COMPUTER MODELING ANALYSIS OF PHOTOVOLTAIC (PV) MODULES WITHOUT AND WITH INTEGRATED COOLING SYSTEMS
This article presents the results of a study focused on modeling the thermal and electrical characteristics of photovoltaic (PV) solar panels. The study analyzes the temperature distribution, thermal energy generation, and the effect of cooling systems on PV panels using numerical methods. In partic...
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2025
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| author | Axtamov , T. Z. Pundev , V. |
| author_facet | Axtamov , T. Z. Pundev , V. |
| author_institution_txt_mv | [
{
"author": "T. Z. Axtamov ",
"institution": "S. A. Azimov Institute of Physical-Technical, Academy of Sciences of the Republic of Uzbekistan,Tashkent, Uzbekistan"
},
{
"author": "V. Pundev ",
"institution": "Institute of Renewable Energy NAS of Ukraine, Kyiv, Ukraine"
}
] |
| author_sort | Axtamov , T. Z. |
| baseUrl_str | https://ve.org.ua/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-18T06:32:23Z |
| description | This article presents the results of a study focused on modeling the thermal and electrical characteristics of photovoltaic (PV) solar panels. The study analyzes the temperature distribution, thermal energy generation, and the effect of cooling systems on PV panels using numerical methods. In particular, it evaluates the relationship between surface temperature and efficiency of the panels under conditions with and without cooling channels. The modeling is performed in COMSOL Multiphysics software, utilizing the finite element method (FEM) to account for both fluid flow and heat transfer. The obtained results demonstrate the potential for enhancing the electrical efficiency of PV panels through thermal management and have significant practical importance in adapting solar energy systems to various climatic conditions. |
| doi_str_mv | 10.36296/1819-8058.2025.4(83).195-208 |
| first_indexed | 2026-02-08T07:59:31Z |
| format | Article |
| fulltext |
195
Відновлювана енергетика. № 4/2025 | Сонячна енергетика
UDC: 621.383:536.24:004.942 https://doi.org/10.36296/1819-8058.2025.4(83).195-208
COMPUTER MODELING ANALYSIS OF PHOTOVOLTAIC (PV) MODULES WITHOUT AND WITH
INTEGRATED COOLING SYSTEMS
Received Aug. 26, 2025; accepted Dec. 09, 2025
Available online Dec. 31, 2025
Axtamov T. Z.1, Pundev V.2
Author for correspondence: Axtamov Tohir Zuhriddin ogli
e-mail: tohiraxtamov@gmail.com
Abstract. This article presents the results of a study focused on
modeling the thermal and electrical characteristics of photo-
voltaic (PV) solar panels. The study analyzes the temperature
distribution, thermal energy generation, and the effect of cool-
ing systems on PV panels using numerical methods. In particu-
lar, it evaluates the relationship between surface temperature and efficiency of the panels under conditions with
and without cooling channels. The modeling is performed in COMSOL Multiphysics software, utilizing the finite
element method (FEM) to account for both fluid flow and heat transfer. The obtained results demonstrate the
potential for enhancing the electrical efficiency of PV panels through thermal management and have significant
practical importance in adapting solar energy systems to various climatic conditions.
Keywords: PV panels, modeling, heat transfer, COMSOL Multiphysics, cooling system, energy efficiency.
КОМП’ЮТЕРНИЙ МОДЕЛЮВАЛЬНИЙ АНАЛІЗ ФОТОЕЛЕКТРИЧНИХ МОДУЛІВ БЕЗ
ІНТЕГРОВАНИХ СИСТЕМ ОХОЛОДЖЕННЯ ТА З НИМИ
Отримано 26 серп. 2025 р.; рекомендовано до публікації 09 груд. 2025 р.
Доступно онлайн 31 груд. 2025 р.
Ахтамов Т. З.1, Пундев В. О.2
Автор для кореспонденції: Ахтамов Тохір Зухріддін огли,
e-mail: tohiraxtamov@gmail.com
Анотація. У цій статті наведено результати дослі-
дження, спрямованого на моделювання теплових та еле-
ктричних характеристик сонячних фотоелектричних
(ФЕ) панелей. У дослідженні проаналізовано розподіл те-
мператури, генерацію теплової енергії та вплив систем
охолодження на ФЕ-панелі з використанням чисельних методів. Зокрема, оцінено взаємозв’язок між те-
мпературою поверхні та ефективністю панелей за умов із наявністю та без наявності охолоджуваль-
них каналів. Моделювання виконано в програмному середовищі COMSOL Multiphysics із використанням
методу скінченних елементів (МСЕ) для врахування як руху рідини, так і теплопередачі. Отримані ре-
зультати демонструють можливість підвищення електричної ефективності ФЕ-панелей шляхом те-
плового керування та мають важливе практичне значення для адаптації сонячних енергетичних сис-
тем до різних кліматичних умов.
