Numerical Investigation of Electrical Efficiency with the Application of Hybrid Nanofluids for Photovoltaic Thermal Systems Contained in a Cavity Channel

Memon, Abid A.; Memon, M. Asif; Haque, Md. Mojammel

doi:https://doi.org/10.1155/2023/5465847

Journal of Mathematics

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Abstract Introduction Results and Discussion Conclusion Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 5465847 | https://doi.org/10.1155/2023/5465847

Numerical Investigation of Electrical Efficiency with the Application of Hybrid Nanofluids for Photovoltaic Thermal Systems Contained in a Cavity Channel

Abid A. Memon,¹M. Asif Memon,^1,2and Md. Mojammel Haque³

Academic Editor: Mubashir Qayyum

Received10 Mar 2023

Revised27 May 2023

Accepted27 Jul 2023

Published11 Aug 2023

Abstract

Photovoltaic thermal systems (PV/T) are devices used to collect both electrical and thermal energies from solar energy. By passing a coolant through flow channels that are connected to the PV/T systems, the temperature of the cells is reduced to enhance their electrical efficiency. Therefore, this study aims at investigating a photovoltaic thermal system via the transport of hybrid nanofluids based on Cu-Al₂O₃/water. We assume that the flow channel can be considered in two dimensions and is composed of the silicon panel, absorber, and flow channel. The flow channel consists of a cavity along the absorber with a fixed length and a certain height. This will be a combined conduction and convection problem, with conduction occurring on the top two layers of the silicon panel and absorber. Modeling and simulation problems are performed using COMSOL Multiphysics 5.6. The aspect ratio from inlet height to cavity height is defined by Ar, and the volume fraction of Al₂O₃ is taken double that of Cu. The cell efficiency is analyzed by performing a parametric study by altering the Reynold number (100–1000), inlet temperature (50°C–450°C), the volume fraction of copper (0.01%–10%), and the aspect ratio (0.5, 0.7, 0.9, and 1). It is found that increasing the inlet temperature and aspect ratio decreases the cell efficiency while increasing the Reynolds number and volume fraction increases it. The maximum efficiency of the cell, about 6%, is achieved when the inlet temperature is 50°C, the volume fraction of copper is 10%, Re = 1000, and Ar = 0.5. It was also concluded that when the volume fraction of copper is 0.1, the increase in Reynolds number from 100 to 1000 is improving the cell efficiency by 0.5%. On the other hand, when increasing the volume fraction of copper from minimum to maximum at Re = 1000, the cell efficiency is increasing by 0.3%.

1. Introduction

The production of electricity via the application of a thermal photovoltaic system PV/T is very feasible for economic growth. It is the system that is the most sustainable to fulfill the energy requirement of society without producing environmental issues [1]. Implementing such a system reduces the cost of electricity gained from the sun’s radiation, and also, cell efficiency can be increased by using a different type of cell material. It is also known that, with rising the temperature of the cell, the efficiency of producing electricity reduces; therefore, more attention and methods are required to reduce the temperature of the photovoltaic cells. In general, when thermophotovoltaic cells are constructed, a container for cooling purposes is attached along the photovoltaic cell to maintain the temperature of the cell within a feasible range. Also, the heat energy gained from such a system can be used for other purposes like maintaining the hot environment of a building and detoxification [2].

