Photovoltaic-thermal system combined with wavy tubes, twisted tape inserts and a novel coolant fluid: energy and exergy analysis

Abstract

To create a highly efficient photovoltaic-thermal (PV-T) system and maximise the energy and exergy efficiency, this study aims to propose an innovative configuration of a PV-T system comprising wavy tubes with twisted-tape inserts. Following the validation of a numerical model, a parametric study has been conducted to assess the geometrical effects of twisted tape and wavy tubes, as well as the coolant fluid type and velocity, on the overall performance of a PV-T system, located in Shiraz, Iran. It is found that employing twisted tape improves the energy and exergy efficiency by approx. 6.3%. The best configuration yields 12.4% and 16.8% increase in energy and exergy efficiency compared to conventional PV systems. This is achieved at 15% volumetric concentration of microencapsulated phase change material slurry. The monthly variation of global horizontal irradiance in Shiraz highly affected the energy and exergy efficiency of PV-T, with July and October exhibiting the most efficient months, corresponding to 90% and 11.3%, respectively.

Highlights

• Energy and exergy of photovoltaic-thermal system with twisted tape and wavy tubes.

• Reduction in the temperature of the PV panel by 8.3°C compared to the base case.

• 12.4% and 16.8% increase in energy and exergy efficiency in the optimum configuration.

• Higher energy and exergy efficiency from microencapsulated phase change material.

KEYWORDS:

• PV-T solar collector
• CFD
• energetic and exergetic efficiency
• twisted tape insert
• microencapsulated phase change material
• wavy tubes

Nomenclature

A	=	Area $\left({\text{m}}^{\text{2}}\right)$
c	=	Volumetric concentration
$C_p$	=	Specific heat $\left(\text{J/kg}\text{.K}\right)$
Ex	=	Exergy (w)
$G_k$	=	Generation of kinetic
g	=	Gravity $\left(\text{m/}{\text{s}}^{\text{2}}\right)$
h	=	Heat transfer coefficient $(\text{W}/{\text{m}}^{\text{2}}\cdot \text{K})$
H	=	Daily irradiation $\left(\text{MJ}/{\text{m}}^{\text{2}}\right)$
$H_t$	=	Twisted tape height (m)
I	=	Hourly irradiation $\left(\text{MJ}/{\text{m}}^{\text{2}}\right)$
$K_T$	=	Daily clearness index
$\overline{K_T}$	=	Monthly daily clearness index
K	=	Turbulent kinetic energy (J/kg)
k	=	Thermal conductivity ($\text{W}/\text{m}\cdot \text{K}$)
$K_B$	=	Boltzmann constant
$L_t$	=	180° twisted pitch (m)
$\dot{m}$	=	Mass flow rate (kg/s)
P	=	Packing factor/pressure (pa)
q	=	Heat flux $\left(\text{W}/{\text{m}}^{\text{2}}\right)$
R	=	Ratio of total radiation on a tilted plane to the horizontal plane
$\overline{R}$	=	Monthly average of R
$R_b$	=	Ratio of beam radiation on a tilted plane to the horizontal plane
$R_d$	=	Ratio of diffuse radiation on a tilted plane to the horizontal plane
r	=	radius $\left(\text{m}\right)$
$r_d$	=	Ratio of diffuse radiation in an hour to diffuse in a day
$r_t$	=	Ratio of total radiation in an hour to total in a day
$Q_s$	=	Solar radiation intensity ($\text{W}/{\text{m}}^{\text{2}}$)
T	=	temperature $\left(\text{K}\right)$
$u_i$	=	Velocity component (m/s)
V	=	volume$\text{(}{\text{m}}^{\text{3}}\text{)}$
$\overrightarrow{V}$	=	Velocity vector $\left(\text{m}/\text{s}\right)$
$W_t$	=	Width of the twisted tape (mm)
$Y_m$	=	Fluctuation dilation

Greek

$\alpha$	=	absorptivity
$\text{β}$	=	Temperature coefficient $\left(1/\text{K}\right)$ /slope
$\delta$	=	Kronecker delta/declination
$ϵ$	=	Emissivity/turbulent dissipation (W/kg)
$\gamma$	=	Surface azimuth angle
${\gamma }_s$	=	Solar azimuth angle
$\eta$	=	Efficiency
$\varphi$	=	Volume fraction/latitude
$\mu$	=	viscosity$(\text{pa}\cdot \text{s})$
$\rho$	=	Density $\text{kg}/{\text{m}}^{\text{3}}$ / reflectance
$\omega$	=	Hour angle
${\omega }_s$	=	Sunset hour angle
${\sigma }_{sb}$	=	Stefan Boltzmann constant $\left(\text{W/}{\text{m}}^{\text{2}}{\text{K}}^{\text{4}}\right)$

Superscripts

$-$	=	Mean value
$\mathrm{\prime }$	=	Random fluctuation

Subscripts

a	=	Ambient
AP	=	Absorber plate
b	=	Beam
c	=	Convection
d	=	Diffuse
e	=	Electrical
ex	=	Exergy
f	=	Carrier fluid
fr	=	Friction
in	=	Tube inlet
l	=	liquid
m	=	Mean thermodynamic/melting
MP	=	Micro-encapsulated PCM
MPS	=	Micro-encapsulated PCM slurry
nf	=	Nanofluid
np	=	Nanoparticle
out	=	Tube outlet
p	=	particle
PV	=	Photovoltaic panel
ref	=	Reference
s	=	solid
th	=	thermal
tu	=	Turbulent

Abbreviation

HTF	=	Heat transfer fluid
MPCM	=	Micro-encapsulated PCM
PCM	=	Phase change material
PEC	=	Performance Evaluation Criteria
PV-T	=	Photovoltaic/thermal
UDF	=	User Define Function

1. Introduction

A key challenge associated with using photovoltaic (PV) modules to produce electricity is an increased panel temperature, leading to reduced electrical efficiency (Essam et al., 2022). To overcome this challenge, heat transfer fluid (HTF) is used underneath the PV panel to cool it down. The heated fluid can then be utilised for thermal applications (Huang et al., 2020). These photovoltaic-thermal (PV-T) systems are cutting-edge renewable-powered technology that combines the power of PV cells and thermal collectors in one integrated system (Li et al., 2022). PV-T systems have gained increasing attention in recent years as an efficient and cost-effective way to meet energy demands while reducing greenhouse gas emissions. They can be utilised in a wide range of applications such as space heating, water heating, building, and industrial process heat.

The geometrical configuration of the PV-T system is crucial for achieving higher efficiency (Kim & Tae, 2022). Researchers have evaluated various configurations to improve the performance of PV-T systems. Shahsavar et al. (2020) experimentally investigated a PV-T system equipped with cooling tubes with different shapes. They found that electrical efficiency was increased by 12% by adding a coolant tube. Moreover, the use of nanoparticles enhanced the exergy and energy efficiencies by 7% and 6.6%, respectively. Tomar et al. (2019) employed glass-to-glass PV modules in the PV-T system and found a maximum hourly-averaged electrical efficiency of ∼13%. In another study, Hossain et al. (2019) focused on the use of serpentine pipe PV-T collector design. The results indicated a 5.34% increase in electrical efficiency with 3.92°C reduction in the PV temperature. Employing polycrystalline and monocrystalline panels in PV-T systems, Özakin and Kaya (2019) achieved 55% and 70% increase in energy efficiency and a 70% and 30% increase in exergy efficiency compared to conventional PV-T systems, respectively.

Wavy tubes have shown great potential to improve the thermal performance compared to straight tubes. This is due to an increased heat exchange area and enhanced mixing, resulting in a more uniform temperature distribution and a greater net efficiency in the PV panel. Eisapour et al. (2020) numerically evaluated the use of wavy tubes in PV-T modules. In their best design, the energy and exergy efficiencies were increased by 6.1% and 4.3%, respectively. In another study by the same research group (Eisapour et al., 2021), the authors examined an innovative layout of wavy tubes with ascending and descending amplitudes. The authors enhanced electrical and thermal efficiencies from 10.94% and 61.04% in the case of a straight tube to 11.32% and 65.21%, respectively. The authors indicated that using SiC and micro-encapsulated phase change material (MPCM) (MPCM-28) as a working fluid instead of water improved the electrical efficiency by 0.4%.