Ключові слова: ФЕ-панелі, моделювання, теплопередача, COMSOL Multiphysics, система охолодження,
енергоефективність.
1 Junior Researcher
https://orcid.org/0000-0003-0587-0999
2 Researcher
https://orcid.org/0000-0003-3750-8812
1 S. A. Azimov Institute of Physical-Technical,
Academy of Sciences of the Republic of
Uzbekistan,Tashkent, Uzbekistan
2 Institute of Renewable Energy NAS of Ukraine,
Kyiv, Ukraine
1 Молодший науковий співробітник
https://orcid.org/0000-0003-0587-0999
2 Науковий співробітник
https://orcid.org/0000-0003-3750-8812
1 Фізико-технічний інститут імені С. А. Азімова
Академії наук Республіки Узбекистан,
Ташкент, Узбекистан
2 Інститут відновлюваної енергетики
НАН України, м. Київ, Україна
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1. Introduction of research work
In the context of growing global energy demand and esca-
lating environmental issues, there is a significant increase
in interest toward renewable energy sources, especially
technologies based on solar energy. Photovoltaic (PV) pan-
els are among the most environmentally friendly means of
generating electricity without harming the environment.
They are known for several advantages, such as mobility,
low maintenance requirements, and modular design prin-
ciples.
However, during operation, solar panels experience perfor-
mance degradation due to elevated temperatures, which
directly affects their electrical output. Therefore, efficient
cooling of PV panels in hot environments, maintaining their
temperature within acceptable limits, and thoroughly stud-
ying their thermal characteristics constitute a pressing sci-
entific and technical challenge.
This article analyzes the performance of PV panels through
computer modeling under two different conditions: with-
out cooling and with an integrated cooling system. The
models determine temperature distribution, pressure
drop, heat flux, and convective heat transfer coefficients.
The results of this study may serve as a basis for developing
optimal designs and cooling strategies for PV systems.
2. Materials and methods
Fig. 1 (a) Geometric view of the photovoltaic (PV) module
without a cooling system, showing the physical layout used
for thermal analysis. (b) Generated mesh structure for the
finite element solver, used to discretize the domain for nu-
merical simulation and ensure accurate resolution of ther-
mal and fluid flow fields. Simulations are conducted de-
pending on the boundary conditions and material
properties, which are given in Table 1.
Fig. 1. a) Geometric view of PV module without a cooling system, b) generated mesh for finite element solver
The finite element method (FEM) was employed to simu-
late the heat transfer and fluid flow in the photovoltaic (PV)
cooling system model. The computational domain was dis-
cretized using a high-resolution mesh to ensure numerical
accuracy and convergence stability. The total and spectral
components of solar irradiance, as well as their modeling
aspects, have been extensively discussed in several studies
[1–3], which play a crucial role in the simulation of photo-
voltaic systems.
The mesh consisted of 3,229,766 tetrahedral elements
used for volumetric discretization, while 934,496 triangular
elements were used on surfaces to capture boundary inter-
actions effectively. Additionally, 22,347 edge elements and
296 node (vertex) elements were included to define the do-
main boundaries and intersections precisely. This mesh
configuration allowed for detailed resolution of thermal
gradients and laminar flow characteristics within the cool-
ing channel. The simulations were performed using COM-
SOL Multiphysics, employing the Laminar Flow and Heat
Transfer in Solids and Fluids interfaces. A time-dependent
solver was used to capture the transient behavior of the
system under varying flow conditions, ensuring a compre-
hensive understanding of thermal performance across dif-
ferent flow velocities.
Table 1. Mesh size for finite element solver
Mesh feature Value
Tetrahedron 3.229.766
Triangle 934.496
Edge element 22.347
Node element 296
The optical properties of photovoltaic module surfaces,
particularly the influence of reflectivity on efficiency, have
been specifically investigated [4].
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Fig. 2 illustrates the surface temperature distribution of the photovoltaic (PV) module without the cooling system during
the daytime period from 08:00 to 19:00. The temperature distribution reveals that the central region of the PV module
experiences the highest thermal load, reaching a maximum of approximately 321 K. This is attributed to the concentration
of absorbed solar radiation and reduced convective heat loss in the middle portion. In contrast, the peripheral areas of
the PV module, especially near the edges, exhibit comparatively lower temperatures due to increased exposure to ambi-
ent air and enhanced natural convection, maintaining values closer to the surrounding ambient temperature.
Fig. 2. Surface temperature variation. PV module without a cooling system
Fig. 3 presents the surface temperature variation of the PV
cells without a cooling system, measured at three repre-
sentative points: T1, T2, and T3. The temperature at T1, lo-
cated near the central region of the PV surface, reached a
peak value of approximately 320 K at around 14:00, indicat-
ing the highest thermal exposure. In contrast, the temper-
atures recorded at T2 and T3, positioned closer to the mod-
ule's edge and lower sections, were slightly reduced,
maintaining values around 315 K. These differences high-
light the uneven thermal distribution across the PV module
surface in the absence of active cooling.