To increase the efficiency of photovoltaic solar systems, many studies have been performed with the application of transport of nanofluids, numerically as well as experimentally. A numerical and experimental investigation was done by Sardarabadi and Passandideh-Fard [3] to enhance the efficiency of PV/T with the usage of nanofluids. They composed nanofluids by mixing the different metal oxides in the water with a maximum of 0.2% concentration. It was concluded that the usage of ZnO, Al₂O₃, and TiO₂ caused to decline in the surface temperature of the solar cell in the range of 11°C–11.85°C and increases the solar cell efficiency in the range of 5.48%–6.46% for producing electricity. It was also shown through numerical outcomes that increasing nanomaterials concentration in the range of 0.05–10% significantly inclines the thermal efficiency. A photovoltaic cell with and without glazing material was also investigated by the transport of water and CuO/water nanofluid with only a 0.0005 volume fraction [4]. A rectangular channel was selected to flow the nanomixture, and impractically, the electrical efficiency declined in the range of 6.18–6.4% for glazing and in the range of 7.62%–8.77% without glazing. The reason stated that using the nanofluids caused to increase the temperature of the cell. It was suggested that to increase the electrical efficiency, a heat exchanger with a high effective rate must be attached. To improve the thermal performance of the PV/T systems, the transportation of hybrid nanofluid, based on aluminum oxide and zinc oxide, was also tested in the range of 0.3–1.7% volume concentration [5]. They used different mixtures of nanofluids and different inlet temperatures. It was found that using the nanomaterial as the transporting material in the flow channel increases the thermal efficiency by 91% and electrical efficiency by 13.8%. It was also indicated that when increasing the mass flow rate of nanofluid in the domain in the range from 0.01 to 0.1 kg/s, the heat on the surface of the solar cell is decreased by 2%. A study was also carried out to enhance the electrical as well as thermal efficiency of the PV/T system via the application of a mono-nanofluid that was based on the TiO₂ and Al₂O₃ present in the base fluid with equal fractions in the solar collector [6]. After getting the numerical outcomes, it was determined that 19%, 21%, and 26% thermal efficiency increased by using the mono- to hybrid nanofluids, respectively. It was also remarked that the use of hybrid fluid to increase the electrical and electrical efficiency is less cheap than using mono-nanofluid. Another investigation was also taken place with the transportation of the mono-hybrid fluids based on CuO-water and Al₂O₃-water and their hybrid mixtures for a flat plate solar collector [7]. These mixtures were allowed to enter the channel with 1–4 l/min in a channel with a 0.01 volume fraction. In the case of Al₂O₃-water and CuO-water, the electrical efficiency calculated was lowest when the mixture was allowed to enter at the rate of 1 l/min and maximum when it is allowed to enter at 2 l/min. It was found that the usage of mono- or hybrid nanofluid can increase the collector efficiency by up to 75% over the usage of conventional fluids. An experimental study was also done by evaluating the effect of a hybrid nanofluid that comprised different nanoparticles on the efficiency of the thermal system for flat plate solar collectors [8].

The hybrid mixture was composed of multiwalled carbon nanotubes with CuO and MgO with a range of concentration of 0.25%–2% and with flow rates of 0.5 l/min–2 l/min. It was concluded that using the hybrid nanofluids involving the MgO, both the energy and exergy increased by 71% and 70%, respectively. However, involving CuO, these values were counted as 70.63% and 69.11%, respectively. A photovoltaic system was investigated by the application of mono-nanofluid with the transport of Ag and Al₂O₃ nanoparticles with the volume concentration ranging from 1% to 10% in the base fluid and with an initial velocity of 0.04 m/s to 0.23 m/s [9]. It was remarked that both the energy and exergy efficiency were increased with the addition of nanofluids. The numerical outcomes revealed that the mixture of Ag/water and Al₂O₃/water boosting up the electrical efficiency by 5.15% and 1.36%, respectively. Also, the thermal efficiency in the case of Ag/water was determined to be 1.88% and it was found in the case of Al₂O₃/water at 0.95%. A numerical study was carried out to investigate the effect of nanomaterial on the PV/T system [10]. It was deducted that implementing the Cu/water nanofluid boosted the thermal and electrical efficiencies by 1.9% and 4.1%, respectively, while in the case of water-alumina, it was found that the thermal and electrical efficiencies were enhanced by 2.7% and 1.2%, respectively. It was also stated that the system performance might be affected when the mass flow rate is increased by 0.01 kg/s. An experimental study was performed to explore the effects of using mono- and hybrid nanofluid on thermal systems [11]. For this purpose, CuO/water, Al₂O₃/water, and CuO-Al₂O₃-water were used to investigate the volume fractions of 0.05–0.1–0.2%. Besides this, the effect of temperature and volume concentration was also determined by altering the thermal conductivity and viscosity of nanofluids. It was determined that using mono- to hybrid nanofluids, the thermal efficiency of PV/T systems improved from 75 to 82 while the electrical efficiency improved from 11% to 15% with the only use of 0.2 volume fraction. A photovoltaic cell was also examined for electrical efficiency with the transport of ZnO-water and water-alumina nanofluids with only a 0.05 volume concentration each [12]. With their experimental and numerical investigation, they have determined that using the hybrid nanofluid, only 4.1% improvement was achieved when compared with conventional nanofluids. However, a 0.65 c decrement in the cell temperature was found. A solar collector was also examined for thermodynamic analysis via the transport of mono-nanofluid water alumina and a hybrid mixture of alumina + Fe/water [13]. The parametric study was performed for inlet temperature, mass flow rate, and the volume fraction of the nanomixtures. Numerical outcomes suggested that the mono-nanofluid increases the cell efficiency by 2.16%, and in the case of a hybrid mixture, the cell performance is decreased by 1.79% when compared to the efficiency with the water. Although the study failed to show that the hybrid nanofluid increases the thermal performance of the cell, it was found that the energy level is increased by 6.9% which was 5.7% in the case of mono-nanofluid. Two different types of nanofluids Al₂O₃/water and TiO/water were chosen to flow through the flow channel to enhance the cell efficiency of the PV/T systems with different volume fractions [14]. It was indicated that the Al₃O₂/water performed better to enhance the cell efficiency than the TiO/water. It was also found that the lowest value of the temperatures occurs when the mass flow rate reached 0.03 kg/s. It was also noticed in the study that with an increasing volume concentration, the cell efficiency of the PV/T systems increases by 0.28% when a 3% volume concentration was used [15]. A photovoltaic cell was also examined in terms of energy and exergy analysis with the application of alumina-water nanofluids with only 3% concentration as the base fluid. Thermal performance was also analyzed for the inlet temperature of working fluid in the range of 5°C to 45°C. It was disclosed that using the inlet temperature in this range increases the thermal level up to 1.9%; however, the electricity generation is negligibly decreased.

