBaiaadYgaa8aabeaak8qacqGH sislcaWGubWdamaaBaaaleaapeGaamOCaiaadwgacaWGMbaapaqaba aak8qacaGLOaGaayzkaaaacaGLBbGaayzxaaGaaeiiaiaabccacaqG GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc cacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeii aiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGOa GaaeOmaiaabMdacaqGPaGaaiiOaaaa@6844@
Q ˙ e,PV =Gk A PV η PV                        (30)  MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaWsaqaaaaa aaaaWdbiqadgfapaGbaiaadaWgaaWcbaWdbiaadwgacaGGSaGaamiu aiaadAfaa8aabeaak8qacqGH9aqpcaWGhbGaam4AaiaadgeapaWaaS baaSqaa8qacaWGqbGaamOvaaWdaeqaaOWdbiabeE7aO9aadaWgaaWc baWdbiaadcfacaWGwbaapaqabaGcpeGaaeiiaiaabccacaqGGaGaae iiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqG GaGaaeiiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiiaiaabc cacaqGGaGaaeiiaiaabccacaqGOaGaae4maiaabcdacaqGPaGaaiiO aaaa@56E5@

The thermal efficiency of the system in terms of hot water production is out of the scope of this paper as it is mainly limited to the potential of PVTRC for cooling. However, the utilization of the produced thermal energy to supply a hot water storage tank, for instance, is a topic that can be discussed in future research.

Integration of the PVTRC into a case-study model

In order to assess the potential of the proposed system, it is imperative to test it within the framework of a generic model. In office buildings, cooling loads during working hours coincide with the availability of the solar irradiance on the face. Depending on the geographical location of the office space as well as the facade orientation, there are differences in both cooling loads and solar irradiance, which will considerably affect the performance of PVTRC. Therefore, Jeddah and Munich represent a hot and cold location for the modeling and simulation framework, respectively. The aim is to overview the impact of the location on the results of the model. The diagram in Figure 2 illustrates the annual average ambient temperatures of both locations on the primary axis. On the secondary axis, the global irradiance on the south facade is presented.

Figure 2: Daily average ambient temperature and global inci-dent radiation on a south façade in different seasons. Left: Jeddah, Right: Munich

It can be seen that the average ambient summer temperature in Jeddah is beyond 35°C during the daytime. In winter, it does not go below 20°C. The global irradiance reaches 700 W/m2 on the south façade, reaching 200 W/m2 when the sun is over the building. This is mainly caused by diffused radiation. In Munich, the average temperature in summer reaches 20°C, whereas it can go below -3°C in winter. Compared to Jeddah, less solar irradiance is received in winter and in autumn. However, in the four seasons, the average solar irradiance is in the range of 300-400 W/m2. The climate data are obtained from the database of Meteonorm[30,31].

Generally, in a typical office space, a relatively high amount of sensible internal cooling loads is generated due to the use of equipment, artificial lighting, and a number of active occupants. Therefore, a generic model for office space is developed. Space should accommodate six users on their desks with their electric consuming and heat-emitting equipment. Artificial lighting is also available. Figure 3 depicts the model of the simulated office space after adding 6 PVTRC elements to the solid part of the south facade. Table 3 outlines the framework of the simulation model.

Figure 3: Simulated office space

Table 3: Framework of the simulation mode

|

Façade

Unit

Value

Window fraction

WF

[%]

50

Frame fraction

FF

[%]

10

Solar heat gain coefficient

gglass

[%]

34

Light transmittance

tglass

[%]

63

Rate of heat transfer

Windows

Uglass

[W/m2.K]

1.21

External opaque surfaces

Uwall

[W/m2.K]

0.22

Integrated window shading

Generic external screen shade

Fc

[-]

0.14

Cooling and air conditioning

Room cooling method

[-]

Air/Water

VAV control method

CO2

Controller setpoints

Tset

[°C]

21-25

Air supply temperature

Tsup

[°C]