Fig. 4 illustrates the surface temperature variation of the
PV cells without a cooling system at T4, T5, and T6 points.
At T4 point, the maximum temperature was about 319 K,
and at T5 and T6 points, it was approximately 314 K.
Setting the problem. In this study, a photovoltaic (PV)
panel cooling system is numerically modeled using COM-
SOL Multiphysics to investigate the effect of water flow
over the panel surface on heat dissipation and thermal ef-
ficiency. The model incorporates a rectangular-shaped wa-
ter duct placed above the PV module to serve as the active
cooling mechanism.
The water flows through the duct at a constant inlet veloc-
ity of 0.3 m/s, which is studied under laminar flow condi-
tions (Re < 2300). The flow domain is modeled using the
"Laminar Flow" interface, while heat transfer within both
the solid PV module and the fluid is captured using the
"Heat Transfer in Solids and Fluids" interface [5]. The sys-
tem is simulated in 3D with realistic boundary conditions
for both thermal and fluid flow.
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The rectangular cooling duct is characterized by a cross-sec-
tional width (w) and height (h), and its hydraulic diameter is
calculated to analyze convective heat transfer. The solar ra-
diation incident on the PV surface leads to heat generation,
which is transferred to the flowing water above through con-
vective mechanisms. The temperature distributions on the
PV surface and within the water, as well as the thermal effi-
ciency, are key parameters evaluated in the model.
Fig. 3. Surface temperature variation. PV cells without a cooling system at T1, T2, T3 points
Fig. 4. Surface temperature variation. PV cells without a cooling system at T4, T5, T6 points
To assess the system performance, several important ther-
mophysical and performance parameters are computed,
including:
− Convective heat transfer coefficient (h)
− Heat flux (q'')
− Reynolds and Nusselt numbers (Re, Nu)
− Pressure drop (ΔP) along the duct
− Cooling system thermal efficiency (η)
The heat removal by the water significantly reduces the PV
surface temperature, which can potentially improve the
electrical efficiency of the photovoltaic panel.
Fig. 5 a) presents a geometric view of the PV module with a
cooling system, b) a geometric view of the PV module’s
back side. The frame of the PV system is made of aluminum.
PV cells are considered silicon. Thermophysical properties
of materials are provided in Table 3. Simulations are con-
ducted depending on the boundary conditions, which are
given in Table 2.
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Відновлювана енергетика. № 4/2025 | Сонячна енергетика
Fig. 5. Geometric view of PV module with a cooling system
Table 2. Boundary conditions
Name Expression Description
U0 0,3 [m/s] Inlet velocity
A 0,992 [m2] Area of PV surface
Tin
293,15 [K]
Inlet temperature
Tinitial Initial temperature
A study conducted by Aad Odeh and Ilyas Aden presents a
MATLAB-based energy model of a photovoltaic/thermal
(PV/T) hybrid panel for residential hot-water supply. Their
model demonstrates high accuracy compared to experi-
mental results, with a temperature prediction error ranging
from –8% to 6%. Analyses indicate that the proposed PV/T
panel has an approximate total daily energy efficiency of
45% compared to a simple PV panel, meaning it is more
than twice as efficient [6].
Table 3. Material properties
Material Heat capacity at constant pressure Thermal conductivity Density
Si - Silicon 700 𝐽/(𝑘𝑔 ∙ 𝐾) 131 [W/(m·K)] 2329 [kg/m3]
Water 4200 𝐽/(𝑘𝑔 ∙ 𝐾) 0,598 [W/(m·K)] 998 [kg/m3]
Aluminum 900 𝐽/(𝑘𝑔 ∙ 𝐾) 238 [W/(m·K)] 2700 [kg/m3]
In addition to energy storage methods, Tursunov and his
co-authors investigated the role of solar radiation side re-
flectors in enhancing the optical concentration on photo-
voltaic modules. Their findings demonstrated that the use
of properly aligned reflectors can substantially increase
incident solar radiation on the panel surface, thereby im-
proving power generation without increasing the active
photovoltaic area [7]. Research conducted by Cristhian
Pomares-Hernández and co-authors involved the compu-
tational modeling of passive and active cooling methods
to improve the efficiency of photovoltaic panels. Their re-
sults show that active cooling systems (e.g., via water cir-
culation) significantly improve efficiency, but require
more energy and technical resources. Passive cooling
methods, on the other hand, stand out for their simplicity
and low cost, though the degree of efficiency improve-
ment is lower than that of active systems. Therefore, the
authors emphasize the importance of selecting the opti-
mal cooling method based on the climatic conditions [8].
