Mitigating PV cell cracking in solar photovoltaic thermal collectors with a novel H-pattern absorber design

This paper introduces a novel absorber design for a Solar Photovoltaic Thermal (PVT) collector, specifically addressing the persistent issue of cell cracking induced by thermal expansion. Despite considerable research efforts to advance PVT technology, cell cracking remains a critical challenge, contributing to decreased collector efficiency. In contrast to previous studies, this research adopts a unique approach. A novel PVT design is proposed, featuring an aluminium alloy structure with a distinctive ’ H ’ -shaped pattern of expansion cavities positioned between Photovoltaic (PV) cells and the absorber. This innovative design is engineered to mitigate thermal expansion and optimize the overall performance of the collector. A 3-D Computational Fluid Dynamic model, simulated using ANSYS software, validates the proposed PVT design against experimental data from a reference collector. A parametric study explores various H-pattern cavity dimensions, revealing that the 2 mm H-pattern plate cavity design achieves the lowest directional expansion, minimizing the risk of breakage. Results show that the proposed design outperforms the reference collector by 10 %, 2 %, and 8 % in thermal, electrical, and overall efficiency, respectively. Furthermore, the H-pattern design reduces thermal expansion by 20 %, enhancing structural resilience and minimizing the likelihood of PV cell cracking. This study represents a significant advancement in PVT technology, providing a practical and easily implementable solution to the critical issue of cell cracking and presenting an optimal design for real-world applications.


Introduction
Climate change is one of our generation's most serious environmental, technological, economic, and social challenges [1].To reduce the effects of global warming to acceptable levels, global greenhouse gas emissions must be drastically reduced.For this, Renewable Energy Technologies (RET) are required to reduce these emissions or achieve a net-zero economy.RETs such as wind, solar, hydropower, and biomass can replace fossil power plants in the energy supply sector [1].Studies show that Photovoltaic Thermal (PVT) collectors are a technology with significant potential to lower the carbon footprint of photovoltaic electricity and solar thermal energy compared to conventional solar systems [2,3].PVT collectors are a promising renewable technology that combines the solar generation of electricity and heat in a single component [4].Conventional Photovoltaic (PV) modules convert about 20-25 % of incident solar radiation into electricity, leaving the majority of the solar resource unused, known as losses (optical and thermal) [4].Hybrid PVT collectors, on the other hand, transfer the heat losses from a conventional PV module to a fluid that circulates behind the PV cells in a thermal absorber.PVT collectors produce electricity and heat in the same area, potentially achieving the highest solar efficiency while utilizing minimal surface area.The IEA (International Energy Agency) technology roadmap on solar heating and cooling recommends "developing the PVT technology to make it commercially viable" due to the energy benefits of PVT collectors [5].
Due to the abundance and inexhaustibility of solar resources, solar thermal collectors and photovoltaic panels are recognized as practical solutions for gathering and converting solar energy into usable energy.Approximately 80 % of the solar energy that the PV module collects is not converted, resulting in a rise in operating temperature and hastening the aging and efficiency decline of the PV module [6].PV cells that operate in hot and sunny environments (such as in tropical or desert regions or during the summer in temperate areas) typically exhibit lower efficiencies because of the significantly hot surrounding temperatures [6].A PVT collector's combined thermal and electrical cogeneration is an efficient way to reduce the amount of solar radiation lost to heat dissipation and regulate the temperature of the PV modules [6].There are several ways to control the temperature of photovoltaic panels, including air cooling, water cooling, heat pipes, phase change materials, and thermoelectric cooling.Considerable amounts of research have been invested into creating hybrid PVT technology in previous years.This study partly focuses on several highly significant studies and experiments conducted in recent years which is discussed in following subsections.This includes various designs for the thermal absorber/ absorber, materials for different components, and simulation methods for the PVT collectors, which are discussed in the following sub-sections.The results of these studies are expressed in terms of either the electrical and thermal performance or overall performance, known as efficiency.

PVT collectors with different absorber designs
To commence the investigation, it is important to note that design elements and operational and climatic factors can all affect PVT performance in several ways.This is why numerous designs have been suggested to increase the heat transfer rate by providing a cooling effect for the PV cells and, thus, enhancing the overall PVT performance [7,8,9].This section focuses on collectors with different thermal absorber designs (i.e., pattern and flow of the pipes) that have intriguing electrical and thermal efficiency values based on literature.The PV cells/module used in these studies are not exactly state-of-the-art, but improvements have been made in the performance of the existing modules by providing a cooling effect with the help of new absorber designs.
A study on micro heat pipe arrays (MHPAs) in air-cooled PVT systems demonstrated a 22.8 • C temperature reduction in PV cells, resulting in a 1.42 % improvement in electrical efficiency and a 30.9 % increase in power generation efficiency.With average thermal and electrical efficiencies of 37.10 % and 13.56 %, respectively, this research provides valuable insights for industrial producers considering energyefficient solutions in air-cooled PVT systems [7].
Misha et al. [8] investigated a dual oscillating absorber copper pipeline flow in a PVT water system in 2020.Numerical simulations using ANSYS predicted outlet water temperature and collector surface temperature under varying irradiation levels, mass flow rates, and inlet water temperature.Outdoors experiments in Malaysian weather revealed a maximum average thermal efficiency of 59.6 %, with electrical efficiencies peaking at 13.8 % for PV panels and 12.7 % for the PVT water system at a mass flow of 6 lit/min, indicating improved efficiency with increased mass flow.Maghrabie et al. [9] employed Computational Fluid Dynamics (CFD) to model a flat-box PVT collector, investigating parameters like tube height, flow rate, and temperature.The study revealed that increasing tube height was the most effective means to enhance temperature distribution uniformity, improving collector efficiency.The electrical efficiency was low (11.06 %) due to the use of multi-crystalline PV with inherently lower energy conversion rates.
Al-Shamani et al. [10] proposed an innovative elliptical collector design positioned beneath a PV module, using water as the heat transfer medium.Achieving an electrical efficiency of 13.7 % and a combined PVT efficiency of 74.3 %, improvements in the absorber-PV panel interface through Ethylene-Vinyl-Acetate (EVA) lamination was suggested for enhanced efficiency in PVT systems, along with the use of specific PV cell types, such as amorphous silicon cells with black mat surface features, to augment thermal absorption.Ranjan et al. [11] studied an innovative bifluid PVT collector featuring a spiral-shaped absorber tube with nanofluid (Al 2 O 3 in water) and air coolant systems.The study's computational investigations reveal the significance of mass flow rates and fluid selection on the PVT collector's efficiency.It highlights that efficiency increases with higher fluid flow rates, up to a certain limit, emphasizing the importance of careful flow rate optimization.S. Das et al. [12] investigated the impact of various design parameters on the thermal efficiency of a novel solar air heater using jet impingement through conical protruded nozzles.The results