A study [16] was conducted to explore the applications of hybrid nanofluids in optimizing the heat transfer rate by changing the positioning of the heater and cooler. The finite element method was used in this research to obtain the numerical solution of the governing equations. The results showed that changing the crosswise position of heaters and coolers could significantly reduce thermodynamic irreversibility and improve the heat transfer rate. Furthermore, it was found that the changes in the position of heaters and coolers result in noticeable changes in both entropy and heat transfer, which can be controlled by flow-controlling parameters. The study also revealed a negative relationship between the heat transfer rate and the magnetic field.

A study [17] was conducted on the application of hybrid nanofluids. In this study, the effects of changing the positions of heat source and cooler on heat transfer rate and entropy generation were observed. A numerical investigation was carried out using a magnetized quarter cavity. Four different types of quadrantal cavities were observed, with nonstraight surfaces and adiabatic subwalls. The study showed that changing the positions of the heater and cooler does not significantly affect the flow behavior, but there is an increase in bulk vortices production. The second and third configurations showed a significant increase in heat transfer rate. Finally, it was also found that the Lorentz forces moderate the rate of heat transfer.

A numerical study [18] was conducted in a research project at the center of a cubical cavity, where a heat source was placed to examine thermomagnetic convection and entropy generation with the help of a ferrofluid. This study aimed at exploring how heat energy and fluid interact with each other, and two different types of magnetic fields were used in this study. It was observed that any configuration of the magnetic field is sufficient for increasing the cooling in the channel. It was also found that the double Halbach configuration performs better than the other configuration. The study showed that there is a positive relationship between entropy and magnetic strength.