In their research, Menacer and co-authors investigated
the impact of cooling methods via air, water, and porous
media on the efficiency of photovoltaic panels. The results
revealed that water-based cooling systems provided the
highest efficiency, while air cooling, though simple and in-
expensive, offered limited efficiency gains. Additionally,
heat exchange through porous materials presented an op-
portunity to further improve efficiency [9]. The depend-
ence of module performance on temperature has been
thoroughly analyzed in both theoretical and experimental
research [10-11]. The development of photovoltaic tech-
nologies and their potential for power generation are
comprehensively reviewed in the literature [12]. Further-
more, the effects of various cooling methods, particularly
evaporative cooling, on module efficiency have also been
highlighted in numerous studies [13]. In their work,
Bevilacqua and co-authors developed a novel thermal
model based on a cooling method that involves spraying
water onto the back surface of PV panels. According to the
research results, the water-spraying system can signifi-
cantly reduce the panel temperature and increase electri-
cal efficiency, which ensures the stable operation of PV
systems in hot climatic conditions [14].
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Відновлювана енергетика. № 4/2025 | Сонячна енергетика
Fig. 6. Generated mesh for PV domains
The generated mesh for PV domains is illustrated in Fig. 6.
Variable solar radiation during the day is applied as a
function for application. Variation of solar radiation during
the day is given in Table 4.
Table 4. Solar radiation during the day
t (h) 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00
𝐼0 (𝑊/𝑚2) 250 450 650 800 950 1000 950 800 600 400 200
The Finite Element Method (FEM) was utilized to model the
thermal and fluid flow behavior of a photovoltaic (PV) mod-
ule integrated with cooling systems. The computational do-
main was discretized into a highly refined mesh consisting
of over 4.4 million elements, predominantly tetrahedral,
along with pyramidal and prismatic elements to accurately
capture complex geometries such as cooling channels and
layered PV components. The mesh density and element dis-
tribution were carefully designed to balance accuracy and
computational efficiency, with finer elements concentrated
in regions of steep temperature gradients and fluid flow
variations. The mesh size directly influences the accuracy of
the FEM solution: smaller element sizes enhance the reso-
lution of thermal and fluid dynamic fields, reducing numer-
ical error in accordance with the element interpolation or-
der. However, finer meshes substantially increase
computational costs, necessitating strategic mesh refine-
ment in critical areas while coarsening fewer sensitive
zones. This approach ensures precise prediction of the cou-
pled heat transfer processes within the PV module and its
cooling system, enabling an effective analysis of the mod-
ule’s thermal performance (Table 5).
Table 5. Mesh size for finite element solver
Mesh feature Value
Number of elements 4.407.682
Tetrahedron 4.019.594
Pyramids 4.200
Prism 383.888
Triangle 1.090.275
Rectangles 940
Edge element 45.905
Node element 499
Variable expressions given in Table 6 are inserted into
COMSOL Multiphysics to define the spatially and tempo-
rally dependent parameters necessary for the simu-
lation. These variables serve to accurately represent the
physical properties and boundary conditions of the PV
module and its cooling system, enabling precise coupling
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Відновлювана енергетика. № 4/2025 | Сонячна енергетика
between thermal and fluid flow phenomena. By incorpo-
rating these expressions, the model can dynamically ac-
count for variations in material properties, heat sources,
and convective heat transfer coefficients throughout the
simulation domain. This approach enhances the fidelity
of the numerical analysis and ensures that the results
closely reflect the real operating conditions of the sys-
tem.
The graph showing the variation of solar radiation versus
time on the day the experiment was conducted is shown in
Fig. 7.
Table 6. Variable mathematical expressions for defining parameters
Variable Expression Description
A_cross 𝑤 ∙ ℎ Cross-sectional area of the rectangular tube (m²)
D_h (2 ·w · h) / (w + h) Hydraulic diameter of rectangular duct (m)
Re 𝜌 · u · D_h) / 𝜇 Reynolds number (dimensionless)
Pr (𝐶𝑝 · 𝜇) / k Prandtl number (dimensionless)
Nu
If (Re < 2300, 3.66, 0.023 ·Re^0.8 ·
Pr^0.4)
Nusselt number (empirical correlation)
h Nu ·k/ D_h Convective heat transfer coefficient (W/m²·K)
hf h · (T_wall - T_bulk) Convective heat flux (W/m²)
q'' hf Convective heat flux magnitude (W/m²)
eta_th (m·𝐶𝑝· (T_out - T_in)) / (A_PV·G) Thermal efficiency of the cooling system (dimensionless)
∆P p_in - p_out Pressure drop across the tube (Pa)
Fig. 7. Variation of daily solar radiation
For Heat Transfer in Solid
Following equation is utilized for solving the Heat Transfer
in Solids Interface.
