A numerical and experimental study of micro-channel heat pipe solar photovoltaics thermal system

Applied Energy 206 (2017) 708–722

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

A numerical and experimental study of micro-channel heat pipe solar photovoltaics thermal system

T

⁎

Mawufemo Modjinou, Jie Ji , Jing Li, Weiqi Yuan, Fan Zhou Department of Thermal Science and Energy Engineering, University of Science and Technology of China, Hefei 230026, China

H I G H L I G H T S photovoltaic/thermal system with micro-channel heat pipe was proposed. • AA novel detailed simulation model for the MHP-PV/T system was presented. • Heat transfer limitations and transient study of the components have been analyzed. • The hydrodynamic and vapor transient periods of the refrigerant was identified. • The thermal and electrical efficiency of the MHP-PV/T has been calculated. •

A R T I C L E I N F O

A B S T R A C T

Keywords: Micro-channel heat pipe c-Si Solar Photovoltaic Thermal

A novel micro-channel heat pipe array incorporated with crystalline silicon (c-Si) solar photovoltaic/thermal system (MHP-PV/T) was designed and constructed by the authors. The proposed design configuration combined c-Si solar cells and wide micro-channel heat pipes (MHP) that were filled with prescribed amount of acetone as refrigerant under a vacuum condition in the same insulated frame to simultaneously provide electrical and thermal energy. Heat and mass transfer characteristics of the MHP-PV/T were preliminary investigated using both numerical and experimental methods. The transient behavior and parametric heat transfer limitations of the heat pipe were also examined using MATLAB. A linear relation between the thermal instantaneous efficiency ηth and the reduced temperature parameter (Tout −Tin ) GT−1 was established. The maximum instantaneous efficiency was found to be 54.0% with an electrical power output of 70 W. The results indicated that the daily thermal and electrical efficiencies were 50.7% and 7.6%, respectively. The transient behavior of the MHP shows a faster thermal response to heat input within the temperature range of 48.8–49.2 °C and slower response when the thermal diffusivity was reduced to 0.05 cm2/s. The results also reveal good agreements between model simulation and experimental measurement with sufficient confidence.

1. Introduction In order to utilize the solar photovoltaic (PV) cell at a low operating temperature, researchers focus on cooling the solar cell and taking advantage of the heat dissipated from the solar cell using fluid channels at the rear of the solar cell or heat pipe. The technology incorporates a solar PV module and a solar thermal collector in the same frame to convert solar energy into electrical and thermal energy simultaneously. This kind of solar system is termed photovoltaic/thermal (PV/T) system. The system can provide hot water while producing electricity at the same time. These dual functions of the PV/T result in a higher overall solar energy conversion rate than the sole use of photovoltaic modules or solar water heaters [1]. The first investigation on a PV/T

⁎

Corresponding author. E-mail addresses: [email protected] (M. Modjinou), [email protected] (J. Ji).

http://dx.doi.org/10.1016/j.apenergy.2017.08.221 Received 29 May 2017; Received in revised form 7 August 2017; Accepted 27 August 2017 Available online 08 September 2017 0306-2619/ © 2017 Elsevier Ltd. All rights reserved.

system was presented by Wolf [2]. Subsequently, several kinds of research on the hybrid solar PV/T system have been carried out to improve its general performance [3]. Since an improvement on PV/T technology makes it cost-effective, a considerable amount of research has been carried out to investigate the performance of PV/T system over the years [4]. However, these studies were done using conventional or standard heat pipes also known as constant conductance heat pipes (CCHPs) [5]. Although researchers recognize the effectiveness of micro-channel heat pipes (MHP) over conventional heat pipes, there were hardly any studies designed to examine the performance of MHP incorporated with PV/T [6]. MHP has noticeable leads over standard round tubes heat pipes (RTHP) and unlike other conventional heat pipes; MHP is precisely flat with width

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Nomenclature

c cond e es eff evap f final g in pv MHP ref L loss l l out sky sat th trans T v w

Symbols A C E FR G g H h I L m ṁ M n R T fh M Nu Q P q qe Ra U u V y z

cross-sectional area [m2] specific heat [J/(kg K)] output electricity [W/m2] heat removal factor of the MHP-PV/T [dimensionless] solar irradiance [W/m2] acceleration due to gravity [m/s2] air gap [m] heat transfer coefficient [W/(K·m2)] current of photovoltaic module [A] latent heat [J/kg] mass [kg] mass flow rate [kg/s] measured data derivative in the normal direction at the interval boundary thermal resistance [K/W] temperature [K or °C] fluid film height mass per unit area [kg/m2] Nusselt number [dimensionless] heat [W/m2] predicted data heat flux [W/m2] or the rate of internal heat supplied [W/ m3] evaporator net heat flux [W/m2] Rayleigh number [dimensionless] conduction heat transfer coefficient per unit length [W/ (m K)] average wind speed [m/s] voltage of photovoltaic module [V] horizontal coordinate [m] or [cm] axial coordinate [m] or [cm]