The use of vortex generators to create swirling patterns and disrupt the formation of boundary layers has gained significant attention in recent years (Darbari et al., 2020; and Tian et al., 2020). Aridi et al. (2022) focused on the hydrothermal performance of a trapezoidal vortex generator in a concentric tube heat exchanger through numerical simulation. They improved the heat transfer ratios and thermal factor by 97% and 210%. Using a longitudinal vortex generator, Carpio and Valencia (2021) increased the thermal performance of the system by 52%. Arasteh et al. (2021) numerically analysed the hydrothermal performance of twisted rotational tape pitch distance inside a heat-exchanging tube. The results showed a higher performance evaluation criterion (PEC) at lower Reynolds in the case of rotating twisted tape. However, the maximum PEC was found at a Reynolds number of 1000 and a pitch distance of L/6 for a stationary twisted tape. Mashayekhi et al. (2021) corroborated the same finding of Arasteh et al. (2021) in terms of better enhancement in the thermal characteristics of rotating twisted tape at lower Reynolds numbers under the laminar regime, 32.8–39.6% increase in the Nusselt number at Reynolds number of 250.

The cooling fluid also plays a crucial role in the overall electrical performance of the PV-T system (Akbar et al., 2021; Moore & Wei, 2021). Menon et al. (2022) evaluatean unglazed PV-T system’s electrical and thermal performance using water and copper oxide-based nanofluid. They reduced the panel temperature by 15°C and 23.7°C and achieved an electrical efficiency of 14.6% and 17.6% when the system was cooled with water and nanofluid, respectively. Some researchers investigated the impact of using two nanoparticles (Ghalambaz et al., 2020a; Mehryan et al., 2020), composite nanoparticles (Ghalambaz et al., 2019; Ho et al., 2020), or non-Newtonian fluids (A. Saleem et al., 2020; S. Saleem et al., 2021) on the heat transfer enhancement of PV-T systems. In this regard, Abdallah et al. (2019) reduced the temperature of the PV panel by 12°C – resulting in a maximum system efficiency of 61% – using multi-wall carbon nanotube nanofluid. Fu et al. (2021) introduced a PV-T collector that utilises two types of coolant fluids: water and MPCM slurry. The use of MPCM slurry as a coolant fluid results in a more considerable decrease in the temperature of PV-T cells, leading to 13.5% and 0.8% increase in the maximum thermal efficiency and average electrical efficiency.

Reviewing the literature highlights that many efforts have been made to develop effective thermal management systems for high-performance PV-T systems. However, despite recent advances, further research and development are required to gain sufficient insight into the combined heat transfer enhancement techniques to boost the performance of PV-T systems. While the use of twisted tapes in other heat transfer applications are emerging in recent years (e.g. Ghalambaz et al., 2020b; Mashayekhi et al., 2020), the increase of convective heat transfer coefficients of PV-T systems still remains not fully understood. Therefore, to address this research gap, the present study aims to investigate the use of twisted tape inserts in wavy tubes to evaluate the performance of PV-T systems from an energy and exergy standpoint. The present work examines the effect of twisted tape/wavy tube geometrical parameters and different types of coolant fluid on the system performance. Unlike previous studies that only considered solar radiation intensity as a constant variable, this research employs an isotropic sky module to calculate location-specific solar radiation intensity for a tilted PV-T system, allowing for a more accurate monthly performance assessment of the proposed configuration.

2. Model description

This study investigates a PV-T system incorporating wavy cooling tubes equipped with twisted tape inserts. Figure 1 shows the proposed PV-T system together with the PV panel, the absorber plate, cooling tubes, and the boundary conditions. In the PV-T collector, the PV module is located on the upper surface, the absorber plate is in the middle, and the cooling tubes are placed at the bottom. As illustrated in Figure 1, the boundary condition of the upper surface is considered to be the incoming solar irradiance and heat losses through convection and radiation mechanisms.

Figure 1. Schematic view of the PV-T system, including the boundary conditions.

The schematic of the present module is shown in Figure 2. As seen in Figure 2(a), the PV system benefits from five wavy tubes under the panel for cooling purposes. All surfaces are considered insulated except the upper layer, which absorbs solar energy from the Sun. Due to the symmetrical condition, only 1/5 of the whole system is considered for the computational domain (Ekramian et al., 2014). The length of the absorber plate is 2000 mm, from which 1640 mm of the absorber plate is enclosed by the PV module (Eisapour et al., 2020). The absorber plate absorbs the solar thermal energy depending on the absorber’s solar radiation intensity and absorptivity.

Figure 2. Schematic view of the helical wavy tube PV-T system: (a) top view, (b) front view.

Figure 3 shows the characteristics of the proposed twisted tape inserts. In this figure, L_t is the pitch of the twisted tape, W_t is the width of the twisted tape, and H_t is the height. Table 1 presents the characteristics of various proposed cases considered in this research. Case 1 is the system with a straight tube, which is assumed to be the base case in this study. Cases 2 and 3 are the system with wavy tubes without twisted tape inserts. Adding twisted tapes to cases 1, 2, and 3 forms cases 4, 5, and 6, respectively.

Figure 3. Characteristics of twisted tape in tube: (a) isometric view, (b) front view.

Table 1. Characteristics of different cases considered in this research.

Cases	Diameter (mm)	Wavelength (mm)	Amplitude (mm)	Ht (mm)	Lt (mm)	Wt (mm)
1 (base case)	8	–	50	–	–	–
2	8	400	50	–	–	–
3	8	200	50	–	–	–
4	8	–	–	4.5	300	1
5	8	400	50	4.5	300	1
6	8	200	50	4.5	300	1

3. Governing equation

3.1. Assumptions

In order to make the PV-T numerical modelling more straightforward, the following hypotheses are applied:

• The fluids are incompressible.

• The problem is assumed to be steady-state.

• The flow regimes in cases 1–3 and cases 4–6 are laminar and turbulent, respectively. The latter is due to the presence of twisted tube inserts.

• The external surface of the cooling tube and the absorber plate is well insulated.

• Nanofluid and MPCM slurries are in thermal equilibrium and single-phase in the calculations (Demir et al., 2011).

• Convection and radiation heat losses are considered.

• No thermal resistance between the PV panel and absorber plate, leading to identical temperatures at the interface (Fontenault & Gutierrez-Miravete, 2012).

3.2. Laminar model

The continuity, momentum, and energy equations for a laminar flow are written as follows (Liaw et al., 2021): (1) $\begin{array}{rl}\mathrm{\nabla }\cdot \overrightarrow{V}& =0\end{array}$(1) (2) $\begin{array}{rl}\rho \left(\overrightarrow{V}.\mathrm{\nabla }{u}_i\right)& =-\frac{\mathrm{\partial }p}{\mathrm{\partial }{x}_i}+\mu \left({\mathrm{\nabla }}^2{u}_i\right)-\rho g_i\end{array}$(2) (3) $\begin{array}{rl}\rho C_p\left(\overrightarrow{V}.\mathrm{\nabla }T\right)& =k{\mathrm{\nabla }}^{2}T\end{array}$(3)

The energy equation for the solid part is given as follows: (4) $k{\mathrm{\nabla }}^{2}T=0$(4)