𝜌𝐶𝑝 (
𝜕Т
𝜕𝑡
+ 𝒖𝑡𝑟𝑎𝑛𝑠 ∙ ∇Т) + ∇ ∙ (𝒒 + 𝒒𝑟) = −𝛼Т:
𝑑𝑆
𝑑𝑡
𝑄 (1)
For a steady-state problem the temperature does not
change with time and the terms with time derivatives
disappear.
The first term on the right-hand side of equation 1 is the
thermoelastic damping and accounts for thermoelastic
effects in solids:
𝑄𝑡𝑒𝑑 = −𝛼𝑇:
𝑑𝑆
𝑑𝑡
(2)
It should be noted that the d ⁄ dt operator is the material
derivative, as described in the Time Derivative subsection
of Material and Spatial Frames.
For Heat Transfer in Fluids
The Heat Transfer in Fluids Interface solves for the
following equation:
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Відновлювана енергетика. № 4/2025 | Сонячна енергетика
ρСр (
𝜕Т
𝜕𝑡
𝑢 ∙ ∇Т) + ∇ ∙ (𝑞 + 𝑞𝑟) = 𝛼𝑝Т (
𝑑𝑝
𝑑𝑡
+ 𝑢 ∙ ∇𝑝) + 𝜏: ∇𝑢 + 𝑄 (3)
the Cauchy stress tensor, σ, is split into static and deviatoric
parts as in:
𝜎 = −𝑝𝐼 + 𝜏 (4)
for ideal gases, the thermal expansion coefficient takes the
simpler form αp = 1 ⁄ T
𝛼𝑃 =
1𝜕𝜌
𝜌𝜕𝑇
(5)
For a steady-state problem, the temperature does not
change with time and the terms with time derivatives
disappear. The first term of the right-hand side of equation
12 is the work done by pressure changes and is the result
of heating under adiabatic compression as well as some
thermoacoustic effects. It is generally small for low Mach
number flows.
𝑄𝑃 = 𝛼𝑃Т (
𝑑𝑝
𝑑𝑡
+ 𝑢 ∙ ∇𝑝) (6)
The second term represents viscous dissipation in the fluid:
𝑄𝑣𝑑 = 𝜏: ∇𝑢 (7)
In Fig. 8, we can observe the variation process of the sur-
face temperature of the photovoltaic module with a cool-
ing system during the experiment.
Fig. 8. Surface temperature variation. PV module with a cooling system
The surface temperature distribution of the PV system with
integrated cooling channels is presented in Figure 8. It can
be observed that the majority of the surface maintains a
relatively uniform temperature around 298 K. However, the
section of the PV module near the outlet of the cooling
channel experiences higher temperatures, reaching a max-
imum of approximately 312 K. This localized temperature
rise is attributed to the reduced cooling efficiency and ac-
cumulated heat near the channel exit.
The temperature variation of PV cells was investigated at
T1, T2, and T3 points in Fig. 9. Maximum PV cell tempera-
ture was observed at the T1 point, reaching approximately
305 K, while the temperature at the T2 point was 298.5 K.
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The minimum temperature of the PV cells occurred at the
T3 point, indicating the most effective cooling region. This
spatial temperature difference suggests that the cooling
performance varies along the surface of the PV panel, likely
due to differences in fluid flow distribution and heat trans-
fer intensity.
The thermal distribution across the PV surface was further
assessed at three monitoring locations labeled T4, T5, and
T6 in Fig. 10. Among these, the T4 location exhibited the
highest temperature, reaching approximately 305K, sug-
gesting limited convective heat transfer in that region. In
contrast, the T5 point showed a moderate temperature of
298.5 K, while the lowest temperature was recorded at T6,
highlighting the area with the most effective cooling per-
formance. These variations underline the non-uniform na-
ture of heat removal across the panel surface due to flow
dynamics and localized heat transfer rates.
Fig. 9. Surface temperature variation. PV cells at T1, T2, T3 points
Fig. 10. Surface temperature variation. PV cells at T4, T4, T4 points
The variation in outlet water temperature from the cooling
tube channels is presented in Fig. 11. It can be observed
that the outlet temperature reached a peak of approxi-
mately 308.15 K between 14:00 and 16:00, indicating the
highest thermal gain from the PV surface during this period
of peak solar irradiance.
Fig. 12 presents the diurnal variation in the amount of heat
removed by the cooling water from 08:00 to 20:00. As
shown, the heat removal rate increases sharply in the morn-
ing, reaching its peak value of approximately 3500 W around
14:00, coinciding with the period of maximum solar irradi-
ance. Afterward, the heat extraction gradually declines to-
ward evening. This trend reflects the direct influence of solar
input on the thermal load of the PV system and the effective-
ness of the water-based cooling strategy in mitigating tem-
perature rise during peak operational hours.