Greek symbols

α δ ε λ σ Ø ζ τ (τα )e

Subscript a amb b

collector condenser external environment heat pipe external surface effective (thermal conductivity) evaporator energy saving final glass cover inlet or input photovoltaic cells micro-channel heat pipe reference loss coefficient of the MHP-PV/T loss coefficient of the system refrigerant film liquid refrigerant outlet or output sky saturated thermal transverse total vapor wall of the heat pipe

υ γ (Δη)

air ambient back or photovoltaic cells back metal contact materials

thermal diffusivity [m2/s] thickness [m] emissivity [dimensionless] thermal conductivity [W/mK] Stefan-Boltzmann constant [5.6697 × 10−8 W/(m2 K4)] MHP-PV/T collector tilt angle [rad] packing factor transmittance [dimensionless] effective transmittance-absorptance product [dimensionless] kinematic viscosity [m2/s] thermal expansion coefficient [K−1] overall uncertainty

experimental studies by Riffat et al. [15] and Hammad [16–19] likewise. Even though MHP has noticeable leads over RTHP, there were hardly any studies designed to examine its performance with PV/T systems. Ji Jie and his team are presenting this paper to fill this gap of the lack study that integrated MHP with PV/T system to optimize performance and increase its efficiency. The originality of the studies done by the Team on PV/T continues to contain sufficient contributions to the new body of knowledge from the international perspective since this novel the MHP-PVT has not been examined so far (Table 6 refers) despites its popularity of MHP in the electronic and telecommunication sector to remove a large amount of heat [20–24]. A novel PV/T with wide micro-channel heat pipe (MHP) was designed and constructed in this study. Experimental and numerical studies on the performance of the proposed MHP-PV/T system were carried out, and the analyzed results presented by this paper.

ranging from 1.2 mm to 4.0 mm. It has better heat transfer capacity, lower pressure difference, lower filling ratio and more compact structure [7]. It has the advantage of eliminating a cost and product thickness compared to RTHP. It is used in electronic systems to remove a large amount of heat and was only reported by limited studies in solar thermal energy conversion area [8]. In spite of the advantages of MHP, only a few studies investigated its performance with collectors [9]. Deng et al. studied the thermal performance of a system of MHP thermal collector and indicated that the system of heat pipe has an excellent performance, including quick thermal respond speed and agreeable isothermal ability [10]. Past innovative studies only focus on other components of the PV/T systems to improve its performance. For instance, Wang and Pei [11] investigated the effects of frame shadow on PV/T system and showed that the frame shadow reduced the efficiency to 3.2% with a total annual energy loss of 53.6 kWh/m2. Huang et al. [12] and Kalogirou et al. [13] also studied the overall energy gain of PV/T to find potentials of improving its performance. Many designs of PV/T systems have been introduced without paying much attention to the heat transfer mechanism. Mat et al. indicated by a review study that the tube-and-sheet and evacuated tubular PV/T systems that were presented in literature made use of RTHP. The heat pipes used were of circular cross section [14]; and

2. Description of novel configuration of PV/T The materials used to build the MHP-PV/T include polycrystalline (c-Si) PV cells, aluminium micro-channel heat pipes (MHP), circular and rectangular aluminium extrusions. The MHPs were designed as 709

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refrigerant based thermal absorber heat pipes to conduct heat away from the c-Si photovoltaic cells effectively to boost the photovoltaic cells’ and the collector performance. Both ends of the MHP were sealed after the pipes were filled with prescribed amount of refrigerant (acetone) under vacuum condition for higher heat transport and performance. The main components of the MHP-PV/T are shown in Figs. 1 and 2 show the novel MHP-PV/T configuration enclosed in an insulated frame. The MHP characterized by a high heat transfer performance was insulated and enclosed in an aluminium frame to reduce thermal losses. These unique aluminium flat tube micro-channel heat pipes contain many independent micro-channels and micro-fins to enhance the heat transfer. When solar radiation hits the glass surface of the MHP-PV/T as shown in Fig. 3, part of the solar radiation is converted into electrical energy by the c-Si solar cells. The dissipating heat that normally increases solar cells temperature is then conducted away by the heat pipes placed at the back of the photovoltaic modules to the heat sink to produce hot water. Inside the heat pipes, a heat driven two-phase thermodynamic cycle takes place. The refrigerant vapor quickly spreads to the other end (condenser side) of the heat pipe using pressure generated by the temperature difference. At that opposite end, the refrigerant in the gaseous state gives up its latent heat which is rejected to the water, the heat sink. The refrigerant then changes back to the liquid state on top of the micro fins and in the micro grooves after losing heat to the heat sink. The structure of the MHP passively pumps the fluid back to the evaporator using capillary force. The MHP operates continuously and passively as it takes way heat from the c-Si photovoltaic cells and supplies that heat to the circulating inlet water and produce hot water for domestic consumption in addition to the electricity produced.