A
Area,m Various authors have contributed by presenting several ideas that have enhanced the performance of the PVT collectors.Absorber designs with extended fins offer a method for increasing the heat transfer rate.However, larger fin lengths may increase the absorber's overall weight, and consequently, the overall efficiency will decrease.The designs should be developed so that the available area is used effectively and will have fewer losses.It can be observed that PVT collectors have additional potential to compete in the market using different absorber designs in order to enhance their overall performance.

PVT collector components with different materials
This section discusses the use of various materials for collector components.Researchers, including Mahdi et al. [13], explored materials for PVT collectors, presenting a hybrid design with a copper sheet and a polymethyl-methacrylate thermal absorber.Their experiments demonstrated a cooling effect, enhancing electrical efficiency by 0.3 % per • C reduction from the initial 10.91 %, while maintaining a thermal efficiency of approximately 80 %.Vaishak et al. [14], incorporated a glazed flat plate PVT collector, solar cell, and transparent materials like TPT (Tedlar-polyester-Tedlar) and EVA, demonstrated enhanced efficiency (50 % overall, 40 % daily thermal).The use of EVA encapsulation improved absorber-PV module contact, enhancing heat transfer and overall system performance.
In a study by Rahmatmand et al. [15], the performance of a low-cost, uninsulated PVT collector was compared with a back-insulated counterpart, incorporating three different insulation materials at varying thicknesses.Experimental data served as boundary conditions for simulations, evaluating collector configurations with respect to solar radiation, mass flow rate, and fluid inlet temperature.The insulated units exhibited enhanced thermal efficiency, ranging from 47.1 % to 47.5 %, a 4 % improvement over uninsulated models.Additionally, electrical efficiency for the collector with insulation reached 13.7 %, marginally lower (0.05 %) than the uninsulated variant.These findings underscore the efficacy of rear insulation in minimizing thermal losses and augmenting overall collector efficiency under standard operating conditions.
It can be concluded from the studies that the variation in efficiencies, especially thermal efficiencies, can be affected depending on the materials used for the PVT collectors.Regarding thermal absorbers and PV cell encapsulation, materials with increased thermal conductance and decreased temperature coefficients can help improve the efficiencies by around 4 to 5 %.

PVT collectors/systems with different simulation methods
This section provides an overview of various simulation tools employed in the analysis of PVT collector performance.It outlines the currently available and widely utilized tools for assessing the performance of PVT solutions.Li et al. [16] introduced a lumped-parameter simulation model, assuming uniform temperature distribution, for analyzing PVT collectors' electrical and thermal performance.Simulated thermal values exceeded actual measurements by 25 %, while electrical energy production closely matched measurements within a 10 % range.
Panchal et al. [17] employed STAR CCM for a 3D numerical simulation, focusing on one channel's thermal boundary conditions rather than the entire cooling system.The study, utilizing the k-epsilon turbulence model, demonstrated a notable increase in thermal efficiency from 60 % to 68 %.Ahn et al. [18] enhanced the thermal performance of an air-type PVT collector by incorporating curved baffles (absorbers) for efficient heat transfer.The absorber, functioning as baffles, directly received solar radiation, resulting in thermal and electrical efficiencies of 37.1 % and 12.4 %, respectively.While STAR CMM offers precision in solving flux and heat transfer issues, its complex CFD solver prompts researchers to opt for more user-friendly software like TRYNSYS.The study emphasizes PVT collectors and system energy performance determination within the broader scope of computer-based modeling and simulation in the PVT community.

Understanding cell cracking in PV cells of PVT collector
Numerous approaches have been suggested to tackle the challenge of cell cracking in PV cells, a significant issue impacting the overall efficiency and performance of PV systems.This section offers a summary of commonly utilized strategies and tools to alleviate the consequences of these cracks.A noteworthy approach entails advancing materials and implementing design modifications to improve resistance against cell cracking, such as the creation of a metallic grid or alternative structures.Hence, it is important to explore technologies that fulfill mechanical criteria, enabling a reduction in cell thickness without compromising structural integrity [19,20].Furthermore, the literature highlights design considerations, such as busbar orientation, bypass diodes, and the number of busbars in PV modules, as integral to minimizing the impact of cell cracking and improving the overall reliability of PV systems [21].Another proposed solution involves the utilization of flexible cell metallization to prevent electrical isolation in cases of damaged cells, thereby enhancing the thermal stability of PV modules [22].
Buerhop et al. [23] comprehensively investigate PV panel cell cracking, emphasizing its significance in module behavior.The study employs field and lab conditions, revealing insights into pre-cracked module behavior through outdoor exposure and loading tests.The research highlights the temporary activity of specific cracks and underscores the need for further studies to enhance PV cell resistance to cracking.Dhimish et al. [24] offer a valuable insight into PV panel performance, exploring the impact of cell cracking on efficiency.Employing statistical analysis, electroluminescence measurements, and virtual instrumentation, the study reveals that a majority of cracks (60 %) substantially impede power output, emphasizing the importance of considering cell cracking in enhancing PV cell resilience.In another study, Dhimish et al. [25] investigate the impact of various solar cell crack modes on temperature, focusing on hotspots in PV cells.The study identifies four crack modes, highlighting their distinct effects.Crack-free and micro-cracked cells show minimal temperature variations, while shading areas and breakdown regions lead to significant temperature increases, with the worst-case hotspot scenario at shading ratios between 40 % and 60 %.Niyaz et al. [20] investigated thermal effects of cracks in crystalline silicon photovoltaic modules, emphasizing two crack types: enhanced recombination (C-ER) and loss of active area (C-LAA).Their study, validated by an electro-thermal model, highlighted C-LAA's potential to induce non-uniform thermal stresses, impacting PV efficiency under diverse operational conditions.