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Fig. 11. Outlet temperature variation of water
Fig. 12. The amount of heat removed by water
Fig. 13 illustrates the temporal variation of pressure at the
inlet (left) and outlet (right) of the cooling channel between
08:00 and 20:00. At the inlet, the pressure initially starts at
approximately 1.015 × 10⁵ Pa and rapidly decreases to
around 1.0133 × 10⁵ Pa shortly after the system starts op-
eration. This pressure remains relatively constant through-
out the rest of the day, indicating a steady-state flow con-
dition at the inlet after initial transients.
In contrast, the outlet pressure exhibits a slight variation
over time. It begins around 1.0133 × 10⁵ Pa, reaches a peak
near 1.0148 × 10⁵ Pa, then gradually decreases before rising
slightly again toward the evening. The minor fluctuation in
outlet pressure suggests changes in the flow resistance or
thermal expansion effects within the cooling channel as the
temperature of the working fluid varies with solar intensity.
Fig. 14 presents the time-dependent variation of the pres-
sure drop across the cooling tube from 08:00 to 20:00. At
the start of the simulation, a sharp pressure drop of
approximately 170 Pa is observed, occurring around 08:00,
which likely corresponds to the initial acceleration phase of
the cooling fluid within the channel. Shortly after, the pres-
sure drop rapidly stabilizes to a nearly constant value of
about 6–7 Pa for the remainder of the day. This significant
initial transient, followed by a stable pressure drop, sug-
gests the system quickly reaches a steady-state flow condi-
tion. The low magnitude of pressure drop after the initial
peak further confirms that the laminar flow regime is dom-
inant and that the hydraulic resistance within the tube is
minimal. Such behavior is typical in well-designed cooling
channels where the flow distribution is uniform and fric-
tional losses are limited.
Fig. 15 illustrates the temporal variations of the Reyn-
olds and Prandtl numbers over the course of the day.
These dimensionless parameters are critical in charac-
terizing the flow and heat transfer behavior within the
cooling channel. The Reynolds number variation reflects
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Відновлювана енергетика. № 4/2025 | Сонячна енергетика
changes in fluid velocity and viscosity, indicating the flow
regime, while the Prandtl number represents the ratio of
momentum diffusivity to thermal diffusivity, highlighting
the relative thickness of the velocity and thermal bound-
ary layers. The Reynolds number increased progressively
with flow velocity and reached a maximum value of
approximately 5500, indicating a transition towards tur-
bulent flow conditions. In contrast, the Prandtl number
remained relatively constant at around 7, reflecting the
thermal diffusivity characteristics of the working fluid,
which is consistent with the properties of water at mod-
erate temperatures.
Fig. 13. Variation of pressure at the inlet and outlet of the cooling channel
Fig. 14. Pressure drops across the tube
Fig. 15. Variations of Reynolds and Prandtl numbers
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Відновлювана енергетика. № 4/2025 | Сонячна енергетика
Fig. 16 investigates the changes in the Nusselt number dur-
ing the given time interval. It can be seen that the maximum
value of the Nusselt number was observed at 43 around
14:00. After that, the property started to decrease signifi-
cantly, reaching 39.5 at 20:00.
Fig. 16. Nusselt number change
3. Results and Discussion
The temperature variations at points T1, T2, T3, T4, T5, and
T6, as shown in Fig. 17 and Fig. 18, are numerically compared
for PV modules without and with cooling systems. Fig. 17 and
Fig. 18 illustrate that the temperatures at points T1, T2, T3,
T4, T5, and T6 in the PV module without cooling channels are
significantly higher than those in the module equipped with
cooling channels. This temperature difference highlights the
impact of thermal management on the performance of the
PV module, as elevated temperatures are known to reduce
photovoltaic efficiency. Therefore, the inclusion of cooling
channels contributes to a more uniform temperature distri-
bution, which in turn helps maintain more consistent and im-
proved efficiency across the PV module.
To ensure consistency between modeling and experimental
results, the international standard ISO 9845-1 was adopted as
a reference for standardized solar irradiance conditions [15].