3.3. Turbulence model

Using twisted tape inserts inside the tube generates vortices, resulting in the transition from laminar to turbulent flow (Liaw et al., 2021). To accommodate this, the Realisable k-ϵ enhanced wall treatment model is used as below (Liaw et al., 2021): (5) $\begin{array}{rl}\frac{\mathrm{\partial }\left(\rho u_i\right)}{\mathrm{\partial }{x}_i}& =0\end{array}$(5) (6) $\begin{array}{rl}\frac{\mathrm{\partial }\left(\rho \overline{u_i}\overline{u_j}\right)}{\mathrm{\partial }{x}_j}& =-\frac{\mathrm{\partial }\overline{P}}{\mathrm{\partial }{x}_j}+\frac{\mathrm{\partial }}{\mathrm{\partial }{x}_j}({\mu }_{\text{eff}}\left(\frac{\mathrm{\partial }{\overline{u}}_i}{\mathrm{\partial }{x}_j}+\frac{\mathrm{\partial }\overline{u_j}}{\mathrm{\partial }{x}_i}\right)\\ & -\frac{2}{3}{\mu }_{eff}\frac{\mathrm{\partial }\overline{u_i}}{\mathrm{\partial }{x}_i}{\delta }_{ij}-\rho \overline{{u^{\mathrm{\prime }}}_i{u^{\mathrm{\prime }}}_j})\end{array}$(6) (7) $\begin{array}{rl}\frac{\mathrm{\partial }\left(\rho C_{\text{p}}\overline{T}\overline{u_j}\right)}{\mathrm{\partial }{x}_j}& =\frac{\mathrm{\partial }}{\mathrm{\partial }{x}_j}\left(k\frac{\mathrm{\partial }\overline{T}}{\mathrm{\partial }{x}_j}+\frac{{\mu }_t}{{\sigma }_{h,t}}\frac{\mathrm{\partial }\left(C_{\text{p}}\overline{T}\right)}{\mathrm{\partial }{x}_j}\right)\\ & +\overline{u_j}\frac{\mathrm{\partial }\overline{P}}{\mathrm{\partial }{x}_i}+\frac{\mathrm{\partial }{u}_i}{\mathrm{\partial }{x}_j}\left({\mu }_{\text{eff}}\left(\frac{\mathrm{\partial }{\overline{u}}_i}{\mathrm{\partial }{x}_j}+\frac{\mathrm{\partial }\overline{u_j}}{\mathrm{\partial }{x}_i}\right)\right)\\ & -\frac{2}{3}{\mu }_{\text{eff}}\frac{\mathrm{\partial }\overline{u_i}}{\mathrm{\partial }{x}_i}{\delta }_{ij}-\rho \overline{{u^{\mathrm{\prime }}}_i{u^{\mathrm{\prime }}}_j})\end{array}$(7) (8) $\begin{array}{rl}\rho \frac{DK}{Dt}& =\frac{\mathrm{\partial }}{\mathrm{\partial }{x}_i}\left[\left(\mu +\frac{{\mu }_{tu}}{{\sigma }_K}\right)\frac{\mathrm{\partial }K}{\mathrm{\partial }{x}_i}\right]\\ & +{\mu }_{tu}\frac{\mathrm{\partial }\overline{u_i}}{\mathrm{\partial }{x}_j}\\ & \left(\frac{\mathrm{\partial }\overline{u_i}}{\mathrm{\partial }{x}_j}+\frac{\mathrm{\partial }\overline{u_j}}{\mathrm{\partial }{x}_i}\right)\\ & +G_k+G_b-\rho ϵ-Y_M+S_k\end{array}$(8) (9) $\begin{array}{rl}\rho \frac{Dϵ}{Dt}& =\frac{\mathrm{\partial }}{\mathrm{\partial }{x}_i}\left[\left(\mu +\frac{{\mu }_{tu}}{{\sigma }_{ϵ}}\right)\frac{\mathrm{\partial }ϵ}{\mathrm{\partial }{x}_i}\right]+C_{ϵ1}\frac{ϵ}{K}\\ & \times \left[{\mu }_{tu}\left(\frac{\mathrm{\partial }\overline{u_i}}{\mathrm{\partial }{x}_j}+\frac{\mathrm{\partial }\overline{u_j}}{\mathrm{\partial }{x}_i}\right)\frac{\mathrm{\partial }\overline{u_i}}{\mathrm{\partial }{x}_j}+C_{3}G\right]\\ & -C_{ϵ2}\rho \frac{{ϵ}^2}{K}\end{array}$(9) where k is the turbulent kinetic energy, ϵ is the turbulence dissipation rate, G_k is the kinetic enhancement due to buoyancy, Y_M is the fluctuation dilation in the compressible turbulence regime, and S_k is a source term specified by the user. The values of $C_{ϵ1}$, $C_3$, $C_{ϵ2}$ are constants in these equations (Liaw et al., 2021). Further information on performance of different two-equation turbulence models can be found in several publications including those by the present authors (Keshmiri et al., 2008, 2015, 2016)

3.4. Boundary conditions

The upper surface of the system absorbs solar energy from the Sun. A fraction of this energy is absorbed, transferred to the HTF, and a fraction is dissipated due to convection and radiation losses. The net heat absorbed where the plate is covered by the PV cell is calculated as (Du et al., 2016): (10) $\begin{array}{rl}{q}_{\text{Ap}}& =Q_{\text{s}}\left({\alpha }_{\text{PV}}-{\eta }_{\text{e}}\right)-{ϵ}_{\text{PV}}{\sigma }_{\text{sb}}\left(T_{\text{PV}}^4-T_{\text{a}}^4\right)\\ & -h_{\text{c}}\left(T_{\text{PV}}-T_{\text{a}}\right)\end{array}$(10) where ${\sigma }_{\text{sb}}=5.76\times {10}^{-8}\left(\text{W}/{\text{m}}^{\text{2}}\text{K}\right)$ and $h_{\text{c}}=3u_{\text{a}}+2.8$ and $u_a=0.5\text{m/s}$ (Kumar & Mullick, 2010). The net heat absorbed by the sections of the absorber plate not being covered by PV cells is obtained by: (11) $q_{\text{AP}}=Q_{\text{s}}{\alpha }_{\text{AP}}-{ϵ}_{\text{AP}}{\sigma }_{\text{sb}}\left(T_{\text{AP}}^4-T_{\text{a}}^4\right)-h_{\text{c}}\left(T_{\text{PV}}-T_{\text{a}}\right)$(11)

The ambient conditions are considered for Shiraz, a southern city in Iran, located at 29.59 N and 52.58 E. Table 2 illustrates Shiraz’s irradiance intensity and atmospheric temperature in 2020 according to the weather data file. Further information is provided in Appendix A.

Table 2. The irradiance intensity and atmospheric temperature for Shiraz city in 2020.

The average day of the month	$Q_s\left(\text{W}/{\text{m}}^{\text{2}}\right)$	$T_a$ (${}^{\circ }\text{C}$)
January 17	625.15	7.21
February 16	624.91	11
March 16	617.62	14.71
April 15	660.37	18.41
May 15	679.91	26.35
June 11	717.04	30.51
July 17	730.74	32.76
Augest16	741.19	31.61
September 15	807.79	26.24
October 15	778.02	22.22
November 14	586.51	14.9
December 10	656.5	11.12

The surfaces in contact are entirely adiabatic. The shared surfaces between the absorber plate and the PV module are symmetrical. Velocity inlet and pressure outlet boundary conditions are assumed at the inlet and outlet of the fluid. The inlet temperature of the HTF is considered ambient for all cases (298.15 K). On the tube walls, a no-slip boundary condition is employed. Table 3 displays the properties of the PV panel and absorber plate. The electrical reference efficiency of the PV cell, ${\eta }_{\text{ref}}$, is evaluated when the PV temperature approaches the reference temperature.

Table 3. Absorber plate and PV panel properties (Bhattarai et al., 2012).

PV panel	Absorber plate
Length: 1.64 m	Length: 2 m
Width: 1 m	Width: 1 m
${\eta }_{\text{ref}}=12\mathrm{\%},T_{\text{ref}}={25}^{\circ }\text{C}$	Material: Copper
${ϵ}_{\text{PV}}=0.88$	${ϵ}_{\text{AP}}=0.05$
$\text{β}=0.0045\frac{1}{K}$	${\alpha }_{\text{AP}}=0.95$

3.5. Properties of different working fluids

The working fluids in this study include (i) pure water, (ii) Ag-water nanofluid, (iii) MPCM slurry, and (iv) MPCM nano-slurry. For Ag-water nanofluid and MPCM nano-slurry, a user-defined function (UDF) is developed to calculate the thermal conductivity of the nanofluid and the specific heat transfer coefficient of MPCM slurry as a function of temperature.

3.5.1. Properties Ag-water nanofluid

The properties of the nanofluids are calculated as follows (Kakaç & Pramuanjaroenkij, 2009): (12) $\begin{array}{rl}{\rho }_{n,f}& =\left(1-\varphi \right){\rho }_f+\varphi {\rho }_{np}\end{array}$(12) (13) $\begin{array}{rl}{C}_{p,n,f}& =\frac{\left(1-\varphi \right){\left(\rho C_p\right)}_f+\varphi {\left(\rho C_p\right)}_{np}}{{\rho }_{n,f}}\end{array}$(13) For $\varphi \le 5\mathrm{\%}$, the viscosity of nanofluid is calculated as (Mishra et al., 2014): (14) ${\mu }_{n,f}=\left(1+2.5\varphi \right){\mu }_f$(14) The effective thermal conductivity can calculate as (Xuan et al., 2003): (15) $k_f=\frac{\left(k_s+2k_f-2\varphi \left(k_s-k_f\right)\right)}{k_s+2k_f+\left(k_s-k_f\right)\varphi }+\frac{{\rho }_s\varphi C_{p,s}}{2k_f}\sqrt{\frac{2k_{B}T}{3\pi d_p{\mu }_f}}$(15)

The thermophysical properties of Ag nanoparticles are listed in Table 4 (Öğüt, 2009). The properties of water are considered at 298.15 K.

Table 4. The properties of Ag nanoparticles (M. Eisapour et al., 2020).

Property	Ag
Density $\text{(kg}/{\text{m}}^{\text{3}}\text{)}$	10,500
Conductivity $\text{ (W}/\text{m}\cdot \text{K)}$	429
Specific heat $\text{ (J/kg}\cdot \text{K)}$	235

3.5.2. MPCM slurry

The PCM material in this study is hydrocarbon n-octadecane. Table 5 presents the properties of the MPCM slurry, the PCM and water composite, and the base fluid. According to the theoretical homogenous models and experimental studies, MPCM slurry properties are given as follows (Alquaity et al., 2012): (16) ${\rho }_{\text{mps}}=c{\rho }_{\text{mp}}+\left(1-c\right){\rho }_{\text{f}}$(16) The MPCM slurry viscosity is obtained from (Vand, 1945): (17) ${\mu }_{\text{mps}}=(1-c-1.16c^2{)}^{-2.5}{\mu }_{\text{f}}$(17)

Table 5. Properties of n-octedane microencapsulate in this research (Hasan, 2011).