ρg Cg δg

∂2Tg ∂2Tg ⎞ = λ g δg ⎛⎜ 2 + ⎟ + h g ,pv (Tpv−Tg ) + h a (Ta−Tg ) ∂y 2 ⎠ ∂t ⎝ ∂x + he,g (Tsky−Tg ) + GT αg

∂Tg

Tsky is given by Swinbank [25,33]; as Tsky =

(1)

0.0552Ta1.5 .

hr ,g a = σεg (Tg2 + Ta2)(Tg + Ta) and ha = 2.8 + 3.0 × ua The heat transfers between the glass and photovoltaic cells consist of radiation and convection. The combined heat transfer coefficient can be expressed as; 2 2 2 2 ⎛ ξ × σ (Tpv + Tg )(Tpv + Tg ) ⎞ ⎛ (1−ξ ) × σ (Tpv + Tg )(Tpv + Tg ) ⎞ +⎜ hg,pv = ⎜ ⎟ ⎟ 1/ εpv + (1/ εg−1) 1/ εblack + (1−ξ )(1/ εg−1) ⎠ ⎝ ⎠ ⎝ Nu × λa + (2) H

where ξ = APV / APV / T . Nusselt number, Nu, for tilt angles ranging from 0° to 75° as presented in Hollands et al. [24] as a function of the Raleigh (Ra) number as follows:

Nu = 1 + 1.44 ⎛⎜1− ⎝

1708(sin(1.8ϕ)1.6 ⎞ ⎛ 1708 ⎞ ⎛ ⎛ Racosϕ ⎞(1/3) ⎞ ⎟ ⎜1− ⎟ + ⎜ −1⎟ Racosϕ Ra cosϕ ⎠ ⎝ ⎝ 5830 ⎠ ⎠⎝ ⎠ (3)

g × γ × (Tpv−TG ) × H 3 ⎞ Ra = ⎜⎛ ⎟ (α × TD ) ⎠ ⎝

(4)

• The heat-balance equation of photovoltaic cells can be summarized as follows:

ρpv Cpv δpv

3. Theory and mathematical model This paper developed a detailed simulation model for the MHP-PV/ T system. The model is based on the following major assumptions: (i) All thermo-physical properties of the MHP-PV/T remain constant. (ii) Temperature stratification of the water in the collector is negligible. (iii) The operation status of a heat pipe in the collector is transient conditions. (iv) The micro-channel heat pipe refrigerant flow is unsteady, laminar, two-dimensional, axisymmetric, incompressible flow with negligible body forces and has a uniform velocity across the wicks in the z axis direction. (v) The micro fins and grooves material is of constant thickness, saturated with wetting refrigerant (Acetone) and uniform in performance. (vi) The effects of gravity are neglected and the temperature of the working fluid is a function of the two dimensional axes [25–32].

∂2Tpv ⎞ ∂2Tpv = λpv δpv ⎛⎜ + ⎟ + h pv,g (TG−Tpv ) + h pv,b (Tb−Tpv ) 2 ∂y 2 ⎠ ∂t ⎝ ∂x −Qin + (τg αpv GT )−ξEpv (5)

∂Tpv

1 . hpv,b − 1 (δ / λ )

The overall resistance of the back material, Rpv,b =

R−1

Also, Upv,b

= can be a function of thermal resistance, U = . Epv is expressed as Epv = GT τg [1−Br (Tpv−Tref )], where Br = 0.0045 K−1 and Tref = 25 °C.

• The heat conduction of cell back layer sandwiched material can be summarized as follows:

ρb Cb

∂Tb ∂ 2T ∂2Tb ⎞ = λb ⎛ 2b + + hpv,b (Tb−Tpv ) + UMHP (Tevap−Tcond ) ∂t ∂ ∂y 2 ⎠ x ⎝

The UMHP =

• The heat-balance equation of the glass cover can be summarized as

⎜

⎟

thermal conductance of Q +Q −Q with = waterT −lossT trans

QMHP ΔTMHP

evap

cond

MHP is Q = f (U )

given and

(6) as; U=

f (Tamb,Twater ,Tcond ) . By decreasing the temperature difference between the evaporator and condenser ΔT, the amount of heat transferred QMHP increases, which can reach the heat transfer limitation of the MHP [32]. The governing equation for aluminium micro-channel heat pipes in the PV/T is transient [33]. The transient phenomena occurring within

follows [25,29]:

Fig. 1. The main materials used to build the MHP-PV/T.

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Fig. 2. MHP-PV/T diagram.