Overview of the study
Performance improvement and optimization in solar energy systems is a broad subject, with recent studies focusing on diverse areas of solar technologies to enhance efficiency.The study by Dabiri et al. [26] investigates thermal characteristics in a trapezoidal cavity of a linear Fresnel solar collector.Results show that increasing the cavity angle enhances total heat transfer rate but reduces heat absorbed by each tube.Radiation is identified as the dominant heat loss mechanism, constituting 85.2 % to 91.3 % of total heat transfer, with a notable impact of cavity angle compared to tube size on heat transfer rates.Mozafarifard et al. [27] studied anomalous heat conduction in the absorber plate of a flat-plate solar collector using a time-fractional single-phase-lag model.The study, validated against the dual-phase-lag model, demonstrated the FSPL model's precision in describing a wide range of thermal behaviors, including diffusive-like and wave-like patterns.Their findings underscore the importance of considering non-Fourier effects, particularly at early times, and highlight the influence of parameters such as dimensionless time, Vernotte number, thermophysical parameter, and dimensionless solar radiation on thermal distribution.
Torabi et al. [28] investigated the impact of geometrical parameters and thermal conditions on the performance of a Solar Chimney Power Plant using CFD.Their findings emphasize the influence of factors such as collector radius, divergent angle of the chimney, and radiation heat flux on power generation, highlighting an optimal performance at a divergent angle of θ = 1 .The study underscores the significance of temperature and fluid velocity in enhancing power generation and suggests exploring 4E aspects (energy, exergy, economic, and environmental) for future efficiency improvement.Esfe and Toghraie [29] conducted a numerical study investigating the impact of solar radiation intensity on freshwater productivity in solar stills equipped with a Thermoelectric Cooling System (TEC) in Semnan's hot and dry areas.Results revealed a direct correlation between radiation intensity and water production, with a significant enhancement (15 % to 62 %) observed by applying TEC, attributed to increased free convection facilitated by elevated flow temperature gradients in the solar still.
Despite the PVT potential and numerous studies over the past several years, there are still a limited number of manufacturers and installers [30], and the majority of products on the market need to be based on designs optimized specifically for PVT applications.From the reviews of PVT technology, the Research & Development progress has highlighted the need to optimize the geometrical structure of PVT collectors to improve their performance and propose new thermal-absorber configurations.At the same time, there is a strong push for significant cost reductions in all solar thermal technologies.Thus, IEA has initiated a new task (Task 60) under the Solar Heating and Cooling (SHC) program to improve the testing, modeling, and good technical characterization of PVT collectors to enhance and expand the correct inclusion of PVT technology in simulation software, and to investigate potential cost reductions in the balance of systems [31].
The solar cell is built of silicon, which is extremely thin (180 to 200 µm) [32].A critical issue for PVT collectors is cell cracking, which still needs to be addressed and is mainly caused by thermal expansion during the heat transfer process between PV cells and the thermal absorber.Due to the high temperatures, these expansions and contractions create small silicon cell flaws, which may result in numerous micro fractures/cracks.These cracks may cause the disconnection of cell parts, resulting in a reduction in the overall power generated by the PV modules, thus, leading to a lower collector efficiency [32].This also has a negative impact on productivity and lifetime.
As described, cell cracking is a critical issue that affects the performance and reliability of PVT collectors, as it can reduce the output power by 10 % and existing literature has suggested some solutions to mitigate this problem as mentioned in 1.1, 1.2, 1.3 and 1. 4. However, these solutions have some drawbacks, such as increased cost, complexity, or heat loss.Therefore, there is a need for a simple and effective modification to the PVT collector design that can address the cell cracking problem while enhancing efficiency.The main objective of this work is to propose a novel design for a PVT collector that can reduce the risk of cell cracking caused by thermal expansion and improve the electrical and thermal efficiency of the system.
Throughout this study, a unique approach has been devised to address the issue by introducing a novel PVT design aimed at reducing thermal stress on the cells.Referred to as the H-pattern, this innovative design consists of a metal structure (aluminum alloy) featuring a cavity pattern in the shape of the letter 'H.' Positioned between the solar cells and the thermal absorber, this plate mitigates the risk of cell cracking, facilitating enhanced heat conduction and resulting in elevated collector efficiencies.
The primary objective of this design is to enable the expansion of the thermal expansion plate (H-pattern plate) in all directions, achieved through its expansion into the cavities.This approach results in a minimal overall expansion in any single direction, significantly reducing the risk of cell cracking.While the utilization of metal in thermal applications traditionally poses challenges related to thermal expansion, the incorporation of expansion cavities within the H-pattern effectively addresses these concerns.
Unlike prior scientific inquiries that predominantly focused on simulating PVT collectors based on individual factors, the proposed approach encompasses a comprehensive consideration of various factors, including design parameters (dimension and pattern) and material properties, concurrently in the simulation.The outcomes derived from this approach have been instrumental in attaining heightened efficiency and mitigating mechanical stresses on the PVT collectors through the implementation of this innovative design.