Density $\text{ (kg}/{\text{m}}^{\text{3}}\text{)}$	Specific heat $\left(\text{J}/\text{kg}\text{.K}\right)$	Latent heat $\left(\text{kJ}/\text{kg}\right)$	Thermal conductivity $(\text{W/m}\cdot \text{K})$	Melting point $\left(\text{K}\right)$	Particle size $\left(\mu \mathrm{m}\right)$
850	2000	245	0.18	297–302	10

The effective thermal conductivity is calculated from the Maxwell model (Alquaity et al., 2012): (18) $k_{\text{f}}\frac{\left(k_{\text{mp}}+2k_{\text{f}}-2c\left(k_{\text{s}}-k_{\text{f}}\right)\right)}{k_{\text{mp}}+2k_{\text{f}}+\left(k_{\text{s}}-k_{\text{f}}\right)c}$(18) The bulk-specific heat is calculated as (Alquaity et al., 2012): (19) $\begin{array}{rl}& C_{\text{p,mps}}\\ & =\{\begin{array}{l}\begin{array}{ll}\frac{c{\left(\rho C_{\text{p,s}}\right)}_{\text{mp}}+\left(1-c\right){\left(\rho C_{\text{p}}\right)}_{\text{f}}}{{\rho }_{\text{m,ps}}}& \text{for}:T\le T_{\text{s}}\end{array}\\ \begin{array}{cc}\frac{c{\left(\rho \left(\frac{C_{\text{p,s}}+C_{\text{p,l}}}{2}+\frac{L}{T_l-T_s}\right)\right)}_{\text{mp}}+\left(1-c\right){\left(\rho C_{\text{p}}\right)}_{\text{f}}}{{\rho }_{\text{m,ps}}}& \text{for}:T_{\text{S}}\\ & \le T\le T_{\text{l}}\end{array}\\ \begin{array}{cc}\frac{c{\left(\rho C_{\text{p,l}}\right)}_{\text{mp}}+\left(1-c\right){\left(\rho C_p\right)}_f}{{\rho }_{\text{m,ps}}}& \text{for:}{T}_l\le T\end{array}\end{array}\end{array}$(19)

It should be mentioned that melting occurs over the temperature range of 297–302 K.

3.5.3. MPCM nano-slurry

In this case, the Ag-water nanofluid is considered a carrier fluid combined with MPCM – containing 5% Ag-water nanofluid and 15% MPCM. Eqs (12–15) and Eqs. (16–19) estimates the average properties of nanofluid and MPCM nano-slurry, respectively. The property of fluids is listed in Table 6. It is to be noted that the properties such as thermal conductivity for nanofluid and MPCM nanofluid and specific heat for MPCM slurry/nano-slurry are not known at the beginning since these parameters are the function of fluid temperature. To address this, a UDF is employed to calculate these properties.

Table 6. Properties of considered HTFs at 298.15 K.

Fluids	Density $\text{ (kg}/{\text{m}}^{\text{3}}\text{)}$	SPECIFIC heat $\text{ (J/kg}\cdot \text{K)}$	Melting point $\left(\text{K}\right)$	Thermal conductivity $(\text{W/m}\cdot \text{K})$	Viscosity $(\text{kg}/\text{m}\cdot \text{s})$	Latent heat of fusion $\left(\text{J/kg}\right)$
water	998.20	4182	–	0.6	0.001003	–
Ag-water Nanofluid $\varphi =1\mathrm{\%}$	1073.25	3795.85	–		0.001057	–
Ag-water Nanofluid $\varphi =3\mathrm{\%}$	1253.30	3189.98	–		0.001114	–
Ag-water Nanofluid $\varphi =5\mathrm{\%}$	1433.36	2736.32	–		0.00118	–
Slurry with c = 5%	990.79		298–302	0.56	0.00118
Slurry with c = 10%	983.38		298–302	0.53	0.001385
Slurry with c = 15%	975.97		298–302	0.50	0.001672
MPCM nano slurry $\varphi =5\mathrm{\%},c=15\mathrm{\%}$	1345.85		298–302		0.001915

3.6. Energy analysis

The electrical and thermal efficiencies of the PV panel are defined as (Yu et al., 2019): (20) $\begin{array}{rl}{\eta }_{\mathrm{I},\mathrm{t}\mathrm{h}}& =\frac{{\int }_{A_{\text{Ap}}}{q}_{\text{Ap}}dA}{Q_{\text{s}}{A}_{\text{Ap}}}\end{array}$(20) (21) $\begin{array}{rl}{\eta }_{\mathrm{I},\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}}& =p\cdot {\eta }_{\text{pv}}\end{array}$(21) where $p$ is the packing factor which is considered equal to 0.82. ${\eta }_{\text{pv}}$ and ${\eta }_{\mathrm{I}}$ are the panel efficiency and the first law efficiency calculated as (Ji et al., 2007): (22) ${\eta }_{\text{pv}}={\eta }_{\text{ref}}\left(1-\text{β}\left(T_{\text{pv}}-T_{\text{ref}}\right)\right)$(22) (23) ${\eta }_{\mathrm{I}}={\eta }_{\text{overall}}={\eta }_{\mathrm{I},\mathrm{t}\mathrm{h}}+{\eta }_{\mathrm{I},\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}}$(23)

3.7. Exergy efficiency

The second thermodynamic law is adopted for the exergy analysis. The energy analysis shows the quantity of energy, while the exergy analysis shows the quality of energy. The exergy balance for the PV-T system can be calculated as (Demirel, 2013): (24) $\begin{array}{rl}E{x}_{\text{fluid},\text{ in}}+E{x}_{\text{solar}}& =E{x}_{\text{fluid},\text{ out}}+E{x}_{\text{electrical}}+E{x}_{\text{destroyed}}\end{array}$(24) (25) $\begin{array}{rl}E{x}_{\text{thermal}}& =E{x}_{\text{fluid},\text{ out}}-E{x}_{\text{fluid},\text{ in}}\end{array}$(25) Eq. (24) can be written as: (26) $E{x}_{\text{destroyed}}=E{x}_{\text{solar}}-\left[E{x}_{\text{electrical}}+E{x}_{\text{thermal}}\right]$(26) The term in the bracket is useful exergy. The exergy efficiency is then given as follows (Khanjari et al.): (27) ${\eta }_{\mathrm{I}\mathrm{I}}=\frac{E{x}_{\text{electrical}}+E{x}_{\text{thermal}}}{E{x}_{\text{solar}}}$(27)

The electrical, thermal, and solar exergy are calculated as follows (Wu et al., 2015): (28) $E{x}_{\text{thermal}}={\dot{m}}_{\text{fluid}}{C}_{\text{p,fluid}}\left(T_{\text{out}}-T_{\text{in}}\right)\cdot \left(1-\frac{T_0}{T_{\text{m}}}\right)$(28) (29) $T_{\text{m}}=\frac{T_{\text{out}}-T_{\text{in}}}{\ln \frac{T_{\text{out}}}{T_{\text{in}}}}$(29) where (30) $E{x}_{\text{electrical}}={\eta }_{\text{pv}}{Q}_{\text{s}}{A}_{\text{pv}}$(30) The solar exergy absorbed by the PV panel is calculated as (Khanjari et al., 2016): (31) $E{x}_{\text{solar}}=Q_{\text{s}}{A}_{\text{AP}}\left(1-\frac{4}{3}\frac{T_{\text{a}}}{T_{\text{sun}}}+\frac{1}{3}{\left(\frac{T_{\text{a}}}{T_{\text{sun}}}\right)}^4\right)$(31) where $T_{\text{sun}}$ is set to 5774 K.

4. Numerical method and validation

After creating the geometry using Ansys Design Modeller, Ansys Meshing software is used to generate the mesh. The SIMPLE algorithm is used to solve the pressure field, and the QUICK scheme is used to discretize the momentum and energy equations. The residual values for the convergence of continuity and momentum are ${10}^{-6}$, while for the energy equation, it is ${10}^{-8}$.

The geometry is divided into blocks to achieve the structured mesh, and then the geometry is meshed using the swipe element method. Figure 4 shows the generated mesh for case 3 as an example. This figure shows that mesh size is refined in the vicinity of solid-fluid interfaces due to larger velocity/temperature gradients. The results of grid independency for case 3 are shown in Figure 5. The total number of mesh elements is varied between 830,000 and 4,560,000. The outlet and PV temperatures are chosen for the purpose of mesh independency checks. As seen in this figure, there is a marginal difference in the temperature by further refining the mesh beyond 3,418,000 grids. As such, this number of grids is chosen for all subsequent simulations.