Fig. 3. Detail views of MHP-PV/T.

a region containing no source of heat, the Eq. (7) reduces the term ∂T (ρCMHP )s ∂t = 0 and q = 0 (Laplace’s equation) [33,36–39]. The boundary conditions which can be applied are as follows:

the heat pipe of the PV/T is divided into the following basic categories: (a) Heat conduction modeling: This considerers conduction as the sole transport mechanism. (b) Hydrodynamic or liquid and vapor flow modeling: The analytical models are derived based on the principle of conservation of energy, mass, and momentum in the axial direction [33]. Governing equation for heat conduction of wide micro-channel heat pipes [34–36]:

(a) Evaporator section

∂T 1 = × qe ∂n λ

•

(8)

(b) Adiabatic section

∂T ∂ ⎛ ∂T ⎞ ∂ ⎛ ∂T ⎞ = + + q (y,z ,t ) ρCMHP λMHP λMHP ∂t ∂y ⎝ ∂y ⎠ ∂z ⎝ ∂z ⎠ ⎜

∂T =0 ∂n

⎟

(7)

This model involves diffusion, decay and is parabolic in nature. In a steady-state mode, where the temperature is not changing with time in

(c) Condenser section (convection) 711

(9)

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∂T 1 = × hc × (Te,MHP−Tw ) ∂n λ (d) Condenser section (radiation)

∂T 1 = −⎛ × σ × ε × (Te4,MHP )⎞ ∂n ⎝λ ⎠

(11)

Tw = δl (qin / λ eff ) + Tsat

Rwf

δw = (λl × wf × d z )

(13)

δw = (λ w × 2wg × d z )

(14)

δw (λ w × 2wg × d z )

(15)

•

ρ × Vl × Tsat × Cl ⎞ ⎛ ρv × Vv × Tsat × Cv ⎞ × δl Tw−Tes = ⎜⎛ l ⎟ × δl = ⎜ ⎟ λ eff λ eff ⎝ ⎠ ⎝ ⎠

(12)

Qu = ṁ water × Cwater × (Tout −Tin)

(27)

(28)

The useful energy gain of the MHP could also be obtained as;

Qu = Ac × FR [GT (ατ )e−UL (Tin−Ta)]

(29)

(16)

The performance of the PV/T system is usually described by a series of efficiency terms. The basic ones of them are the thermal efficiency ηth and the electrical efficiency, ηpv which describe the performance of PV/ T system in the aspects of thermal energy and electrical energy gain respectively. Some researchers describe the performance of PV/T system as total efficiency ηtotal which sums the thermal efficiency and electrical efficiency;

(17)

ηtotal = ηth + ζηpv

(30)

In consideration of the fact that electrical energy is high-grade energy, the definition of overall efficiency is unfair for PV/T collectors. Energy saving efficiency is more appropriate to evaluate the performance of PV/T collectors, expressed as [50]:

Governing equations for hydrodynamics heat transfer of the microchannel heat pipes:

The refrigerant contained in the grooves undergo a phase transformation to transmit heat to the heat sink [35,44]. The liquid-vapor interface of the heat pipe is illustrated in Fig. 5. Heat-balance equation at the control volume interface can be written using thermodynamics principles as;

qin = qL + qconv + qcond

(26)

The elements of useful energy, Qu gain by the system can be calculated using Fig. 6 as;

RRT

Rtrans = Rwf + Rwg + Rref + RTF + Rf

(25)

Eqs. (24) and (26) can be reshaped to determine maximum temperature difference as,

hf 2wg

δw (λ w × 2wf × d z )

(24)

where Tl is the fins and clapboard fluid/vapor temperature of the MHP.

( ) ⎞⎠ ⎤⎥⎦

⎡0.185tanh ⎛5.4 ⎢ ⎝ = ⎣ λl d z

Rf =

Tevap ≅ Tes = (qin−(ρl × Vl × Cl × Tsat )/ λ eff ) × δl + Tsat

qin = −λ eff (∂Tl / ∂n)

(e) The axial resistance of the heat pipe can be approximated by adopting the techniques used by Zohuri and Supowit [33,35] as; Raxial = dz / λA . (f) The transverse resistance of the heat pipe is approximated referencing Peterson [40] and Chi et al. [41] using the illustration in Fig. 4 [42].

Rref =

(23)

Tes can be used to predict the wall temperature, Tw using previous models the expressions. For only heat conduction in fins and clapboards;

The relationship between resistance and the heat input can be denoted as; ΔT = QRtotal as Rtotal = Rtrans + Raxial .

Rwg

qcond = qin−ρl × Vl × Tsat × Cl = λ eff (Tes−Tsat / δl ) (10)

ηf = ηth + ζ (ηpv / ηpower )

(31)

ηpower , the conversion factor from thermal energy to electrical energy of the thermal power plant, its value can be taken as 38%. For natural

(18)

Convective heat flux due to vapor velocity at the liquid-vapor interface, qconv given as;

qconv = m v × Cl × Tsat = ρv × Vv × Cl × Tsat

(19)

Notably, Vv = m v / ρv ; where Vv > 0 (evaporation), Vv < 0 (condensation), and Vv = 0 (adiabatic). The heat flux due to heat conduction into the vapor qcond is represented as;

qcond = −λ v (∂Tv / ∂n)

(20)

Again, in Fig. 5, qL represents the latent heat due to phase change from liquid to vapor, or vice versa leaving the fluid together with qconv and qcond [31,36,32,45].

qL = m v × Llv = ρv × Vv × Llv

(21)

Neglecting the kinetic energy since the velocity Vv at the interface comparatively is small, qL turns to zero and the expression for qin becomes;

qin = qcond + qconv ≡ qin = −λ eff (∂Tl / ∂n) + ρl × Vl × Cl × Tsat

(22)

For steady-state operation for MHP grooves filled with refrigerant, we have;

Fig. 4. Schematic diagram of transversal resistances at the groove of the MHP.