Methodology and materials
After a thorough review summarizing diverse geometric configurations, thermophysical properties, and manufacturing solutions for PVT systems, this study utilizes a commercially available PVT collector [33] as the baseline, with a modified thermal absorber design that includes integrated pipes and features an H-pattern plate.The 3-Dimensional Computer Aided Drawing (CAD) model of proposed PVT collector was created in Solidworks and then imported into the ANSYS workbench for steady-state analysis.In the newly proposed design, an H-pattern plate has been inserted between the bottom EVA layer and the thermal absorber plate of the reference PVT collector, rendering it identical to the reference PVT collector except for the inclusion of the H-pattern layer.
The significance of ANSYS software lies in its 3-D graphic capabilities, allowing for intricate modeling of geometries that would be challenging with alternative software.This analysis facilitates the assessment of thermal expansion in the H-pattern plate and other components, either independently or as part of the entire collector, in response to temperature variations across different dimensions, materials, and layers.This becomes particularly crucial when dealing with diverse materials.The temperature values for the absorber were extracted from the steady-state model and utilized as boundary conditions in the ANSYS FLUENT flow analysis to determine the outlet temperature from the collector's thermal absorber.Fig. 1 illustrates the steps undertaken and the methodology employed in the simulation study.
Simulation results are validated against an experimentally derived performance curve provided by the reference collector test results [33].The 3-D CFD model of the reference PVT collector has been created and validated using experimental data.It has been utilized to assess the thermal performance of various alternative H-pattern plate geometries in the proposed modified collector.Subsequent designs are then simulated using the same model but with adjustments to capture the specifics of each alternative H-pattern plate geometry and construction material.In accordance with European Standards for solar collector testing [34], parameters such as zero-loss efficiency (ɳ 0 ), along with linear and quadratic heat-loss coefficients (c 1 and c 2 ), crucial for comparing the thermal performance of PVT collectors, can be computed based on fluid temperature rise and heat flux data obtained from simulations conducted under diverse steady-state operating conditions.Finally, a thermal structural analysis is conducted to evaluate the expansion occurring within the H-pattern plate.

Proposed PVT collector design
The commercially available PVT [33] is used as the reference PVT collector in this work.Fig. 2a shows the new collector design, which is made up of the following components (from top to bottom): (i) a transparent glass cover, (ii) a top EVA layer, (iii) a mono-crystalline silicon cells in a series connected PV module, (iv) bottom EVA layer, (v) H-pattern plate for thermal expansion, (vi) a thermal absorber that transfers heat to the heat transfer fluid (water), and (vii) an insulation layer.
The thermal absorber comprises integrated pipes as a heat exchanger, with the heat transfer fluid (water) flowing through 8 parallel aluminum pipes, each with an ellipsoid section measuring 2.275 m in length.The net area is 0.365 m 2 , the nominal PV module efficiency is 15.6 %, and the PV temperature coefficient is 0.0045 1/K.The electrical characteristics at STC are presented in Table 1 below.All PVT collector parameters relating to its various layers are kept constant in this work (dimensions, cover layers, PV cells, etc.), with only the parameters associated with the H-pattern plate varying for comparison purposes.
A thermal contact sheet for a PVT collector incorporates a pattern of through cavities to enhance thermal contact and improve reliability in terms of electrical insulation and thermal expansion (durability).Additionally, this design facilitates cost savings in components.The thermal contact sheet with the H-pattern is a metallic structure (e.g., aluminum alloy 6063 T-1) positioned between the solar cells and the absorber of a PVT collector.This arrangement enhances heat conduction while safeguarding the solar cells from the thermal expansion of the absorber.Table 2 displays the list of components along with their material properties utilized in the simulation work.For the parametric analysis, eight different H-pattern plate designs with varying dimensions of cavities (ranging from 0 to 7 mm) are studied as alternatives to the reference case.Furthermore, the impact of the flow rate on the heat loss and directional thermal expansion for different designs is also discussed.

Thermal structural analysis
Thermal structural analysis is the process of calculating the temperature distribution within a solid structure caused by thermal inputs (heat loads), outputs (heat loss), and thermal barriers (thermal contact resistance) in the design using the finite element method [40].The thermal structural analysis addresses the conjugate heat transfer problem by simulating thermal conduction, convection, and radiation.In this study, structural analysis is done using ANSYS Structural Workbench.The boundary conditions applied are global solar irradiance of 750 W/ m 2 , convection (with ambient air) of 5 W/m 2 K, and the bottom part of the collector is perfectly insulated.For this analysis, additional boundary conditions and constraints are required to specify how the collector is held within its frame and overall structure.The collector is assumed to be fixed with its frame at the collector water inlet.
The collector frame has some tolerance, allowing expansion in xdirection and along its width (y-direction) but not allowing displacement along its height (y-direction).The conditions given to the model (temperature and pressure) in steady-state structural analysis are used to analyse the structural performance, here, thermal expansion occurring   on the H-pattern plate.In this case, the pressure is low.Temperature is an important parameter which is the reason for thermal expansion.The temperature at the surface of the plate varies due to the varying heat flux.The temperature is different due to the material's properties [40].
In this analysis, no other load is applied except pressure and temperature, so all these expansions are because of temperature.