Figure 4. The generated mesh for case 3 using 3.4 million cells.

Figure 5. The grid independency for case 3 for pure water with $u_{in}=0.1\text{m}/\text{s}$ in shiraz city on October 15.

For model validation, the results are compared with the data published in the literature for both laminar and turbulent flow. To validate the laminar flow model (cases 1–3), the numerical results of Yu et al. (2019) are used, who used straight tubes under the PV module to cool down the panel and increase the electrical/thermal efficiency of the PV cell. For this purpose, they used a microencapsulated slurry with water-based fluid. The length and width of the module considered in their research were 2000 mm and 1000 mm, of which 1640 mm was covered by the panel. The length of the cooling tube is 2000 mm, while its diameter is 8 mm. The temperature of the cooling fluid at the inlet is 298.15°C, and the solar radiation intensity is 1000 W/m². Figure 6 shows the variation in PV temperature relative to the water inlet velocity for the present study and Yu et al. (2019) model. As shown, the results follow a similar trend with acceptable accuracy.

Figure 6. The validation study of the PV-T system compared with Yu et al. (2019).

The validation of the turbulent flow (cases 4–6) is performed with the numerical results of Liaw et al. (Liaw et al., 2021). In their research, twisted tape inserts in straight and helical tubes were studied using the k-ϵ model to solve the flow equations. The tube length was 1.258 m for the straight tube, and in the case of the helical tube, the coil pitch was 0.02 m. In addition, the width and height of the twisted tape were considered 0.4 and 10 mm, respectively. The operational conditions, including inlet temperature, wall temperature, and outlet pressure, were 298, 353 K, and zero relative pressure, respectively. Figure 7 illustrates the variation of the heat transfer coefficient with the Reynolds number for the straight pipe, where good agreement is obtained between the results.

Figure 7. The twisted tape and turbulence model validation study compared with Liaw et al. (2021).

The accuracy of the model in terms of nanofluid flow is assessed with the numerical study of Khanjari et al. (2016). The proposed PV-T model consisted of a glass cover, a set of PV cells, a thermal sheet, and a tube collector in a header and riser configuration. To reduce the computational time, the model is simplified to include one riser tube just. In addition, the boundary condition and geometry configuration are adjusted according to Yu et al. (2019) study. Figure 8 shows the outlet temperature as a function of inlet velocity. The results indicate an acceptable agreement with those reported by Khanjari et al. (2016).

Figure 8. The validation study of using Nanofluids in PV-T system compared with Khanjari et al. (2016).

The MPCM slurry fluid is validated with the experimental data of Chen et al. (2008). The authors employed the MPCM slurry passing through a circular stainless-steel tube for cooling the PV module with constant heat flux. The same physical domain is used for the model validation. The MPCM concentration and particle diameters are 15.8% and 8.2 $\mu \mathrm{m}$ (Chen et al., 2008). Figure 9 shows the Nusselt number as a function of cylinder dimensionless length for the present work and those obtained by Chen et al. (2008) under the constant heat flux of $3\times {10}^4\left(\text{W}/{\text{m}}^{\text{2}}\right)$. The comparison of the results shows acceptable accuracy of the present model.

Figure 9. Validation of MPCM slurry thermal performance in a cylindrical cavity with Chen et al. (2008).

5. Results and discussions

The panel temperature and heat absorbed by the HTF for case 4 are compared against case 1 to assess the advantages of using twisted tape to enhance the cooling performance of a PV panel in a straight tube. This is followed by a detailed sensitivity analysis of geometrical parameters of twisted tape/wavy tube, types of coolant fluid, and monthly solar irradiation intensity on the overall exergy and exergy efficiencies of the PV-T systems.

5.1. Effect of twisted tape inserts in a straight tube

Figure 10 shows that the panel temperature is higher when there is no twisted tape inside the tube, reaching the maximum temperature of 326 K compared to 320 K with twisted tape. This is attributed to the twisted tape creating a rotational motion in the flow near the wall, which generates secondary flow, enhances flow mixing, and disturbs the boundary layer (Mashayekhi et al., 2022). This, in turn, leads to a reduction in the PV panel temperature and an increase in the electrical efficiency of the PV panel.

Figure 10. Contours of the temperature distribution in the PV-T system with (a) a straight tube and (b) a straight tube with a twisted tape.

Figure 11 shows the velocity contours at different cross-sections of a straight tube with/without twisted tape at 0.1 m/s inlet velocity (cases 4 and 1). The minimum and maximum velocities are obtained near the tube wall and centre of the tube in the case without twisted tape. However, when the twisted tape is inserted inside the tube, the boundary layer is disturbed, and the thickness of the boundary layer is reduced due to enhanced mixing effects (Ghalambaz et al., 2020b).

Figure 11. Cross-sectional velocity contours for straight tube (case 1) and straight tube with twisted tape insert (case 4) at u = 0.1 m/s.

Table 7 lists the values of the average PV temperature as well as the total heat absorption by the cooling fluid with and without twisted tape in a straight tube at an intake velocity of 0.1 m/s (cases 4 and 1). The solar radiation intensity is assumed to be 778 W/m² from the weather data file for Shiraz in October. The panel temperature decreases by 4.1 K, while the net heat absorbed by HTF increases by 36.3 W for a case with twisted tape compared to the base case.

Table 7. Values of the average PV temperature as well as the total heat absorption by the cooling fluid for the PV-T system with straight with and without twisted tape.

Cases	Panel temperature $\left(\text{K}\right)$	Heat absorbed by HTF $\left(\text{W}\right)$
Straight tube (case 1)	314.3	226.6
Straight tube with twisted tube (case4)	310.1	262.9

Table 8. The average PV temperature and the total heat absorption by the cooling fluid for the PV-T system with straight with and without twisted tape for different inlet velocities.

Cases		0.05 $\left(\text{m/s}\right)$	0.1 $\left(\text{m/s}\right)$	0.15 $\left(\text{m/s}\right)$	0.2 $\left(\text{m/s}\right)$	0.25 $\left(\text{m/s}\right)$
Case 1	PV temperature $(\text{K)}$	318.6	314.3	312.3	311.1	310.2
	Heat absorbed by HTF $\left(\text{W}\right)$	209.4	226.6	234.3	239	242.3
Case 4	PV temperature $\left(\text{K}\right)$	316.9	310.1	306.1	305.0	304.2
	Heat absorbed by HTF $\left(\text{W}\right)$	216	262.9	266.2	271.5	279

Figure 12(a) shows the energetic and exergetic efficiencies of the PV module for cases 4 and 1. According to Eq. (10), reducing the PV panel temperature is accompanied by a reduction in the temperature difference between the panel and the environment and, as a result, lower heat loss due to convection and radiation. The energy and exergy efficiencies increase when the twisted tape is inserted inside the straight tube. The thermal, electrical, and overall energy efficiencies increase by 6.8%, 4.1%, and 6.2%, while the thermal, electrical, and overall exergy efficiencies increase by 28%, 2%, and 6.3% in the case of twisted tape as compared to the base case, respectively.

Figure 12. The thermal, electrical, and overall efficiencies of the straight tube with and without twisted tape (cases 4 and 1) (a) energy efficiency and (b) exergy efficiency.

The results of this study suggest that the use of a twisted tape inside a straight tube under a PV panel is an effective method for enhancing the cooling performance of the panel and increasing the overall energy and exergy efficiencies of the system.

5.2. Effect of fluid velocity

The effect of inlet velocity ranging from 0.05 m/s to 0.25 m/s is investigated in this section. Figure 13 shows the fluid temperature distribution for cases 4 and 1 under various values of inlet velocity. Inserting twisted tapes reduces the cross-sectional area of the cooling channel, increasing the flow velocity and centrifugal force – leading to a better redirection of the core flow toward the heated wall and a reduction in the fluid flow temperature. At a lower inlet velocity of 0.05 m/s, the generated centrifugal force is not strong enough to lower the PV panel temperature. However, moving to higher Reynolds numbers increases the flow velocity and momentum of the fluid – assisting the fluid in energy absorption from the heated wall and reduction in the PV panel temperature.

Figure 13. Temperature distribution of the PV panel at different inlet fluid velocities for the straight tube with and without twisted tape (cases 4 and 1).

Table 8 lists the average PV temperature as well as the total heat absorption by the cooling fluid for different fluid velocities considering the mean solar radiation in October. It can be noticed that at higher inlet velocities, the panel temperature decreases, and the heat absorbed by the cooling fluid increases. Due to the secondary flow formation and the vortex generation, heat transfer in the twisted tape case is more significant. As a case in point, the change in the inlet velocity from 0.05 to 0.1 m/s is associated with the increase in the heat absorbed rate by 21.71% in case 4 and by 8.21% in case 1.