16

Relative humidity (min)

Rh

[%]

20

Relative humidity (max)

Rh

[%]

80

Heat exchanger efficiency

ηx

[%]

60

Mech. Return airflow (min)

V'return,min

[l/s.m2]

0.3

Mech. Return airflow (max)

V'return,max

[l/s.m2]

7

CO2 limits (max)

CO2, max

[ppm]

400

CO2 limits (min)

CO2, min

[ppm]

1000

Pressure diff. envelop (min)

dPmin

[Pa]

-20

Pressure diff. envelop (max)

dPmax

[Pa]

-10

Cooling efficiency

COP

[-]

3

Internal loads

Occupants

Number

[-]

6

Activity

[MET]

1

Clothing

[CLO]

0.85*

Schedule

[-]

08-17 weekdays

Lighting

Number

[-]

6

Total power

[W]

30

Schedule

[-]

08-17 weekdays

Equipment

Number

[-]

6

Total power

[W]

150

Schedule

[-]

08-17 weekdays

The input radiant cooling capacity is given based on the above sizing and lies at 480 W. The room integrated air handling unit is responsible for the air conditioning of the adequate amount of fresh air needed to maintain a CO2 level of 400-1000 ppm. The set temperature range is 21-25°C. The glass portion of the facade is equipped with external shading devices that are drawn by irradiance of about 100 W/m2. Also, they are drawn if the incident solar angle is below 90°. The simulation results include details on indoor temperatures under the given conditions. It is also important to ensure that the size of the radiant cooling system is sufficient to meet the comfort requirements of the users.

*Clothing is automatically adapted between limits - or + 0.25 CLO to obtain comfort.

Results

Surface Temperatures

The diagram in Figures 4 and 5 presents the resulting surface temperature in the case of PVTRC and PV elements with respect to the generated output in the different seasons of the year. While the first diagram is related to the conditions of Jeddah, the second one is for Munich. The primary axis indicates the average irradiance per unit area. The secondary axis presents the data of ambient temperature and surface temperature in the case of PVTRC and PV. It is clear that the surface temperature correlates with the amount of irradiance and ambient temperature among other factors. However, it seems evident that the available amount of solar irradiance affects the temperature more significantly. A remarkable difference is noted between PV and PVTRC in winter where the irradiance is higher due to the vertical angle of the south mounted modules. The cold-water circulation behind the surface of PV module in the case of PVTRC reduces surface temperature. While the surface temperature of PV in winter reaches 30°C and beyond, it reaches 10°C in the PVTRC. In summer, the PVTRC is cooler than PV by more than 12K.

`

Figure 4: Surface temperatures; Location: Jeddah

Figure 5: Surface temperatures; Location: Munich

In the case of Munich, a clear difference in surface temperature levels can be seen, especially in spring and summer, due to the relatively low altitude of the sun position. The large amount of solar irradiance causes an increased level ofsurface temperature. For the south-oriented vertical PV panel, the surface temperature exceeds 27°C during operation in spring, summer, and autumn, while it reaches 35°C and higher in winter. Conversely, the surface temperature in the case of PVTRC elements remains in considerably low magnitudes. In winter, the surface temperature lies around 17°C, while it cools down to ca. 9°C during the remaining seasons.

Yield and coverage of radiant cooling demand

The diagram in Figure 6 shows the relationship between the electric energy output and the cooling energy demand for radiant cooling only on an average day in each of the four seasons. At this stage, it is important to distinguish between the cooling load that is used to maintain the level of CO2 concentration at a certain degree and the effort needed to extract the sensible cooling loads from the space. The first is associated with air conditioning, which includes cooling/heating, humidification, and dehumidification. The second type of cooling load is extracted mainly via radiation through the radiant cooling panels which are indicated by the black curve in the diagram. It is important to consider that the cooling energy is converted into electricity considering a coefficient of performance (COP) of 3.0.