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Fig. 5. Wide MHP vapor-liquid energy conservation control volume.

circulation in PV/T, the heat and electric energy are stored in the water tank and battery respectively. Thus the daily thermal and electrical efficiency can be written as:

ηth =

ṁ water × Cwater × (Tout −Tin) GT APV / T

(32)

ηpv =

∑ (VI Δt ) GT × APV

(33)

Table 1 Experiment instruments models and accuracy.

The overall uncertainty of the study was determined using the Eq. (34) [47]. The experimental testing accuracy of the parameters is listed in Table 1.

2

2

⎛ ∂η ΔGT ⎞ + ⎛ ∂η Δṁ water ⎞ + ⎛ ∂η ΔTout ⎞ + ⎛ ∂η ΔTin ⎞ ⎝ ∂GT ⎠ ⎝ ∂Tout ⎠ ⎝ ∂Tin ⎠ ⎝ ∂ṁ water ⎠ (34)

⎜

⎟

⎜

⎟

⎜

⎟

⎜

1 n

Type

Ambient air temp Pyranometer Anemometer Flow meter Heat pipe temp Inlet & outlet temp

1 1 1 1 3 2

± 0.2 °C ± 2% 0.2 m/s ± 3% ± 0.2 °C ± 0.1 °C

−200 to +350 °C 0–2000 W/m2 0–30 m/s 0.03–3 m3/h −200 to +350 °C 0–100 °C

T-thermocouple TBQ-2 NRG # 40 C LXSR T-thermocouple Pt100

n

∑ t=1

M −P M

i=1

(Pi−Mi )

n

∑i =1 (Pi−Mi)2

(37)

The experimental study on MHP-PV/T was conducted under the actual meteorological conditions of Hefei (latitude 31°N; longitude 117°E), China and installed at a 45° tilt angle facing south. Pyranometer together with the anemometer was mounted beside the PV/T as shown in the actual experimental photograph of the MHP-PV/T system test rig in Fig. 7. The solar irradiation was measured using a pyranometer to give both the global and the diffuse intensity. Temperatures and wind speed were measured using thermocouple sensors and anemometer respectively. A flow meter was also used to measure the water mass flow rate from and to the water tank. The inlet and outlet temperature and mass flow rate enabled us to calculate the useful energy gain using Eq. (28). All testing instruments used have been calibrated before the test and information about the instruments that were used in this study are presented in Table 1.

(35)

n

∑

1 n

4. Experimental setup

The average deviation or overestimation indicator of the predicted values from measured data can be calculated as follows:

MBE =

Full-scale

⎟

In order to evaluate the proposed models for this paper, three statistic errors are used, which are mean absolute percentage error (MAPE), mean bias error (MBE), and root mean square error (RMSE) [49]. The general accuracy of an algorithm can be highlighted by MAPE. MAPE can be defined as follows:

1 n

Accuracy

RMSE = 2

2

MAPE =

Number

predicted data around the experimentally measured data.

(Δη) overall =

Sensor

(36)

The short-term performance information of the model can be evaluated by RMSE. It represents the measurement of the variation of the

Fig. 6. Discretized partition of the condenser section water box.

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Fig. 7. Photo of the experimental setup.

Test performance was conducted following Chinese standard GB/ T4271-2007 [48]. A day-long experiment was carried out from 8:30 a.m. to 6:30 p.m. Values were recorded at 10 minutes’ intervals. The experiments covered different days of December. A schematic diagram of the experimental setup is also presented in Fig. 8 showing additional thermocouple sensors fixed along the MHP to measure the temperature at the evaporator, adiabatic and condenser sections (see dimension characteristics of MHP-PV/T in Table 2). The experimental test rig of the MHP-PV/T system (Fig. 8 refers) generates electricity from the c-Si photovoltaic module with rated power of 91.53 W, a rated short circuit current of 7.6 A and an open circuit voltage of 15.78 V. The current and voltage outputs from the system are measured and recorded by the computer based data logger systems. The solar module is wired directly into a charge controller to control its output and charge the battery bank. The output from the battery is fed to a load of lamps as demand (Fig. 7 refers). Simultaneously, heat in the form of hot water is measured using Pt100 thermocouples. The average values from the experiment were used to analyze the MHP-PV/T system numerically. The instantaneous