Figure 14. Effect of inlet velocity on (a) thermal and electrical energy efficiencies, (b) thermal and electrical exergy efficiencies, and (c) overall energetic and exergetic efficiencies of the PV module.

Figure 14(a) shows the PV-T system thermal and electrical energy efficiencies for different inlet velocities of the fluid. Increasing the inlet velocity increases both the thermal and electrical efficiencies. At 0.1 m/s, the thermal and electrical efficiencies of a straight tube with a twisted tape are 6.9% and 2% higher than that for the base case because of the higher reduction in the PV module temperature as a result of the enhancement in the heat transfer coefficient.

Figure 14(b) shows the PV-T system thermal and electrical exergy efficiencies for different velocities. Increasing the inlet velocity decreases the thermal exergy efficiency and increases the electrical exergy efficiency. The electrical exergy efficiency of a PV module with twisted tape is higher than that of a PV module without twisted tape. As velocity increases from 0.05 $\text{m}/\text{s}$ to 25 $\text{m}/\text{s}$, the thermal exergy decreases as a result of higher heat transfer to the HTF. According to Eq. (30), the electrical exergy of the system increases due to a decrease in the PV panel temperature. Over this range of velocity, the thermal and electrical efficiencies in the case with a twisted tape drop by 44.36% and increase by 6.2%, respectively. For the same case without a twisted tube, the thermal and electrical efficiencies decrease by 52.4% and increase by 4.2%, respectively.

Figure 14(c) shows the overall energy and exergy efficiencies of the PV-T system. Based on Eqs. (23) and (27), higher energy and exergy efficiencies are obtained for the PV system equipped with a twisted tape than for the base case. The increase in the inlet velocity from 0.05 to 0.25 m/s is associated with an increase in the energy efficiency by 20.3% and a decrease in the exergy efficiency by 5.7% for the system with a twisted tape. In contrast, for the straight tube case, the energetic and exergetic efficiencies increased by 14.1% and reduced by 8.6%, respectively.

5.3. Different types of configurations

Figure 15 shows the temperature distribution of the PV panel for different geometries at an inlet velocity of 0.1 m/s for the mean solar radiation in October. As seen in this figure, the straight tube suffers from effective cooling in the corners of the PV panel, which reduces the system performance. This can be resolved by employing wavy tubes with twisted tape. It is evident that using the wavy tube – with 200 mm wavelength and 50 mm amplitude – and twisted tape (case 6) results in a better temperature distribution than other cases due to higher heat transfer characteristics and lower stagnation regions in the fluid flow.

Figure 15. Temperature distribution in PV-T system for different types of configurations at the inlet velocity of 0.1 m/s.

Figure 16(a and b) show the overall energy efficiency for different geometries. As seen in this figure, the energy efficiency for cases 2–6 increases by 5.1%, 7.8%, 6.2%, 11.5%, and 12.4% compared to the base case (case 1), respectively. The exergy efficiency in wavy-shaped tubes is higher than that of the straight tube because of the more significant heat transfer area and, consequently, more reduction in the temperature of the PV panel. Using a twisted tape in the tube also increases the exergy efficiency compared to the base case. The exergy efficiencies of cases 2–6 increased by 6.9%, 7.4%, 6.3%, 15.8%, and 16.8% compared to the base case (case 1). This is attributed to the amounts of average PV temperature and total heat absorption by the HTF for these geometries, listed in Table 9 for different fluid velocities. As seen in this table, the panel temperature decreases as the inlet velocity increases, which is more noticeable at lower velocities. Moreover, the panel temperature in cases 2–6 is 3.3, 5.2, 4.1, 7.8, and 8.3 K, cooler than the base case at the inlet velocity of 0.1 m/s.

Figure 16. Effect of PV system configuration on the (a) energy efficiency and (b) exergy efficiency at the inlet velocity of 0.1 m/s.

Table 9. The average panel temperature and heat absorbed by HTF for the PV-T system with different cases for different velocity inlets.

Cases		0.05 m/s	0.1 m/s	0.15 m/s	0.2 m/s	0.25 m/s
Case 1	PV temperature $\left(\text{K}\right)$	318.63	314.3	312.31	311.08	310.21
	Heat absorbed by HTF $\left(\text{W}\right)$	209.38	226.57	234.28	238.98	242.26
Case2	PV temperature $\left(\text{K}\right)$	316.97	311.03	308.91	307.54	306.83
	Heat absorbed by HTF $\left(\text{W}\right)$	215.58	261.4	265.34	269.76	275.54
Case3	PV temperature $\left(\text{K}\right)$	314.19	309.11	306.9	305.8	305.09
	Heat absorbed by HTF $\left(\text{W}\right)$	238.32	271	276.69	276.92	280.06
Case4	PV temperature $\left(\text{K}\right)$	316.9	310.15	306.05	304.97	304.23
	Heat absorbed by HTF $\left(\text{W}\right)$	215.96	262.86	266.22	271.46	279
Case5	PV temperature $\left(\text{K}\right)$	310.68	306.53	304.98	304.14	303.56
	Heat absorbed by HTF $\left(\text{W}\right)$	239.1	278.3	285.26	293.3	299.38
Case6	PV temperature $\left(\text{K}\right)$	309.75	305.97	304.36	303.6	302.81
	Heat absorbed by HTF $\left(\text{W}\right)$	243.83	283.5	289.5	296.7	307.82

Figure 17(a) shows the thermal and electrical energy efficiencies at different velocities. As the velocity increases, the thermal and electrical efficiencies increase. By changing the inlet velocity from 0.05 $\text{m}/\text{s}$ to 0.25 $\text{m}/\text{s}$ for cases 1–6, the thermal efficiency increases by 20%, 18.3%, 15.5%, 22.5%, 11.5%, and 10%, and the electrical efficiency increases by 4.1%, 5%. 4.5%, 6.3%,3.4% and 3.3%, respectively. Figure 17(b) illustrates the thermal and electrical exergy efficiencies for different geometries at different velocities. As the efficiency increases, the thermal exergy efficiency decreases, and the electrical exergy increases. In cases 2, 3, 4, 5, and 6 at the inlet velocity of 0.05 m/s, the thermal exergy efficiency increases by 5.1%, 25.3%, 6.3%, 26.2%, and 30.5% compared to the base case. The electrical efficiency increases by 8.8%, 2.3%, 9.2%, 3.9%, and 4.4% for cases 2–5 compared with the base case. In case 6, with increasing the inlet velocity, the thermal exergy efficiency decreases from 3.3% to 1.4%, and the electrical exergy increases from 9% to 9.3%. Figure 17(c) shows the overall energetic and exergetic efficiencies for different geometries at different velocities – higher velocity results in higher energy and lower exergy efficiency. Case 6 has the best performance from energy and exergy, in which a twisted tape is inserted inside a wavy tube with a wavelength of 200 mm and an amplitude of 50 mm. The overall energy efficiency for cases 2, 3, 4, 5, and 6 increases by 2.6%, 7.1%, 2. 9%, 12.8%, and 14.8% compared to the base case, while these numbers are 1.8%, 7.4%, 2%, 9% and 10.3% for exergy efficiency at the inlet velocity of 0.5 m/s. Increasing the inlet velocity from 0.05 m/s to 0.25 m/s increases the energy efficiency from 76.1% to 83.13% and decreases the exergy efficiency from 12.3% to 10.7%. Figure 17(d) shows the amount of thermal and electrical exergy. The results show that the amount of thermal exergy decreases for a higher velocity while the electrical exergy increases. In the best case (case 6), the thermal exergy decreases from 11.2 W to 4.7 W with increasing velocity, and the electrical exergy increases from 30.6 W to 31.6 W.

Figure 17. Effect of inlet velocity on (a) thermal and electrical energy efficiencies, (b) thermal and electrical exergy efficiencies, (c) overall energetic and exergetic efficiencies, and (d) thermal and electrical exergy.

5.4. Different types of coolant fluid

To study the effect of fluid type on the performance of the PV-T system, eight different fluids have been used, including Ag-water nanofluid with 1%, 3%, and 5% volume fractions, n-octedane microcapsules with 5%, 10%, and 15% volume concentrations, and MPCM Nano slurry with 5% nanoparticles and 15% microcapsule. It should be noted that there is a limit for the volumetric concentration of MPCM because of the non-Newtonian behaviour of MPCM at high concentrations of MPCM; fluid behaviour becomes non-Newtonian – which dictates the upper limit of pumping. As such, the maximum concentration of 15% is considered for the MPCM.