For conventional applications of copper and aluminum oxide, a square cavity was constructed for use with a base that was constructed in the shape of a half-sinusoidal function with different frequencies [19]. This cavity was filled with a porous material, and a nonuniform magnetic field was imposed on the bottom. This study aimed at improving heat transfer through the porous material and magnetic effects. It was finally concluded that increasing the volume fraction of nanofluids, magnetic field strength, porosity, and frequency of the sinusoidal function resulted in a significant improvement in heat transfer performance. In this study, different heating frequencies, superposed temperatures, and amplitudes of vibration of the sinusoidal channel were analyzed. A study [20] was conducted on hybrid nanofluids, in which gold, copper, iron oxide, and silver were used as nanomaterials with blood as the base fluid. A numerical solution was obtained using a parallel disc setup. The researchers indicated that nanofluids improve heat transfer compared to conventional fluids. The article suggests that nanofluids can be utilized in heat sinks, medicine, thermal storage, and thermal systems to benefit from their properties. In a study [21], uranium oxide and multiwalled carbon nanotubes were used as nanoparticles. The purpose of this study was to explore the potential benefits of these nanofluids in biomedical science, specifically in applications such as drug delivery and medical implants. The examination focused on utilizing blood as the base fluid for a blood-based hybrid nanofluid, which was observed between a rotating disk and convective boundaries. Additionally, the researchers investigated the influence of magnetic effects and chemical reactions on heat transfer. In another article [22], ternary-based nanofluids were observed to improve the applications of heat and mass transfer. A double-disc setup was employed, and the effects of magnetic and heat sources were implemented. This study discussed the special effects on temperature, velocity, and nanoparticle concentration. It was mentioned that increasing the concentration of nanoparticles leads to improved thermal conduction and a significant enhancement in the heat transfer rate. It was also noted that the temperature profile is particularly affected when the Prandtl number is increased, and the thermal relaxation parameter affects the thermal distribution. Finally, it was stated that the applications of this problem can be easily utilized in surgical techniques, drug delivery, and biomedical technology. Also, different applications of the nanofluids can be looked in the side [23–25] where the nanofluids are used to improve the biomedical sciences, producing efficient heat exchangers to increase heat transfer rate, solar collector, etc.

After thoroughly investigating the literature review and the importance of the current problem, in this article, we intended to enhance the electrical efficiency of the photovoltaic cell via the application of the hybrid nanofluid with a different configuration of PV/T systems which was not used previously. The numerical investigation will be carried out in the finite element-based software COMSOL Multiphysics 5.6. The Cu-Al₂O₃/water hybrid mixture was chosen to flow in the flow channel. The photovoltaic cell is assumed to compose a silicon cell, absorber, and flow rectangular channel which is having a cavity connected with the absorber. We will be investigating the cell efficiency by altering the inlet temperature, the height of the cavity, the Reynolds number, and the volume concentration of the hybrid nanofluids. In the first stage, a grid independency test will be done to ensure the reliability of the results, and then, numerical results were compared with the correlation. After achieving the numerical results, postprocessing is carried out, and therefore, the impact of chosen parameters on the cell efficiency will be described through graphs.

1.1. Application and Motivation for the Work

The best application of this study is that we are examining a PV/T system through the convection properties of hybrid nanofluids. Our goal is to create a PV/T system for residential and commercial buildings that can generate maximum electricity from solar heat energy so that a significant amount of electricity can be produced during this era of high prices, and electricity bills can be reduced to a considerable extent. The purpose of this study is to develop a private system that can be improved with the help of a hybrid nanofluid in terms of electricity production and finally create a design with excellent electrical efficiency. Industries such as sugar mills, thermochemical industries, textile industries, automobile industries, and hot roof buildings, where electricity is consumed in large quantities and the need for electricity is increasing day by day, require a system that can produce energy from solar radiation. The solution to this problem is undoubtedly the PV/T system, but not the PV/T system is efficient due to the increasing heat of the sun, which reduces its performance. Therefore, there is a need for a fluid material that can keep it cool and also increase cell efficiency. That is why we have tested the convectional properties of nanofluids, which will prove to be a better solution. We are also testing the fluid’s velocity and aspect ratio to see if it can be beneficial.

2. Problem Formulation

The photovoltaic cell is assumed to be a two-dimensional channel because of having symmetries in the channel along the z-axis. The photovoltaic cell is simplified to a silicon cell, absorber made of copper, and flow channel. The flow channel is the rectangular channel in which a deep cavity is connected with the absorber. Let L_c be the length of the channel of the lower base and H be the height of the inlet as shown in Figure 1. Let Ar be the aspect ratio from the height of the inlet to the height of the cavity. The upper boundary of the flow channel is divided into three parts L₁, L₂, and L₃ where L₁ and L₃ are taken as both 10% of the channel and L₃ is taken as 80% of the total length of the channel. Constant heat flux is applied on the top surface of the cell. Cu-alumina water-based nanofluid is allowed to enter from the left entrance of the channel with inlet temperature T_in 5°c to 45°c. Pressure at the outlet is assumed zero, and the remaining all other walls are no-slip boundaries and adiabatic. The geometrical construction of the channel is given in Table 1.