Table 2 Characteristics of micro - channel aluminium heat pipe (MHP) and MHP-PV/T. Length of PV/T Width of PV/T Thickness of PV/T Length of MHP Width of MHP Thickness of MHP Air gap Insulation layer thickness Photovoltaic thickness PV back metal contact thickness Thermal conductivity

100 cm 72 cm 9 cm 93 cm 6 cm 0.4 cm 3 cm 5 cm 0.1 cm 0.4 cm 170 W/mK

1000 mm 720 mm 90 mm 930 mm 60 mm 4 mm 30 mm 50 mm 1 mm 4 mm 170 W/m °C

boundary conditions, such as solar radiation, ambient temperature, and mass flow rate of circulating water are directly reported from experimental data for testing and modeling of the system. The inlet temperature of the collectors is set to be equal to the outlet temperature of the storage tank, and the inlet temperature of the storage tank is set to be equal to the outlet temperature of the collectors. Based on these Fig. 8. Schematic diagram of the MHP-PV/T system test rig.

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in the predicted data from the measured data. The transient response solution of the wide micro channel heat pipe’s wall temperature within the PV/T system to a pulsed heat input is presented by slicing through evaporator and condenser section at the bottom, center, and top as shown in Figs. 14 and 15. The transient response changes with time and the models have been implemented using boundary conditions, and initial values of heat pipes top contact material temperature and saturated refrigerant temperature of 18.5 °C and 56.5 °C respectively.

data, the derived equations can be calculated by iterative computations. The ambient temperature and the solar radiation data obtained from the experiment measurement are shown in Fig. 9. 5. Results and discussions The flow chart of the solution procedure for estimating the temperature profile of MHP-PV/T components is shown in Fig. 10. The transient temperature and heat variations along the micro-channel heat pipe walls and other components of the MHP-PV/T were captured using MATLAB. The behavior of the system was simulated using a developed algorithm with high precision after the physical domain of the MHPPV/T was discretized into grid points. Unequal grids in the y and z axis directions were utilized, consistent with the physical dimensions for the discretization of the equation and numerical simulation. Finite difference method is also applied to discretize the above energy equations by time and space. The initial boundary conditions, picked from experimental data, include the average back temperature of the PV cells (18.5 °C), and saturated temperature of refrigerant (56.5 °C), the inlet water temperature (20 °C). The evaporator, adiabatic and condenser temperature are 48.8 °C, 20.4 °C, and 19.1 °C respectively. The model average temperature data for the heat pipe resulting from the thermal resistance was compared to experimental data for validation as shown in Figs. 11 and 12. Fig. 11 presents condenser section temperatures of the wide microchannel heat pipe in the MHP-PV/T. Compared with the evaporator section in Fig. 12, both heat pipe sections showed very similar patterns of fluctuation in temperatures. The evaporator section, frequently, has higher temperature value than the condenser section that serves as heat sink for the system. The results indicated that the temperature difference between the evaporator and condenser sections of the heat pipe was at a maximum of 3 °C in the morning and decreased gradually in the afternoon, and then increase in the evening as shown in Fig. 13. A pattern that is similar to the solar radiation intensity of the outdoor condition. It can, therefore, be agreed that the results indicate a good thermal conductance in performance for the micro-channel heat pipes. The results show the efficiency of the developed model for the prediction of the system compared to the experimental data. The proposed models were evaluated and presented in Table 3. A negative MBE value indicates the amount of underestimation in the predicted values and vice versa. RMSE indicates the level of deviation

A. Evaporator bottom, center, and top slice transient hourly temperature (°C) distribution. B. Condenser bottom, center and top slice transient hourly temperature (°C) distribution. The outer wall boundary conditions of MHP include a specific heat capacity of 903 J/(kg K); specific heat capacity of the fluid, Cl = 898 J/ (kg K); vapor density, ρv = 0.00461 kg/m3; vapor velocity, Vv = 1 m/s; and saturated temperature of refrigerant, Tsat = 56.5 °C. The predicted temperature differences between the groove of thickness, δl = 1 mm and wall interface are presented in Table 4. Remarkably, the temperature difference is very small [36]. Since the maximum temperature difference is small and negligible, it can be agreed that the vapor transient periods are very short. Referencing Cao and Faghri’s work, that period of vapor flow dynamics is only about 0.001–0.01 s [36]. This is one of the reasons why many studies found conduction model to be more appropriate to describe heat transfer in the walls and wick for the heat pipes [37]. As such, conduction in the fluid or vapor is neglected for this study [46]. The Finite Difference (FD) Method computational scheme was also used to approximate the unknown transient temperature profile along the z and y axis of the MHP as shown in Figs. 16–18. This was done using the approximation to the two dimensional (2-D) Laplace Operators after discretizing the dimensions of the heat pipe. The FD approximation is equalized to a linearized function ( f jk ) which is a linear combination of 5 different values of ujk at 5 grid points in the y and z axis direction. The average experimental data was used initial boundary conditions ujk at the evaporator, adiabatic and condenser section of the heat pipe. The total number of equations and unknowns solved was (nj − 1)(nk − 1) for j = n y and for k = nz . These unknowns were solved using ujk = (A) ⧹ (f jk ) where A is a nj by nk or (nj × nk ) matrix [43]. The rate of heat transfers of the MHP material from the evaporator Fig. 9. Solar radiation intensity and ambient temperature.