The following analysis compares the temperature-depend-
ent current-voltage (I–V) characteristics and efficiency var-
iations of photovoltaic (PV) panels. M1 refers to the PV
module without a cooling channel, while M2 refers to the
module equipped with a cooling channel. The model as-
sumes the following initial parameters: Standard Test Con-
ditions (STC, 25 °C, 1000 W/m²): Voc = 40 V, Isc = 9 A, η =
18 %, Temperature coefficients:
Voc → – 0,30 %/°C
Isc → + 0,05 %/°C
Pmax → – 0,45 %/°C
Fig. 17. Temperature variation of PV modules with and without cooling channels at different points. M1 is PV module
without cooling channel, M2 is PV module with cooling channel
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Відновлювана енергетика. № 4/2025 | Сонячна енергетика
Fig. 18. Temperature variation of PV modules with and without cooling channels at different points. M1 is PV module
without cooling channel, M2 is PV module with cooling channel
The temperature of the photovoltaic panel was determined
at points T1–T6 using Fig. 17 and Fig. 18. The I–V
characteristics recorded at 14:00 are presented in the fol-
lowing table:
Table 7. Effect of temperature on the current-voltage characteristics and efficiency of the photovoltaic module
Criteria M1 (without cooling) M2 (cooled) Achievement
Photovoltaic (PV) panel temperature, °C 44.9 30.9 ↓ 14 °C
Open-circuit voltage, Voc 32.6 V 38.4 V +18 %
Short-circuit current, Isc 9.9 A 9.8 A ≈ equal
Maximum power, Pmax 225 W 265 W +18 %
Efficiency, η 16.3 % 18.4 % +2.1 abs. = +13 %
Current-Voltage Characteristics:
At higher temperatures (M1), the open-circuit voltage (Voc)
decreases, and the I–V curve shifts downward and to the
left, leading to a reduction in maximum power. The cooled
module (M2), however, mitigates these losses and broad-
ens the curve.
Efficiency and Temperature:
Each 1 °C increase in temperature results in approximately
a 0.45% power loss. For the M2 module, maintaining a tem-
perature 15 °C lower provides a relative efficiency gain of
about 6.5% (≈2% absolute).
This analysis was performed using a simplified parametric
model. For an actual device, it is recommended to use the
precise coefficients (αVoc, βIsc, γPmax) provided by the
manufacturer, along with the exact daily solar irradiance
profile.
Conclusions
Based on the calculations performed through mathemati-
cal modeling, the temperature-dependent performance
characteristics of photovoltaic (PV) modules were thor-
oughly analyzed, and the effect of cooling channels on effi-
ciency was determined. The graphs and Table 7 illustrate
the temperature variations at points T1–T6 and the corre-
sponding differences in efficiency between PV modules
without cooling channels (M1) and those equipped with a
cooling system (M2).
According to the simulation results, in the M1 case, the PV
module temperature reached a maximum of 44.9 °C,
whereas in the M2 case, it remained around 30.9 °C. Such
a significant difference arises due to the effective removal
of heat from the modules by the cooling system. An in-
crease in the temperature of photovoltaic panels nega-
tively affects their electrical characteristics—particularly,
the open-circuit voltage (Voc) decreases as the tempera-
ture rises. This reduction leads to a decrease in the overall
maximum power output and efficiency of the module.
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Відновлювана енергетика. № 4/2025 | Сонячна енергетика
At 14:00, the I–V characteristic graph demonstrated this ef-
fect clearly: in the M1 case, the Voc value was approxi-
mately 32.6 V, while in the M2 case, it reached 38.4 V, rep-
resenting an increase of about 18%. Although the short-
circuit current (Isc) was not significantly affected by tem-
perature, the overall maximum power (Pmax) was substan-
tially higher in the M2 case – 225 W for M1 versus 265 W
for M2 (more than an 18% gain).
The efficiency graph further shows that the efficiency of
photovoltaic modules decreases linearly with increasing
temperature. For M1, the maximum efficiency was about
16.3%, while for M2 it reached 18.4%. This indicates an ab-
solute efficiency gain of 2.1% (approximately 13% relative
improvement) when a cooling system was employed. Re-
ducing the module temperature by 15 °C through cooling
led directly to this level of efficiency enhancement.
In conclusion, the temperature sensitivity of photovoltaic
modules significantly impacts their overall operational effi-
ciency. The integration of cooling channels not only helps
maintain the module temperature under control but also
increases the power output and substantially improves the
overall energy yield. Particularly in hot climates or during
summer months, such passive cooling systems are a critical
factor for maintaining stable PV performance. This ap-
proach can be regarded as one of the key technological so-
lutions for developing environmentally friendly, energy-ef-
ficient, and reliable photovoltaic systems.