Thermal modelling
A thermal model is an equivalent electrical circuit model that corresponds to the transient thermal resistance and is used to perform calculations of a thermal circuit on an electrical circuit (see Fig. 4).It can be used to conduct simulations involving heat.During the initial stage of thermal design, simulations utilizing thermal models are undertaken to make a preliminary estimate [41].Multiple modes of heat transfer occur in the different layers of a PVT collector and with the ambient, including radiation, convection, and conduction.Heat transfer from and to the PVT collector will affect the temperatures attained in the collector's various layers and the heat transfer fluid flowing through the pipe [41].
The Fig. 3. depicts a cross-section of the PVT collector with all the composing layers and their corresponding subscripts -glass (g), PV layer (pv), thermal absorber (ab), insulation (ins), fluid, i.e., water (w).This model analyzes various layers, including glass, EVA (top and bottom), PV, H-pattern plate, thermal absorber, fluid, and insulation.Some models [42] incorporate the behavior of the air gap layer, but it's excluded from this study.Therefore, the model is simplified to compute only the layers of interest above.The PVT collector is systematically modeled layer by layer, allowing observation of the temperatures of each layer and the coolant fluid outlet temperature.The glazed PVT collector's glass cover captures solar energy, facilitating convection and radiation heat transfer with the sky, ambient surroundings, EVA, and PV panel beneath the glass cover.Solar radiation is partially reflected, absorbed, and transmitted through the glass cover.The transmitted radiation is then conveyed to the PV cells, where it is initially absorbed by the EVA.Subsequently, the PV cells transfer the heat to the H-pattern and thermal absorber through conduction heat transfer.Heat is further transmitted from the thermal absorber to the pipe via convection and to the insulation via conduction.Collector is insulated and therefore the sole mechanism of heat transfer to ambient is through convection [43].
The numerical model is based on the previous section's description of heat transfer processes.The energy analysis of the PVT collector is based on the first law of thermodynamics, and the system's energy   performance can be evaluated based on the study [44].First, the energy balance equations are developed for each layer and the coolant fluid.The governing equations are based on the variation of internal energy in a physical body [44]: where M is the mass of the body [kg], c p is the specific heat capacity of the body [J/kgK], dT is the temperature difference between the two bodies [K], and dU is the change in internal energy [ J ].
The energy balance for all the components/layers considers on the right-hand side the heat losses to the environment or adjacent components consisting of either forced convective heat transfer due to wind and radiative losses or conductive heat losses.

i. Glass cover
The glass cover absorbs solar radiation and exchanges it via convection heat transfer with ambient radiation heat transfer with the sky on the other hand, and there is the convective and radiative heat transfer from the glass to the top EVA layer, and heat absorbed by the glass is (Q g ).
5.7 + 3.8 v air for v air < 5 m s 6.47 + v air 0.78 for v air > 5 m s (5) T sky = 0.0552 T amb 1.5 (7) ii.EVA1 The top EVA layer (EVA1) absorbs solar radiation which is transferred from the glass cover in the glazed system and exchanges it by convection and radiation heat transfer with the glass cover through conduction heat transfer to the Photovoltaic panel.
iii.Photovoltaic cells The PV cells absorb heat which is transferred from the top EVA1 layer (Q pv ) where it is encapsulated and exchanges it via conduction heat transfer to the bottom EVA2 layer.
The heat absorbed by PV cells ( Q pv ) is given as; (τα) pv is its effective absorbance, which is given by; E pv = Gr c η cell (13) And, Also, the conductive heat transfer is given; (15) iv.EVA2 The bottom EVA layer (EVA2) absorbs the heat from encapsulated PV cells and exchanges it via conduction heat transfer to the H-pattern plate. )

H-Pattern Plate
The H-pattern plate absorbs the heat from EVA2 which and exchanges it via conduction heat transfer to the thermal absorber.
vi. Thermal absorber The absorber exchanges heat through conduction heat transfer with the H-pattern plate, tube, and insulation.
h ab− tube = k ab t ab (21) h ab− ins = k ins t ins (22) vii.Tube and bonding The tube exchanges heat through conduction heat transfer with the absorber and insulation, also convection heat transfer with water in the tube.
viii.Working fluid in tube The convection heat transfer mechanism acts between the working fluid and tube.
ix. Insulation The insulation exchanges heat through conduction heat transfer with the absorber and convection heat transfer with ambient air.
h amb− ins = h c,amb− ins + h r,amb− ins (27) The heat transfer coefficient of forced convection (h c,g− amb ) is the same as equation ( 5) and h r− g− amb is the radiative heat transfer coefficient similar to equation ( 6) and is given as; h r,g− amb = ε ins × σ (( T ins Thus, the equivalent thermal resistance equation for the PV/T collector is It is crucial to emphasize that the 1-D thermal model is employed in the steady-state 3-D FEM analysis of the collector within ANSYS.The temperature node distribution depicted in Fig. 3 is utilized to assess the temperature at each component.This information can then be applied in the subsequent ANSYS Fluent analysis to determine the outlet water temperature.

PVT thermal performance
Standardization institutions define and publish methods and procedures for performance testing of solar collectors [47].In the case of PVT collectors, performance testing should be separated into thermal and electrical components, as no standards currently exist to define and detail a procedure for simultaneous electrical and thermal performance testing of PVT collectors.PVT collectors represent a new type of technology for both PV and thermal collectors.Thus, a standard that encompasses simultaneous electrical and thermal performance tests has not yet been established.This lack of a globally recognized standard was noted in the PV Catapult report of 2006 [47], and it persists today.ASHRAE first standardized the thermal performance measurement of a solar collector in 1980 with the standard ASHRAE 96-1980: Methods of testing to determine the thermal performance of unglazed flat-plate liquid-type solar collectors [47].This standard proposes a collector model that relates collector efficiency to irradiance, temperature differences, and heat transfer coefficients.The collector model proposed in ASHRAE is provided below: with, where η th is the thermal efficiency, A is the collector area [m 2 ], T m is the The expression (ΔT/G) is referred to as the collector performance coefficient.In the theoretical analysis, the performance of the system is predicted by solving the mathematical equations by varying the values of the following parameters: ambient air temperature (T amb ), collector's mean fluid temperature (T m ) and global solar radiation (G).denotes the measurement of the temperature difference between the collector and its surroundings relative to the solar radiation.