Figure 18(a) presents the energy efficiency of a PV-T system at an inlet velocity of 0.1 m/s for case 5, considering the mean solar radiation in October. The addition of nanoparticles increases the overall heat transfer coefficient and the performance of a PV-T system. Using microencapsulation also increases the fluid heat capacity, and, as a result, the fluid absorbs more heat. The highest thermal and electrical energy efficiencies are found in the case of water with 15% slurry due to more decrease in the temperature of an absorber plate. Figure 18(b) shows the exergy efficiency for different cooling fluids. The thermal exergy efficiency decreases by increasing the nanofluid volume fraction due to higher viscosity and thermal conductivity – leading to higher entropy generation and lower exergy efficiency of the PV cell. The opposite trend is observed in the case of the volume concentration of MPCM. The increase in the volume concentration of MPCM is accompanied by an increase in thermal exergy efficiency due to an enhancement in heat capacity. Electrical exergy efficiency in both nanoparticle and MPCM increases with the enhancement of the volume fraction of fluids due to a reduction in PV temperature. Increasing the volume fraction of nanofluid and MPCM reduces and increases the exergy efficiency of the PV module compared to pure water. As such, the MPCM microcapsule with a 15% volume concentration performs best based on the overall exergy efficiency. Table 10 shows the PV-T system average panel temperature, heat absorbed, and pressure drop in the tube for different fluids. According to this table, the panel temperature decreases with increasing nanofluid concentration. In the best case, using nanoparticles with a volume concentration of 5% reduces the panel temperature to 305.71 K. When using an MPCM slurry with a concentration of 15%, the panel temperature decreases by almost 0.91 K compared to the base fluid. The heat absorbed by the fluid declines by increasing the nanofluid concentration. The highest heat-absorbed rate of 49.17 W is achieved in the case of MPCM slurry with a 15% volume concentration. The maximum pressure drop obtained in different cases is 153.8 Pa.

Figure 18. Effect of coolant fluid on the (a) energy efficiency and (b) exergy efficiency at the inlet velocity of 0.1 m/s.

Table 10. Average panel temperature, heat absorbed, and pressure drop for different types of coolant fluid at the inlet velocity of 0.1 m/s.

Cooling fluid	Panel temperature $\left(\text{K}\right)$	Heat absorbed by HTF $\left(\text{W}\right)$	Pressure drop (Pa)
Pure water	306.53	255.264	108.44
Ag-water Nano-fluid $\varphi =1\mathrm{\%}$	306.44	196.65	115.34
Ag-water Nano-fluid $\varphi =3\mathrm{\%}$	305.89	138.21	126.27
Ag-water Nano-fluid $\varphi =5\mathrm{\%}$	305.71	115.15	150.83
Slurry with c = 5%	306.19	272.17	109.38
Slurry with c = 10%	305.91	283.43	110.62
Slurry with c = 15%	305.62	304.44	111.50
MPCM Nano slurry $\varphi =5\mathrm{\%},c=15\mathrm{\%}$	305.72	230.46	153.76

5.5. Seasonal effects

Due to the difference in the solar radiation intensity in a typical year, the performance of a PV panel varies with the geographical location and throughout the year. Figure 19(a) shows the monthly energy efficiency of the PV panel at the inlet fluid velocity of 0.1 m/s. The highest and lowest thermal energy efficiency occurred in July and January. According to Eq. (10) and Table 2, absorber heat increases due to solar radiation intensity and ambient temperature enhancement. As a result, the thermal energy efficiency rises in July and decreases in January.

Figure 19. Monthly performance of the PV system in terms of (a) energy efficiency and (b) exergy efficiency for Shiraz city at the inlet velocity of 0.1 m/s.

In contrast to the previous case, the highest and lowest electrical energy efficiency occurred in January and July due to the ambient temperature reduction presented in Table 2. The highest and lowest overall energy efficiency is in July and January. Figure 19(b) illustrates the monthly exergy efficiency of the PV panel at the inlet fluid velocity of 0.1 m/s. According to Eq. (28), an increase in solar radiation intensity and a reduction in ambient temperature enhance the exergy efficiency. The best thermal exergy is related to October, while the lowest is related to January. The best electrical exergy is in January, and the lowest is in October. The highest and lowest overall exergy efficiency is in October and January. The proposed system has the best and worst performance in October and January, respectively.

Table 11 shows the monthly average panel temperature and heat absorbed by the fluid. The highest panel temperature is in October (i.e. 306.53 K), and the lowest is in January (i.e. 302.08 K). The highest and lowest heat absorption occurs in October and January – equivalent to 255.26 and 108.25 W, respectively.

Table 11. Monthly average PV temperature and the total heat absorption by HTF for the PV-T system located in Shiraz at the inlet fluid velocity of 0.1 m/s.

Month	Plate temperature $\left(\text{K}\right)$	Heat absorbed by HTF $\left(\text{W}\right)$
January	302.08	108.25
February	302.52	122.93
March	302.85	130.27
April	303.64	149.37
May	304.7	174.33
June	305.37	178.74
July	305.93	204.75
August	305.89	204.12
September	305.9	206.43
October	306.53	255.26
November	302.56	121.67
December	302.77	124.82

5.6. Comparison against the existing data

This section compares the results obtained from the present study with those found in the literature. Table 12 shows the energy and exergy efficiency improvement based on the proposed method in the literature and present work relative to the base case with no design improvement. As seen in this table, the geometrical configuration of the PV-T module plays a crucial role in the energy and exergy performance of the system. This study indicated that changing the geometry of the tubes from a straight to a wavy shape with a twisted tape inserted under the PV panel resulted in significant improvements in energy and exergy efficiencies, corresponding to 12.4% and 16.8% increase compared to the base case, respectively. The results showed that increasing the volume concentration of nanoparticles in the coolant fluid led to an increase in energy efficiency and a decrease in exergy efficiency. Similarly, increasing the volume concentration of the MPCM coolant fluid also led to an increase in energy and exergy efficiencies. MPCM slurry with a 15% volume concentration exhibited the best energy and exergy efficiencies among the coolant fluids considered. Compared to other papers published in the literature, the co-implementation of a wavy tube and twisted tape provides a more uniform temperature distribution along the tube wall due to the secondary flow induced in the core and near the wall regions. These dual mixing effects prohibit the formation of hot zones and boundary layers, leading to better cooling performance. This is the main reason for higher energy and exergy efficiencies obtained from this work relative to other papers published in the literature.

Table 12. comparison between the current study and other methods in terms of energy and exergy efficiency.

${\eta }_{\text{Improvement}}=\left(\frac{{\eta }_{\text{with method}}-{\eta }_{\text{without method}}}{{\eta }_{\text{without method}}}\right)$
Reference	Method of Study	Energy improvement (%)	Exergy Improvement (%)	Remarks
Eisapour et al. (2020)	3D numerical	6.1	4.3	Comparison between PV-T wavy tube and straight tube
Eisapour et al. (2021)	3D numerical	6.3	3.8	Comparison between PV-T ascending and descending wavy tube and straight tube
Ahmadinejad and Moosavi (2023)	3D numerical	14	2.4	Comparison between PV-T baffled channel and simple channel collector with different types of nanofluids
Alktranee et al. (2022)	Experimental	29.6	–	Comparison between PV-T system with tungsten trioxide nanofluid and without nanofluid
Present study	3D numerical	12.4	16.8	Comparison of the best PV-T configuration and straight tube

6. Conclusion

Maintaining the temperature of a photovoltaic (PV) system in the range of 35°C to 45°C requires an effective cooling system in place. The present study aimed to improve the cooling performance of a photovoltaic-thermal (PV-T) system by employing twisted tape inserts in wavy tubes. Having the model validated first, a parametric study was subsequently conducted using CFD to obtain the effect of various parameters, including the inlet velocity, geometry design, different types of coolant fluid, and monthly/seasonal effects on the energy/exergy efficiencies.

It is found that increasing the cooling fluid velocity from 0.05 m/s to 0.25 m/s increased the energy efficiency and decreased the exergy efficiency of the PV-T system, suggesting that there is an optimal velocity to achieve the best balance between energy and exergy efficiencies. The implementation of the wavy tube with twisted tape showed to increase the energy and exergy efficiencies by 12.4% and 16.8%, respectively, due to the dual mixing effects. These, in turn, prohibited the formation of hot zones and boundary layer, leading to enhanced performance. Increasing the volume concentration of the microencapsulated phase change material (MPCM) coolant fluid led to an increase in energy efficiency from 79.4% to 80.3% and an increase in exergy efficiency from 11.3% to 11.6%. Among the coolant fluids considered, MPCM slurry with 15% volume concentration exhibited the best energy and exergy efficiencies. The best monthly performance of the PV panel (assumed to be installed in Shiraz, Iran) in terms of energy and exergy efficiencies was obtained in July and October, corresponding to 90% and 11.3%, respectively.