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http://dx.doi.org/10.1115/1.4065552
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http://dx.doi.org/10.3390/app112311370
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| id | veorgua-article-584 |
| institution | Vidnovluvana energetika |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:17:57Z |
| publishDate | 2025 |
| publisher | Institute of Renewable Energy National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | veorgua/4a/ee898861619400319e470ce5b61b184a.pdf |
| spelling | veorgua-article-5842026-07-18T06:32:23Z COMPUTER MODELING ANALYSIS OF PHOTOVOLTAIC (PV) MODULES WITHOUT AND WITH INTEGRATED COOLING SYSTEMS КОМП’ЮТЕРНИЙ МОДЕЛЮВАЛЬНИЙ АНАЛІЗ ФОТОЕЛЕКТРИЧНИХ МОДУЛІВ БЕЗ ІНТЕГРОВАНИХ СИСТЕМ ОХОЛОДЖЕННЯ ТА З НИМИ Axtamov , T. Z. Pundev , V. PV panels, modeling, heat transfer, COMSOL Multiphysics, cooling system, energy efficiency. ФЕ-панелі, моделювання, теплопередача, COMSOL Multiphysics, система охолодження, енергоефективність. This article presents the results of a study focused on modeling the thermal and electrical characteristics of photovoltaic (PV) solar panels. The study analyzes the temperature distribution, thermal energy generation, and the effect of cooling systems on PV panels using numerical methods. In particular, it evaluates the relationship between surface temperature and efficiency of the panels under conditions with and without cooling channels. The modeling is performed in COMSOL Multiphysics software, utilizing the finite element method (FEM) to account for both fluid flow and heat transfer. The obtained results demonstrate the potential for enhancing the electrical efficiency of PV panels through thermal management and have significant practical importance in adapting solar energy systems to various climatic conditions. У цій статті наведено результати дослідження, спрямованого на моделювання теплових та електричних характеристик сонячних фотоелектричних (ФЕ) панелей. У дослідженні проаналізовано розподіл температури, генерацію теплової енергії та вплив систем охолодження на ФЕ-панелі з використанням чисельних методів. Зокрема, оцінено взаємозв’язок між температурою поверхні та ефективністю панелей за умов із наявністю та без наявності охолоджувальних каналів. Моделювання виконано в програмному середовищі COMSOL Multiphysics із використанням методу скінченних елементів (МСЕ) для врахування як руху рідини, так і теплопередачі. Отримані результати демонструють можливість підвищення електричної ефективності ФЕ-панелей шляхом теплового керування та мають важливе практичне значення для адаптації сонячних енергетичних систем до різних кліматичних умов. Institute of Renewable Energy National Academy of Sciences of Ukraine 2025-12-27 Article Article application/pdf https://ve.org.ua/index.php/journal/article/view/584 10.36296/1819-8058.2025.4(83).195-208 Vidnovluvana energetika ; No. 4(83) (2025): Scientific and applied Journal renewable energy ; 195-208 Возобновляемая энергетика; ##issue.no## 4(83) (2025): Scientific and applied Journal renewable energy ; 195-208 Відновлювана енергетика; № 4(83) (2025): Науково-прикладний журнал Відновлювана енергетика; 195-208 2664-8172 1819-8058 10.36296/1819-8058.2025.4(83) en https://ve.org.ua/index.php/journal/article/view/584/495 Copyright (c) 2025 T. Z. Axtamov , V. Pundev https://creativecommons.org/licenses/by-nc-nd/4.0 |
| spellingShingle | PV panels modeling heat transfer COMSOL Multiphysics cooling system energy efficiency. Axtamov , T. Z. Pundev , V. COMPUTER MODELING ANALYSIS OF PHOTOVOLTAIC (PV) MODULES WITHOUT AND WITH INTEGRATED COOLING SYSTEMS |
| title | COMPUTER MODELING ANALYSIS OF PHOTOVOLTAIC (PV) MODULES WITHOUT AND WITH INTEGRATED COOLING SYSTEMS |
| title_alt | КОМП’ЮТЕРНИЙ МОДЕЛЮВАЛЬНИЙ АНАЛІЗ ФОТОЕЛЕКТРИЧНИХ МОДУЛІВ БЕЗ ІНТЕГРОВАНИХ СИСТЕМ ОХОЛОДЖЕННЯ ТА З НИМИ |
| title_full | COMPUTER MODELING ANALYSIS OF PHOTOVOLTAIC (PV) MODULES WITHOUT AND WITH INTEGRATED COOLING SYSTEMS |
| title_fullStr | COMPUTER MODELING ANALYSIS OF PHOTOVOLTAIC (PV) MODULES WITHOUT AND WITH INTEGRATED COOLING SYSTEMS |
| title_full_unstemmed | COMPUTER MODELING ANALYSIS OF PHOTOVOLTAIC (PV) MODULES WITHOUT AND WITH INTEGRATED COOLING SYSTEMS |
| title_short | COMPUTER MODELING ANALYSIS OF PHOTOVOLTAIC (PV) MODULES WITHOUT AND WITH INTEGRATED COOLING SYSTEMS |
| title_sort | computer modeling analysis of photovoltaic (pv) modules without and with integrated cooling systems |
| topic | PV panels modeling heat transfer COMSOL Multiphysics cooling system energy efficiency. |
| topic_facet | PV panels modeling heat transfer COMSOL Multiphysics cooling system energy efficiency. ФЕ-панелі моделювання теплопередача COMSOL Multiphysics система охолодження енергоефективність. |
| url | https://ve.org.ua/index.php/journal/article/view/584 |
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