Results and discussion
Firstly, a mesh validation was performed to find the optimal mesh for the 3-D CFD-FEM problem, aiming to reduce the computational time and resources as much as possible without losing accuracy in the results.The 3-D CFD-FEM model of the reference PVT collector was then validated against experimental data provided by the manufacturer in Section 3.2 to verify the accuracy of the result.This will help verify if the proposed approach and idea agrees with the practical situations.As the main focus was on the collector's thermal performance, details on the electrical efficiency are only provided in the final analysis.The thermal efficiency, ɳ th , was plotted against the reduced temperature ΔT/G.Section 3.3 summarizes the results of the parametric study undertaken for different plates with variations in the expansion cavity dimensions in the proposed PVT collector design.Heat losses obtained for selected H-pattern cavity designs are also analyzed with the effect of variations in the flow rate in section 3.3, followed by a structural analysis focusing on the amount of expansion of different collector designs in section 3.3.1,which leads to the selection and more detailed study of a few potential designs that promise improved performance relative to the reference case.

Mesh dependency test
Meshing can be defined as dividing the geometric shape by the number of elements and nodes.Therefore, when the load is applied to a geometric shape, the load can be uniformly distributed to the geometric shape.More elements and nodes indicate smaller elements, which take more computational time to process.Conversely, too few elements will produce unreliable results [48].Using structured mesh elements at the wall allows for good resolution of the boundary layer and temperature field gradients by using sizing functions that allow more node points close to the wall.This was particularly important for natural convection boundary layer flows.The use of unstructured elements in these zones can result in high levels of skewness in corners and at geometry shifts which can result in low accuracy and even destabilize the solution.Unstructured grids will also often require more cells to maintain similar mesh density and quality.Table 3 below shows how different mesh sizes result in the results' convergence.
The term "mesh size" refers to the dimensions of the discrete elements constituting the mesh, commonly within the realm of numerical simulations.It can be seen that the temperature values at the absorber (obtained from the steady state simulations after the meshing) for three different mesh sizes are almost constant and converge at mesh size 0.00005, 0.00001 and 0.000005 m.The variation between mesh sizes of 0.1125 m and 0.00005 m is predicated on the constraint for refinement within specific regions of interest.Diminutive mesh sizes find application in areas necessitating heightened detail and precision, whereas more extensive mesh sizes employed in less critical domains, thereby mitigating computational time and power.Therefore, based on these results and the significantly reduced computational resources required, it was decided to use the simplest mesh (mesh size = 0.00005 m) for this work which was a wise choice as it was around 5 times faster than mesh size = 0.00001 mm and 8 times faster than mesh size = 0.000005 m (with less than one-third of the RAM requirements).The total number of nodes and elements for the collector design are 100,003 and 37947, respectively.A mesh dependency assessment has been conducted, involving an incremental refinement of the mesh size, commencing with simulations employing fewer elements and subsequently augmenting the element size.This iterative process explains the convergence of the solution.In regions where convergence is ascertained, subsequent simulations have been conducted with refined mesh sizes.The type of mesh convergence test employed in this study is the "Optimal Mesh Size," i.e., identifying the point where the solution is deemed acceptably accurate and further mesh refinement does not yield a significant improvement.This mesh size is often regarded as the optimal size for the simulation.
Fig. 5 shows various mesh configurations used in this study.A meticulous approach was undertaken to address the challenge of resolving the near-mesh zone on the boundaries in the context of computational simulations.To achieve this, structured mesh elements were primarily employed in regions proximate to the boundaries, particularly at surfaces critical to heat transfer and fluid dynamics, such as the thermal absorber.Structured grids were utilized due to their superior capacity to provide precise control over mesh size and shape, allowing for the strategic placement of nodes in close proximity to the boundary, essential for the accurate depiction of boundary layer phenomena.Concurrently, regions characterized by geometric complexity or flow irregularities were meshed using unstructured mesh elements to ensure mesh quality and mitigate skewness.Furthermore, adaptive meshing techniques were implemented to dynamically adjust mesh size based on gradients in flow variables, facilitating a concentration of mesh elements in areas marked by substantial variations in temperature, velocity, and pressure.This methodological amalgamation ensured both efficient allocation of computational resources and the preservation of a high level of precision, essential for acquiring dependable outcomes in the computational fluid dynamics and finite element analysis simulations.

Model validation
The significance of validation lies in confirming that the results garnered from data analysis effectively fulfil the core aims that shaped this study's foundation [49].Therefore, validation of the 3-D CFD model developed in ANSYS was pursued against the manufacturer's experimentally derived collector performance curve.This approach aimed to set a robust foundation by utilizing a design consistent with existing models.Adopting a phased validation strategy allowed for an initial evaluation of a model in line with conventional standards.This guaranteed the precision of the simulation methodologies, boundary conditions, and other relevant parameters.Consequently, any deviations in the performance of the H-pattern design from later simulations can be confidently linked to the unique characteristics of the design, rather than possible anomalies in the simulation process.
To validate the foundational model, the heat transfer problem was tackled under ambient and operational conditions consistent with the manufacturer's specifications: flow velocity of 0.1 m/s, fluid inlet temperature of 293 K, ambient temperature of 295 K, and solar irradiance of 750 W/m 2 .This experimental data, extracted under steady-state conditions and aligning with international solar collector testing standards EN 12975-2 [47], provided a rigorous foundation for validation.Utilizing ANSYS Fluent workbench, the simulations were conducted under the specified boundary conditions.The resultant thermal efficiency (η th ) of the collector was depicted in Fig. 6, plotted against the collector performance coefficient (ΔT/G).This coefficient, representing a reduced temperature difference, is indicative of the collector's operational temperatures.The collector performance coefficient is also called a reduced temperature difference which corresponds to the collector operating temperatures.
The derived data from ANSYS aligns commendably with the experimental findings under similar conditions.Interestingly, the efficiency of the H-pattern PVT collector, compared with the reference PVT collector, shows marginal deviations at a lower collector performance coefficient.This congruence in efficiencies-at a zero-temperature coefficient value of 54 %-is attributable to their shared optical properties, a result of identical materials utilized for their glass covers.Notably, as the temperature coefficients rise, the H-pattern collector surpasses its reference counterpart by a relative 10 %.However, while these findings are promising, potential overestimations in performance should be approached with caution.Such overestimations might stem from the model presuming an impeccable thermal contact between the PV cells and the H-pattern plates.Notably, prior research indicates that subpar contact between the PV module and the thermal absorber, resulting in an insulating gap, can curtail the collector's thermal efficiency by up to 12 % [50].Finally, it should be noted that the experimental performance curve is obtained from a scatter of experimental points, which might also result in some deviations of the reported curve from the range of actual experimental performance results.The experimental data contain errors attributed to the accuracy and precision of the instruments and data collection methods employed for measuring thermal efficiency.These errors approximate around 5 %, with about three-quarters of this uncertainty stemming from the measurement of Direct Normal Irradiance (DNI).This may introduce some variability and uncertainty into the results [33].The fitting of the experimental data to the model equation, involving collector parameters, is carried out through a curve-fitting process using the least squares (LS) method.However, the LS method comes with certain challenges, particularly in its assumption of constant uncertainty (deviation) for all observations.Recognizing that uncertainties can vary across measurement points, the weighted least squares (WLS) method would help reduce the differences between simulation and experimental data.WLS assigns different weights to measurements based on their uncertainty levels, giving less influence to points with higher uncertainty and, conversely, emphasizing those with lower uncertainty.This approach aligns more closely with reality, where uncertainties differ among observations.