Figure 6: Yield against radiant cooling demand; Location: Jeddah

The orange curve demonstrates the energy output by the PV part of the PVTRC element. Another dashed orange curve can be also seen to show the energy output using a conventional PV panel that does not include circulating water. Moreover, the green curve indicates the remaining electric energy after covering the cooling load required for radiant cooling. On an average day in the hottest season in summer, the surplus of the generated electric energy reaches 1247W at the peak point of the noon. Once again, while the continuous line indicates the PV of the PVRTC element, the dashed line reflects the performance of conventional PV option. Though, high surplus is reached with this option too, a remarkable increase in efficiency can be noticed in the case of the PVTRC options.

In the city of Jeddah, during the four seasons, it appears that the radiant cooling load can be covered with the generated energy of the installed six PV panels of either system, PVTRC or PV. Yet, there are notable differences in the remaining amount of energy that can be utilized for other functions; these differences are indicated in green continuous and dashed curves. This is understandable due to the differences in cooling loads as well as irradiance on the south facade posed by seasonal conditions. From the diagram, it is clear that the increase in PV efficiency of the PVTRC against PV correlates with the available irradiance. This means that the increase in efficiency due to the back-surface cooling of the PV in the case of PVTRC is remarkable in times of low solar altitudes.

More insight into the performance of the PVTRC is made available in Figure 7. The diagrams demonstrate the total energy balance on an average day in each season. It illustrates the sum of output via PVTRC and used electric energy for cooling. Here, it is important to mention that the entire cooling load is considered; including air conditioning as well as radiant cooling. As in the previous diagram, the energy output is indicated with the orange curve. The red curve depicts the total cooling load. The blue curve depicts the energy balance, i.e., supplied energy vs. used energy. According to the diagram the electric energy balance in Jeddah reaches 1150W. This analysis is useful in understanding the amount of energy deficit and energy surplus in relation to the time of the year. The energy deficit in the evening in all the seasons is clearly due to the absence of sunlight. While there is always a positive energy balance during daytime in winter, spring and autumn, a negative energy balance is notable in summer due to the increased cooling load. Despite the high sun altitude and low irradiance, the reduced efficiency is caused by the high ambient temperature. Moreover, positive energy can always be used for artificial lighting and other plug loads. Therefore, a two-way AC/DC inverter is recommended for operating the chiller in the few times where it needs to run via other sources of electricity using AC current. Surely, the efficiency of the inverter needs to be taken into consideration.

Figure 7: Energy balance; Location: Jeddah

Since cooling in the winter of Munich is not needed, the entire energy generated by the PVTRC is usable. In the other seasons, when the demand for radiant cooling increases, the electric energy yield is reduced. However, it is also remarkable that the potential of the façade-incorporated PVTRC in Munich is high. The impact of the back-surface cooling is evident, and a substantial increase in efficiency over conventional PV panels can be seen.

The diagrams in Figure 8 indicate positive electric energy balance when considering the cooling aspect of the office space that includes the radiant part as well as air conditioning. Obviously, little electric energy needs to be extracted from other sources to maintain the availability of cooling energy in the early morning and evening. Moreover, the shown large amount of excess energy suggests the consideration of energy storage systems such as batteries. This is particularly useful in a location where cloudy and overcast sky conditions often occur. Another use of the excess energy from the south oriented facade is in supplying other rooms with less solar potential such as north oriented spaces. Even the facades of east oriented spaces, for instance, receive solar irradiance in the early morning and suffer the drop for the rest of the day. The opposite happens in the case of the west facade where the sun starts to be available in the afternoon. Therefore, considering a mechanism for electric energy exchange between the different rooms is a sensible step for increasing the total efficiency of an office building. A general energy balance under the given framework for Munich is shown in Figure 9.