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Fig. 10. Numerical algorithm flow diagram.

Measured Condenser Temperature (Experiment) Simulated Condenser Temperature (Simulation) Ambient Temperature

70 Temperature in Degree Celcius

Temperature in Degree Celcius

70 60

40 30 20 10 0 8:30 9:30 10:30 11:30 12:30 13:30 14:30 Time (h)

Measured Evaporator Temperature (Experiment) Simulated Evaporator Temperature (Simulation) Ambient Temperature

60

40 30 20 10 0 8:30 9:30 10:30 11:30 12:30 13:30 14:30 Time (h)

16:30 17:30 18:30

16:30 17:30 18:30

Fig. 12. Comparison of evaporator temperature of the heat pipe.

Fig. 11. Comparison of condenser temperature of the heat pipe.

heat pipes hence the overall performance of the MHP-PV/T gets more efficient. Fig. 18 shows a faster transient thermal response of the heat pipe to heat input with thermal diffusivity of 0.5 cm2/s within the temperature range of 48.8–49.2 °C compared to lower thermal diffusivities of 0.3 cm2/s, 0.1 cm2/s, and 0.05 cm2/s shown in Figs. 19, 20 and 21 respectively. When the MHP is set to a thermal diffusivity of 0.05 cm2/s, there is a greater sensitive delay in the rate of heat transfers or heat flow (inflated shape at the input as shown in Fig. 21). Materials with higher thermal diffusivity noted as α = λ/(ρ × Cp);

(right) to the condenser (left) side presented in Figs. 18–21 refers). The base parameter of the MHP was varied as well. The physical thermal diffusivity properties of the MHP is 0.5 cm2/s. This parameter was varied while considering an outer wall boundary condition of the heat pipes at the condenser as a convective boundary (Figs. 18–21 refers). As graphically presented, the higher the thermal diffusivity of the heat pipe, the better the thermal performance of the 716

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Measured Evaporator Temperature (Experiment) Simulated Evaporator Temperature (Simulation) Simulated Condenser Temperature (Simulation) Measured Condenser Temperature (Experiment) Measured Temperature difference

Temperature in Degree Celcius

70 60 50 40 30 20 10 0

8:30 9:30 10:30 11:30 12:30 13:30 14:30 15:30 16:30 17:30 18:30 -10

Time in hour

Fig. 13. Comparison of experimental and simulated results of the heat pipe.

Table 3 Evaluation statistics for the all the MHP models. MHP section

MAPE (%)

MBE (%)

RMSE (%)

Evaporator Condenser

3.5262 0.6102

−3.6550 0.6065

3.6550 0.6065

Fig. 15. Transient response of heat pipe at the condenser section.

Table 4 The calculated temperature difference between the groove and wall of MHP.

λ eff (W/mK)

Tsat (°C)

Tw−Te (°C)

30 35 40 45

56.5 56.5 56.5 56.5

0.031964 0.027398 0.023970 0.021309

such as silver material is better diffuser of thermal energy and achieve faster thermal equilibrium than the current aluminium material used to design the micro-channel heat pipe. In other words, aluminium has lower thermal diffusivity. Hence future studies can be done using silver micro-channel heat pipes to boost the performance of the MHP-PV/T. The model data were also used to illustrate the temperature profile of the photovoltaic cells and the temperature profile of the back layer sandwiched between the cells and the heat pipes (Figs. 22 and 23 refer). The c-Si photovoltaic cells are discretized into 6 by 19 nodes (7 by 20 nodes for the cells back contact metal and sandwich materials). Temperatures profile of the photovoltaic cell and base material gradually reduced with a temperature difference of about 3 °C. Obviously, the condenser section of each graph is represented by a lower temperature than the evaporator section and follows almost a similar pattern. The electrical power output of the MHP-PV/T is shown in Fig. 24. The electrical gains had very similar variation patterns based on solar radiation-intensity results. The electrical gain increased from 17 to 74 W, when the solar radiation intensity increased from 0.05 to 883 W/ m2 in the morning and decreased to 21 W in the late afternoon. The simulated results for the heat sink, water outlet temperature of the PV/T were also compared to the experimental water outlet

Fig. 14. Transient response of heat pipe at the evaporator section.

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Fig. 16. Temperature distributions along the wide micro-channel heat pipe wall.

Fig. 17. Temperature profile across the width sections of MHP.

Fig. 18. Temperature flow along heat pipe with thermal diffusivity of 0.5 cm2/s.

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Fig. 19. Temperature flow along heat pipe with thermal diffusivity of 0.3 cm2/s.

Fig. 20. Temperature flow along heat pipe with thermal diffusivity of 0.1 cm2/s.