Parametric analysis
As an alternative to the reference collector, various H-pattern hole dimension designs were studied to analyze the efficiencies of the PVT collector.To this end, parametric analysis was performed for 8 different H-pattern hole dimensions (0,1,2,3,4,5,6 and 7 mm) for a fixed total collector width (B = 160 mm) equal to that of the reference collector (see Fig. 7).The following figure shows different H-pattern plate designs used in the collectors with variations in the expansion cavity dimensions.
The simulations were performed for all the designs with different boundary conditions, i.e., variation in flow velocity of inlet water (0.1, 0.5, 1 m/s) with constant inlet water temperature and global  Irradiation/heat flux of 750 W/m 2 in ANSYS FLUENT for all collector designs.The amount of heat loss from the collector was obtained from these simulation results for all the collector designs, and the graphs are plotted against the reduced temperature (T r = T m -T amb ).Fig. 8 shows the H-pattern collector designs with respect to different flow rates.
For the 0 mm design (reference collector), there is a linear increase in heat loss with increased reduced temperature across all inlet water velocities (0.1 m/s, 0.5 m/s, and 1 m/s).However, for non-0 mm designs (1 mm, 2 mm, and 3 mm), there is a noticeable reduction in heat loss at the same reduced temperatures.In the context of PVT systems, efficient heat removal is crucial to maintain optimal photovoltaic performance while also harnessing thermal energy.The non-0 mm designs demonstrate enhanced thermal performance due to reduced heat loss.This can be attributed to an improved H-Pattern design that facilitates better fluid  dynamics and thermal management within the PVT system.This underscores H-Pattern design potential for enhancing both electrical and thermal efficiency in PVT systems by minimizing operational temperatures and maximizing energy yield.
The flow rate of the heat transfer fluid running through a PVT collector was one factor that influenced how well the collector performed [51].Fig. 9 shows as flow velocity decreases and reduced temperature increases, the amount of heat loss increases.As increasing velocity maximizes heat transmission to the fluid and therefore increases the relative cooling of the PV cells, it follows that the heat transfer fluid's velocity or flow rate can affect the collector's performance or efficiency.The heat losses occurring in these collectors at different flow rates are not much higher, when exposed to the solar irradiation of 750 W/m 2 .This is mainly because of the H-pattern plate as it enhances the heat transfer from PV cells to the absorber and decreases the amount of heat loss within the collector.The graphs above display the heat losses occurring at each H-pattern collector design for a given velocity are almost the same for all the designs.

Thermal expansion on the H-pattern plate
As mentioned previously, one of the main goals of this design was to allow thermal expansion in all directions (by expanding into its cavities), thus creating a smaller total expansion in any single direction, which in turn was expected to diminish the risk of cell cracking drastically.Using metal in thermal applications can bring higher thermal expansion problems [52], but the H-pattern's expansion cavities can address these.Initially, from ANSYS steady state analysis, temperatures on the different H-pattern designs were calculated further to determine the amount of thermal expansion on each design.As seen from the following figures, the temperature gradient is maximum at the center of the plates which is between 384.5 and 383.5 K.However, there is not much difference in the temperatures throughout the plate as the heat transferred to the H-pattern plate from the layers above it is through conduction.Fig. 10 and Fig. 11 give a detailed look at temperature distribution on different H-pattern plate designs in kelvin.
Figs. 10 and 11 illustrate that temperatures at the H-pattern plate are elevated (with a maximum of 384.17 K) during conduction heat transfer from glass to the absorber, significantly impacting mechanical properties, particularly expansion.To quantify the thermal expansion on these plates, steady-state and structural analyses were conducted using ANSYS, with conditions such as an ambient temperature (T amb ) of 295 K and irradiance of 750 W/m 2 .Fig. 12 presents the graph of directional thermal expansion in the Xdirection on various H-pattern plate collector designs.It is evident that the directional expansion values are lower for H-pattern expansion cavity dimensions of 1, 2, 3, and 4 mm compared to the plate with no cavity (0 mm).Beyond 4 mm, a notable increase in expansion is observed for the H-pattern plate with a 5 mm cavity dimension.Additionally, the expansion values for cavity dimensions of 6 and 7 mm are slightly less than 5 mm, but all surpass the H-pattern plate with no cavity.Similar trends are apparent in Fig. 13, depicting the total expansion across all designs.Notably, designs 0, 1, 2, 3, and 4 exhibit lower total expansion values, whereas designs 5, 6, and 7 experience a significant increase.Designs 5, 6, and 7, due to their higher temperatures, may be prone to breakage, given the reduced surface area around the expanding cavities.Therefore, the optimal design appears to be the one with 2 mm H-pattern plate cavity dimensions, exhibiting the lowest directional expansion among all designs.This is attributed to the longer "legs" in the "H-shaped cavity pattern," resulting in less total expansion and a lower risk of breakage.
It should be noted that mechanical property values can vary widely depending on the specific copper and aluminum alloys used for bonding in each case, so more accurate values (provided by the collector manufacturer) are required for a more detailed structural analysis.