Figure 8: Yield against radiant cooling demand; Location: Munich

Figure 9: Energy balance; Location: Munich

Potential for extra energy output

An overview comparison between the energy balances in both case-study cities is seen in Figure 10. Each season is highlighted with a different type of curve. The black curve indicates the daily average energy balance on the annual level. In the hot-humid Jeddah, it is noticeable that a negative energy balance is expected before 07:00 and after 18:00 in all the seasons. This is mainly due to the available cooling loads due to the high outside ambient temperature. This is obviously not the case in Munich where the temperatures in the mornings and evenings are relatively acceptable and do not remarkably affect the cooling load. Moreover, the ambient temperature during the day in the summer of Jeddah can go beyond 40°C. This clearly impacts the cooling energy balance. In Munich, it is clear that a positive energy balance is expected all over the year during the daytime.

Figure 10: Daily average electric cooling energy balance (PVT vs.radiant and convective cooling loads); Left: Jeddah, Right: Munich

The seasonal difference in energy yields, which directly affects the energy balance, is clear in Jeddah. This is also understandable as it is related to the changes in the cooling loads even between spring and autumn. Conversely, a recognizable difference between summer and winter in Munich is obvious. Owing to the relative similarities in the cooling loads as well as the available irradiance on the south facade in spring and autumn, the electric energy balance appears to be in close ranges.

Indoor temperature under the simulated conditions

The diagram in Figure 11 describes the impact of the installed system of the PVTRC elements on the average indoor temperature in both locations. From the general overview, it can be confirmed that the temperatures lie in the acceptable comfort range according to ASHRAE standards (2017). The seasonal impact is apparent in Munich as the temperature in winter is relatively lower than in the other seasons. It swings between 21-22°C. In spring and autumn, the indoor temperature ranges between 23-24°C; in summer, it reaches 25°C.

Figure 11: Daily average indoor temperature under the given conditions

In Jeddah, there seems to be a homogeneous distribution of indoor temperature all over the year. This is in the range of 24.5-25.5°C. However, in summer, the average indoor temperature reaches a maximum of 26.4°C. While this is also within acceptable comfort ranges, there are many other practical energy efficient solutions to improve thermal sensation in an indoor environment without having to increase the cooling capacity of the system such as increasing air velocity in the room [32-34]. The combination of natural ventilation with radiant cooling is also a sensible approach.

Discussion

Radiant cooling systems have garnered much interest due to their achievable high thermal comfort, low energy demand, quiet operation, and space-saving features. In radiant cooling systems, water pipes are attached to the back of a radiating panel. The circulating chilled water is delivered through the pipe and cools down the panel. The chilled surface extracts a great portion of the generated heat inside a room via radiation and transports it to the chilled water via conduction [35,36]. As the specific heat capacity of water is much higher than that of air, the use of water for room heat extraction is substantially more energy efficient [37]. Furthermore, in hybrid cooling [38], the supplied and conditioned air volume is reduced to the adequate level to maintain a desired indoor air quality. While radiant cooling is considered as an air-water cooling system, the conventional air conditioning approach is mainly based on extracting cooling loads via convective heat transfer and is called (all-air) system. Radiant cooling can be integrated into floors, ceilings, wall or any room surface. However, the surface temperature of the radiant cooling panel needs to remain above the dew point temperature of the room air to avoid condensation on the surface. Several studies have explored the different methods to eliminate the risk of condensation [38-44].