The experimental value for FR UL is 1.45011 and FR (τα )e is 0.5398 (intercept of the line). The maximum thermal efficiency obtained from the MHP-PV/T is 54.0% as shown in Fig. 26. Comparing the thermal efficiency of 54.0% and electrical efficiency of 7.6% of the novel MHPPV/T to previous studies carried out on other PV/T configuration by researchers in Table 6, we realized that the MHP-PV/T has a better thermal performance.

temperature data as shown in Fig. 25. The outlet temperature of the novel MHP-PV/T is seen rise steadily from 24.6 to 30.1 °C from morning till noon in a similar pattern with the solar intensity. Due to the variation of the solar radiation, the temperature at the outlet exhibited an upward and fluctuating trend with an increased in the morning and gradually decreased in the afternoon. Both the water outlet temperatures drop for the rest of the afternoon slightly after 12:30 pm. It can be seen that the agreement results between the experimental data and the numerical solutions are generally good with sufficient confidence. The evaluation of the simulation results using root mean square error was found varying between 0.6065% and 3.6550%. The experimental data (Table 5 refers) presents the instantaneous efficiency curves for the study shown in Fig. 26 using an average mass flow rate of 0.055 kg/s. The results indicated that the daily thermal and electrical efficiencies were 50.7% and 7.6%, respectively. The linear relation between the thermal efficiency ηth and (Tout −Tin ) GT−1 is also achieved as;

ηth = 0.5398−1.45011((Tout −Tin)/ GT )

6. Conclusions A novel PV/T is introduced in this paper. The dynamic performance of the PV/T is simulated and tested experimentally. The results are summarized as follows: (a) The numerical results of the MHP and the PV/T systems agreed well with the corresponding experimental data with sufficient confidence. The numerical model and computer program properly predicted the transient behavior of the novel MHP-PV/T. (b) The maximum instantaneous thermal and electricity efficiency is

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Fig. 21. Temperature flow along heat pipe with thermal diffusivity of 0.05 cm2/s.

Fig. 22. The photovoltaic temperature profile of the PV/T.

Fig. 23. Cells back contact metal and sandwich materials temperature profile.

wall and wet groove of the micro-channel heat pipes is small with a periodic vapor flow dynamics of about 0.001–0.01 s. Since the vapor transient periods of the refrigerant were very short, conduction model calculation was more appropriate for describing heat

found to be 54.0% and 7.6% respectively. The electrical gain of the MHP-PV/T increased from 17 W to 74 W under a radiation intensity of 367–787 W/m2. (c) The hydrodynamic temperature difference estimated between the 720

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Fig. 24. Electrical power of MHP-PV/T and solar radiation against time.

Fig. 25. Comparison of simulated and experimental outlet water temperature.

Fig. 26. Instantaneous thermal efficiency curve of the MHP-PVT.

Table 5 Daily experimental results in MHP-PV/T.

Table 6 Comparing the novel MHP-PV/T systems to other PV/T studies.

No.

GT (W/m2)

Q u (W/m2)

Epv (W/m2)

ηth (%)

ηPV (%)

η0 (%)

Year

PV/T

Thermal (%)

Electrical (%)

Authors

Reference

1 2 3 4 5

366.69 628.27 784.34 822.22 786.72

155.43 268.75 336.23 357.54 428.32

39.15 38.25 37.33 36.39 36.18

47.09 47.53 48.32 55.63 55.12

13.34 7.61 5.94 5.53 5.70

60.44 55.14 53.57 53.85 60.92

2001 2007 2007 2009 2009 2011 2014 2015

ST + RT ST + SRT PV/T-SAHP SL ST + SRT RTHP-PV/T ALCPC-PV/T ST + SRT

38.9 45.0 50.0 34.8 40.0 41.9 52.0 35.0

9.0 10.0 12.0 11.9 6.0 9.4 6.6 6.7

Huang et al. Ji Jie et al. Ji Jie et al. Ibrahim et al. He et al. Pei et al. Ji Jie et al. Ji Jie et al.

[12] [51] [54] [52] [53] [55] [56] [57]

transfer of MHP. (d) Heat transfer limitations parametric solutions have shown that by increasing thermal diffusivity of the heat pipes, a faster thermal equilibrium can be achieved quickly and also the transient thermal response of the MHP to input heat become faster. Hence the overall performance of the systems can be increased significantly.

SL = Steel; ST = Sheet and tube; SRT = Single/rectangular tube; MHP = Micro-channel heat pipe. ALCPC = Air-gap-lens-walled compound parabolic concentrator; RTHP = Round tube heat pipe.

Science & Technology Pillar Program during the Twelfth Five-Year Plan Period (No. 2015BAA02B03) and Dong Guan Innovative Research Team Program (No. 2014607101008).

Acknowledgements This work was supported by the National Natural Science Foundation of China (No. 51378483), Projects in the National 721

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Appendix A. Supplementary material [27]

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.apenergy.2017.08.221.

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