Based on the conclusions drawn from this study, some suggestions for future work include (i) investigating the interaction between several passive and active cooling to improve the PV-T performance, (ii) experimental testing of the proposed configuration, (iii) optimising the design parameters to further increase energy and exergy efficiencies, (iv) techno-economic assessment of the proposed technology, (v) examining the lifetime and stability of the PV-T system under harsh environment, and (vi) investigating the scalability of the proposed cooling system for large-scale PV-T systems.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The corresponding author, Dr. Amir Keshmiri would also like to acknowledge the funding by the UK Engineering and Physical Sciences Research Council (EPSRC) under the Impact Acceleration Account (IAA) provided to the University of Manchester, which has supported the present research.

Appendix A

Solar radiation intensity

The isotropic diffuse model proposed by Liu and Jordan (B. Y. H. Liu & Jordan, 1963) was used to obtain the solar radiation intensity. In this method, solar radiation consists of direct, isotropic diffuse, and solar radiation diffusely reflected from the ground. The total solar radiation on the tilted plate for an hour is obtained from the following equation: (32) $I_{\text{T}}=I_{\text{b}}{R}_{\text{b}}+I_{\text{d}}\left(\frac{1+\cos \text{β}}{2}\right)+I{\rho }_{\text{g}}\left(\frac{1-\cos \text{β}}{2}\right)$(32) ${\rho }_{\text{g}}$ is ground reflected which is considered 0.2 for all of the months in this study.$\text{β}$ is the slop of the collector and in this study considered ${30}^{\circ }$. $R_{\text{b}}$ is the ratio of beam radiation calculated by (Duffie et al., 2020): (33) $R_{\text{b}}=\frac{a}{b}$(33) where (34) $\begin{array}{rl}a& =\left(\sin \left(\delta \right)\sin \left(\varphi \right)\cos \left(\text{β}\right)-\sin \left(\delta \right)\cos \left(\varphi \right)\sin \left(\text{β}\right)\cos \left(\gamma \right)\right)\\ & \times 180\left({\omega }_2-{\omega }_1\right)\pi \\ & +\left(\cos \left(\delta \right)\cos \left(\varphi \right)\cos \left(\text{β}\right)+\cos \left(\delta \right)\sin \left(\varphi \right)\sin \left(\text{β}\right)\cos \left(\gamma \right)\right)\\ & \times \left(\sin \left({\omega }_2\right)-\sin \left({\omega }_1\right)\right)-\left(\cos \left(\delta \right)\sin \left(\text{β}\right)\sin \left(\gamma \right)\right)\\ & \times \left(Cos{\omega }_2-Cos{\omega }_1\right)\end{array}$(34) (35) $\begin{array}{rl}b& =\left(\cos \left(\varphi \right)\cos \left(\delta \right)\right)\times \left(Sin{\omega }_2-Sin{\omega }_1\right)+\left(\sin \varphi \sin \delta \right)\\ & \times \frac{1}{180}\left({\omega }_2-{\omega }_1\right)\pi \end{array}$(35) $\varphi$ is the latitude which is 29.59 for Shiraz city. $\omega$ is the hour angle.$\gamma$ is the surface azimuth angle and set zero due south in this study. $\delta$ is declination and calculation by (Cooper, 1969): (36) $\delta =23.45\times \sin \left(360\frac{284+n}{365}\right)$(36) which n is the day of the year. The ratio of hourly total to total daily radiation is calculated by (Collares-Pereira & Rabl, 1979): (37) $r_t=\frac{I}{H}=\frac{\pi }{24}\left(a+b\cos \omega \right)\frac{\cos \omega -Cos{\omega }_s}{Sin{\omega }_s-\frac{\pi {\omega }_s}{180}Cos{\omega }_s}$(37) The coefficients a and b are given by (Duffie et al., 2020): (38) $a=0.409+0.5016\sin \left({\omega }_s-60\right)$(38) (39) $b=0.6609-0.4767\sin \left({\omega }_s-60\right)$(39) ${\omega }_S$ is sunset hour angle is given by (Duffie et al., 2020): (40) ${\omega }_s={\cos }^{-1}\left(-\tan \left(\varphi \right)\tan \left(\delta \right)\right)$(40) To obtain the daily clearance index, KT is defined as follows (Santos et al., 2003): (41) $\begin{array}{rl}{K}_{\text{T}}& =\frac{1}{\gamma }\ln \left[\left(1-\frac{n{d}_{\text{k}}-\frac{1}{2}}{n{d}_{\text{m}}}\right)\right]\mathrm{e}\mathrm{x}\mathrm{p}\left(\gamma K_{\text{T,min}}\right)\\ & +\left(1-\frac{n{d}_{\text{k}}-\frac{1}{2}}{n{d}_{\text{m}}}\right)\mathrm{e}\mathrm{x}\mathrm{p}\left(\gamma K_{\text{T,max}}\right)\end{array}$(41) where $n{d}_{\text{m}}$, is the day of the month, $n{d}_{\text{k}}$ is the number of days of the month and $\gamma$ is a dimensionless parameter given by: (42) $\gamma =-1.498+\frac{1.184\zeta -27.182exp\left(-1.5\zeta \right)}{K_{\text{T,min}}-K_{\text{T,max}}}$(42) $\zeta$ is a dimensionless parameter given by: (43) $\zeta =\frac{K_{\text{T,min}}-K_{\text{T,max}}}{K_{\text{T,min}}-\overline{K_{\text{T}}}}$(43) The value of $K_{\text{T,min}}$ and $K_{\text{T,max}}$ defined as follow: (44) $K_{\text{T,min}}=0.05$(44) (45) $K_{\text{T,max}}=0.6313+0.267{\overline{K}}_{\text{T}}-11.9({\overline{K}}_{\text{T}}-0.75{)}^8$(45) The solar irradiation and monthly means of the daily clear index for different months in Shiraz city of Iran are presented in Table A1.

Table A1. Irradiation and monthly means of the daily clear index for different months in Shiraz city (Yaghoubi & Sabzevari, 1996).

Month	Daily mean of irradiation $\left(\text{MJ}/{\text{m}}^{\text{2}}\right)$	Monthly mean of clear sky index $\overline{K_T}$
January	12	0.63
February	14.88	0.58
March	14.65	0.45
April	24.2	0.67
May	25.1	0.66
June	27	0.72
July	25.6	0.68
August	23.2	0.64
September	22.2	0.65
October	17	0.61
November	13.1	0.65
December	12.2	0.7

The daily diffuse radiation $H_{\text{d}}$ is defined by Erb’s correlations as followed (Santos et al., 2003):

For ${\omega }_{\text{s}}\le {81.04}^{\circ }$ (46) $\frac{H_{\text{d}}}{H}=\{\begin{array}{l}1-0.2727K_{\text{T}}+2.4495{K_{\text{T}}}^2-11.9514{K_{\text{T}}}^3\\ +9.3789{K_{\text{T}}}^4,K_{\text{T}}<0.715\\ 0.143,K_{\text{T}}\ge 0715\end{array}$(46) And for ${\omega }_{\text{s}}>{81.04}^{\circ }$ (47) $\frac{H_{\text{d}}}{H}=\{\begin{array}{l}1-0.2727K_{\text{T}}+2.4495{K_{\text{T}}}^2-11.9514{K_{\text{T}}}^3\\ +9.3789{K_{\text{T}}}^4,K_{\text{T}}<0.715\\ 0.143,K_{\text{T}}\ge 0715\end{array}$(47) The hourly diffuse radiation $I_{\text{d}}$ is obtained with the ratio of hourly diffuse to daily diffuse radiation $r_d$ as (Duffie et al., 2020): (48) $r_{\text{d}}=\frac{I_{\text{d}}}{H_{\text{d}}}=\frac{\pi }{24}\left(\frac{\cos \omega -Cos{\omega }_{\text{s}}}{Sin{\omega }_{\text{s}}-\frac{\pi {\omega }_{\text{s}}}{180}Cos{\omega }_{\text{s}}}\right)$(48) Hourly beam radiation $I_{\text{b}}$ is calculated by subtracting $I_{\text{d}}$ from I. Finally, the solar intensity for the average day for all of the months for the city of Shiraz is presented in Figure A1. Then the moderate solar radiation intensity from 10 am to 2 pm is calculated and shown in Table 2.

Figure A1. Solar radiation intensity for different months of Shiraz, Iran.

Ambient temperature

To obtain the average ambient temperature for different months, the minimum temperature and maximum temperature for days of the month based on weather data for 2020 in Shiraz are given in Figure A2. Then, after passing the curve of the lowest temperature and the highest temperature of the two curves obtained in each graph, the average of the lowest temperature and the highest temperature for the days are averaged, and the results are presented in Table 2.

Figure A2. Average low and high-temperature distribution for Shiraz city according to AccuWeather report for the year 2020.