At present, various PVT systems are being developed with numerous options of a PV system (monocrystalline, polycrystalline, amorphous silicon or thin-film photovoltaic systems), collector types (air, liquid, evaporative), concentrator types, design, and features. Engineering approaches select the thermal to electrical yield ratio, solar fraction, heat removal fluid, the collector type, etc. These factors determine the system operating mode, working temperature, and energy performance. The system described in the present work features a combination of PVT panel with the radiant cooling panel and is named as PVTRC. This approach is attractive because the absorbed solar radiation energy is not fully converted to electricity and increases the temperature of solar cells. The PV temperatures can be decreased by fluid circulation to extract heat. Hybrid PV/thermal systems comprising PV modules coupled to heat extraction devices have been applied to PV building installations. The total energy output of the hybrid system depends on the ambient temperature, the heat exchange mode, and on the solar energy input. The electrical output is the main parameter, which is used to optimize the operation condition of the hybrid system. In hybrid photovoltaic/thermal systems, pipes are located at the rear side of the PV panel, and water circulates to absorb heat, cool the PV part, and be used for applications such as heating. In hot climates, however, the decrease in the surface temperature of the absorber is not high as the temperature of the circulating water is close to the outdoor temperature. Moreover, in radiant cooling systems, water pipes are attached to the back of a radiating panel that radiates cooling energy into the room. Such systems are interesting due to high thermal comfort, low energy demand, quiet operation, and space-saving features. The paper focuses on the inlet temperature to improve the overall efficiency of the system. The system features the PVT part located on the external side of a building and the radiant cooling system facing the interior. The module efficiency and the related surface temperature of the PV absorber are studied as influenced by the PVTRC design. The main findings indicate that the PVTRC elements being integrated with PV systems decrease the PV surface temperatures in both hot and cold climates. On analyzing the system yield, we found the increase in PV efficiency of the PVTRC against PV that correlates with the available irradiance. In other words, the back-surface cooling of the PV in the PVTRC boosts efficiency when solar altitudes are low. Further, the system does not need much energy to maintain the availability of cooling energy in early morning and evening. Also, the system suggests the use of energy storage to accumulate excess energy. This system feature is extremely useful in cloudy sky conditions. The total efficiency of the system can be increased by implementing electric energy exchange between different areas of a building.

The proposed system offers a range of novel design features: (i) it combines energy generating and cooling elements in one device that can be incorporated into a building’s façade; (ii) it allows a direct usage of solar energy through facade integration as cooling loads occur during the times of high irradiance; (iii) the proposed system makes use of return chilled water to cool the PVT and thus improve the efficiency of the PV panel; (iv) the suggested combination is one form of a more efficient application for the PVT because it is usually used for domestic hot water generation and supported by an auxiliary heater as the generated thermal energy is not sufficient. However, the PVTRC approach is not free of limitations, of which the following can be considered. The proposed PVTRC elements need to be integrated into the opaque part of the façade, meaning that they are limited to the available opaque area in the facade. If the available opaque area in the facade is not sufficient to extract the sensible cooling load in the room, more radiant cooling elements can be installed in the ceiling. Otherwise, the remaining portion can be extracted by conventional air conditioning. In radiant cooling, the risk of condensation is always present in times of high relative humidity. This is usually associated with natural ventilation. If mechanical ventilation with humidity control is on, this risk is not to be considered.

Conclusions

Cooling loads mostly occur in times of high solar irradiance on facades. Therefore, it is sensible to develop solutions that consider instantaneous cooling energy generation using façade-integrated photovoltaic cells. The concept of the hybrid PVT panel is useful as it improves the efficiency of the PV through cooling its back surface. This paper has argued that the suggested combination of both systems in the form of façade-incorporated PVTRC element provide a sound solution for energy efficient cooling and electric energy generation in office spaces in hot and cold climate zones represented by the cities of Jeddah and Munich, respectively. The study shows that the proposed PVTRC can reach an increase of efficiency up to 35%.

The simulation results indicated great potential for the proposed elements in meeting the cooling energy demand as well as efficiently generating electricity. In every season in Munich, positive energy balance within the framework of this study can be achieved. Except in summer, there are also good chances not only for efficient electric and cooling energy generation via PVTRC elements but also for generating a substantial amount of surplus for other electric usages.

These results add to the rapidly expanding field of building integrated PV, PVT, and radiant cooling elements. The findings suggest a good application potential for the PVTRC elements and, therefore, it is worth to take it to the next level where they are experimentally tested in real conditions.

Conflicts of Interest

The author declares to have no conflict of interest

Funding Statement

Nothing to disclose

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