Contribution to research knowledge and critical challenges of the study
The introduction of the H-pattern design in PVT collectors is, in itself, an innovative stride.While there have been numerous studies on improving the efficiency of PVT collectors, the structural and functional attributes of the H-pattern design break new ground.This design navigates the challenges of thermal expansion, optimally balancing performance improvements and structural resilience, a feat that hasn't been extensively explored in past literature.Furthermore, the detailed analysis of different cavity sizes within the H-pattern design, and the resulting insights into their impact on performance and structural integrity, add layers of depth to the existing body of knowledge.The study moves beyond mere efficiency metrics and delves into the nuanced interplay of design elements, heat transfer phenomena, and real-world application potential.Thus, this research, while building on the foundation laid by previous studies, carves its niche by presenting detailed, actionable insights into the H-pattern design's potential and challenges, enriching the broader discourse in the field.
The proposed PVT collector with an H-pattern can be applied to various thermal processes and applications requiring low to mediumtemperature heat, including domestic hot water, space heating, process heat, swimming pool heating, heat pump sources, and solar cooling.This design addresses challenges related to PV cell cracking [51].The proposed PVT collector can integrate with other components, such as thermal storage, heat exchangers, pumps, fans, and controllers, forming a complete PVT system meeting specific thermal and electrical demands.The research contributes to PVT technology advancement by proposing a novel collector design enhancing thermal and electrical performance, reducing costs (due to expanded collector lifespan), minimizing environmental impact (reducing disposal of malfunctioning collectors due to PV cell cracking), and broadening potential applications.Results demonstrate higher thermal efficiency, lower PV cell temperature, and comparable electrical efficiency compared to conventional PVT collectors.The proposed design also reduces material and installation costs, as well as embodied energy and greenhouse gas emissions associated with production and operation.Therefore, the proposed PVT collector offers a viable and sustainable solution for harnessing solar energy for various thermal and electrical applications.
The current study compared the thermal efficiency of two different types of PVT systems using simulation and experimental data.However, the simulation model may not fully capture the complex heat transfer phenomena in the PVT systems, and the experimental data may have some errors due to the measurement instruments and the environmental conditions.Therefore, the accuracy of the simulation model can be improved in future studies by validating using PVT with H-Pattern prototype and calibrating the model, using appropriate solvers and settings, using ensemble models, using modeling techniques that   improve performance, and using data-driven models [53].These techniques can help reduce the discrepancies between the simulation and experimental results and enhance the reliability of the PVT systems.Future studies can explore these techniques and compare their effectiveness and efficiency in modeling the PVT systems.

Conclusions
The study underscores the significant potential of the novel PVT collector with an H-pattern plate, showcasing an improved performance.The innovative design effectively addresses the critical issue of cell cracking induced by thermal expansion, minimizing heat loss, and demonstrating superior thermal efficiency in comparison to commercially available collectors.The H-pattern plate outperforms the reference collector by 10 %, 2 %, and 8 % in thermal, electrical, and overall efficiency, respectively.Additionally, the H-pattern design reduces thermal expansion by 20 %, enhancing structural resilience and minimizing the likelihood of PV cell cracking.Emphasizing the delicate balance in expansion dynamics, the study recognizes the H-pattern as one among various possible designs, encouraging further exploration and innovation in PVT collector design.The research outlines avenues for future exploration, particularly through demo case laboratory evaluations, while acknowledging limitations, such as the need for practical implementation considerations and a broader exploration of geometric variations.Despite these limitations, this study provides valuable insights into PVT collector design, offering a promising solution to the challenge of cell cracking.By presenting numerical results and highlighting the practical significance of adopting the proposed design, this research contributes to the existing body of knowledge in the field.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.A Flowchart of the steps involved in the simulation study using ANSYS.
Ethylene-vinyl acetate (EVA) film comprises the PV layer.The operation of a PVT collector is dynamic, and thus, the assumptions made for developing the model (1-D) are: • The temperature distribution is uniform in the layers • Optical and thermal properties of the materials and fluids are constant • No surrounding shading or dust is taken into account • Ambient temperature is constant around the PVT collector • Solar irradiance and wind speed are uniform over the collector's surface area • Total water mass flowrate is distributed uniformly amongst all collector channels with uniform inlet temperature

Fig. 3 .
Fig. 3.A Schematic heat transfer process in the layers of the H-pattern PVT collector.

Fig. 5 .
Fig. 5. (a) Mesh configuration of size 0.1125 m for the collector (b) Mesh configuration of size 0.00005 m for the collector (c) Mesh configuration of size 0.00001 m for the collector (d) Mesh configuration of size 0.000005 m for the collector.

Fig. 6 .
Fig. 6.Thermal efficiency curves of the reference PVT collector and the 3-D model of the H-Pattern collector versus the collector performance coefficient.

Fig. 13 .
Fig. 13.Total thermal expansion curve for different H-pattern plate designs.

Table 2
List of components and materials used for performing simulations on new H-pattern PVT collector.

Table 3
Mesh refinement parameters with different mesh configurations for collector design with H-pattern expansion cavity dimension of 2 mm.