A constant heat flux of sun irradiation is assumed to fall on the silicon cell, and heat is transmitted to the absorber. To model the current fluid flow and heat transfer problem, the conduction process is taken place in the above two surfaces cell and absorber while the fluid flow and heat transfer jointly take place in the flow channel. The detail of the material used in the top 2 layers is given in Table 2.

To increase the electrical efficiency of the photovoltaic cell, a rectangular container with a cavity is attached to the absorber. The idea behind choosing such an arrangement is that while fluid will be entered the region, vortices are creating and recirculating in the region. Our main focus is whether these vortices will give a favor to increase the electrical performance of photovoltaic cells or not. Although various types of fluids can be used to achieve the target, we know from past experiences that nanofluid transportation has a tremendous role in increasing thermal conductivity and decreasing temperature. Therefore, the transport of a hybrid nanofluid is chosen to model the current problem. A mixture of alumina and copper nanoparticles with water as base fluid is chosen. As copper has a large thermal conductivity, therefore, the volume fraction of alumina is taken twice that of copper. The parametric study will be done by altering the inlet temperature of the mixture, T_in, the volume fraction of copper , Reynolds number, Re, and aspect ratio, Ar. Table 3 displays the thermophysical properties of the hybrid nanofluid used in modeling and simulation for the current scenario.

2.1. Governing Equations and Computational Parameters

To develop the simulation for the combined conduction and convection problem, COMSOL Multiphysics 5.6 is used. This software is a finite element-based software and implements the built-in codes written in Java language. The present application of thermophotovoltaic cells will be simulated by two-dimensional incompressible Navier–Stokes equations and heat transfer equations along with the boundary conditions described earlier in Figure 1. The detail of constitutive partial differential equations is given as (1)–(4). After running the code, for postprocessing, we compute the numerical results by using computational parameters (5)–(11).

Let be the velocity of the nanomixture in the flow channel, and then, the governing equations can be written as follows:

We call equation (1) the continuity equation which can be derived from the mass conservation law. Equations 2 and 3 are derived from the law of conservation of momentum, where and represent the density and viscosity of the nanofluids, respectively, which are given in Table 3. These three equations (1) to (3) control the flow and provide us with the velocity components v1 and v2 as well as the pressure. Equation (4) is a two-dimensional energy equation, which can be derived from the law of conservation of energy. Equations (1) to (4) are nonlinear partial differential equations because we can estimate the convective term. Obtaining an exact solution for this system of differential equations is impossible unless we make some assumptions, which will compromise the accuracy of the results. Therefore, we will apply numerical techniques to solve this system of partial differential equations subject to the given boundary conditions as shown in Figure 1. We have used COMSOL Multiphysics 6.0, which is a finite element-based software, to create the simulation of the given partial differential equations subject to boundary conditions using the general code of the finite element method. The working procedure of this software is explained in the flowchart as follows: Local Nusselt number is as follows: Heat transfer coefficient is as follows: Bulk temperature is as follows: Prandtl number is as follows: Nusselt number correlation is as follows [5]: Cell efficiency is as follows [29, 30]: Percentage change in the cell efficiency is as follows:

2.2. COMSOL Working and Finite Element Methods

In general, we use the finite element method in COMSOL Multiphysics 6.0, which is a robust numerical technique that can easily solve all kinds of boundary conditions. We used the working procedure of COMSOL to simulate the phenomenon in this application. To solve this application, we followed the steps described in the working flow procedure as follows: Step 1: First, open the shortcut of COMSOL Multiphysics 6.0 on the desktop and select 2D in the Dimensions menu. Step 2: After selecting the dimensions, we need to select the physics. We will choose conjugate heat transfer. Step 3: After selecting the physics, we need to select the study. Since our problem is time-independent, we will select a steady state. Step 4: In the next step, we need to choose parameters that will help us create the current geometry on the graphical interface of COMSOL Multiphysics. We also need to recognize some parameters through which we will impose material properties on each domain. It should be noted that our full domain consists of three different subdomains: polycrystalline silicon at the top, absorber in the middle, and flow channel at the bottom. We will select parameters to impose the thermophysical properties of these materials, which are given in Tables 1–3. Step 5: Then, we need to impose the material on each domain. For this, we will right-click on the material option and select blank material, which will automatically ask us for the required properties. It should also be noted that the two upper domains will have pure conduction, while in the lower flow channel, both conduction and convection will occur. Step 6: In the next step, we will use the physics toolbar to apply boundary conditions, which are mentioned in the geometry. Step 7: The next step is the mesh procedure, in which we will apply the mesh-independent study procedure. This will ensure that the numerical results we present are reliable. Step 8: We need to validate the results by comparing them with some experimental results or correlations. Step 9: Finally, we will use the postprocessing procedure to select targeted variables, analyze them through a parametric study, and present our suggestions and recommendations.

We will use the parallel direct sparse linear solver (PARDISO) when we convert the governing partial differential equations into the weak form using the weighted residual method of finite element analysis. The weak form will become a system of nonlinear equations when we integrate it over each element. Finally, we will use the PARDISO process described in [31] to solve this system of nonlinear equations. In Table 4, we are presenting the linear error and linear residual error for the last ten simulations.

Finally, we are also presenting a working flow pattern for the finite element method, which is commonly applicable to almost every problem. The block diagram is provided as follows.

3. Mesh-Independent Test and Validation

The present modeling and simulation are being done to enhance the thermal performance of the photovoltaic cell with the use of numerical software which implements the numerical scheme to discretize the governing partial differential equations. It is the beauty of numerical methods that they tackle the problem by decomposing the whole domain into a small domain called elements. The accuracy level of numerical results depends upon the number of elements or density of the meshing process. It is, therefore, to assure the accuracy level, and a mesh-independent study is carried out. According to this method, numerical results are achieved for a targeted variable, and numerical results are achieved by increasing the number of elements unless the error is negligibly reduced to a certain level. In Figures 2(a) and 2(b), the mesh-independent test is analyzed for the pressure and velocity magnitude at the outlet of the flow channel. The number of elements is used from 5000 to 120,000. It can be seen that the accuracy level of numerical outcomes for both variable pressure and velocity magnitude is improved by increasing the number of elements. Grid independence is almost achieved when the number of elements is used greater than 80,000. Instead, to assure the level of reliability, the present problem is stimulated by using 128,000 regular and irregular triangular elements.

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To validate the results, Nusselt number-based correlation (10) is used. The comparison of present numerical results with the experimental correlation is shown in Figures 3(a)–3(d). It can be seen that by increasing the Reynolds number and the volume fraction of the copper, the accuracy level is fluctuating by 93 to 97% approximately which proved that the present code is working better when compared with experimental observations.

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We have compared a present numerical solution with a previous numerical solution [9] using a slight change in the parameters. In this simulation, we set the Reynolds number to 1000 and the volume fraction of alumina to 0.05, while we set the volume fraction of copper to zero. The reason for this is that the numerical computation we are comparing is also for a photovoltaic thermal system but uses a mono-nanofluid to increase its thermal performance. In Figure 4, it can be seen that as the average velocity at the outlet increases, the outlet temperature decreases. This figure shows that our present numerical result can be compared to previous numerical results. However, since the modeled channel in the previously published article was different, a difference can be observed. We can call this kind of comparison a slight variation, and the basis of the error that occurred can be referred to as a modeling error.

4. Results and Discussion

The motive to investigate and develop the present modeling simulation is to analyze numerically the cell efficiency of the photovoltaic cell when altering inlet temperature, the volume fraction of the copper Reynolds number, the aspect ratio of the cavity, and the Nusselt number by the transport of the hybrid mixture of copper and aluminum oxide taken water as base fluid. The impact or consequence of each parameter will be illustrated graphically.

4.1. Impact of Inlet Temperature and the Aspect Ratio

In the present numerical simulation, we have the motive to evaluate the cell efficiency by altering the inlet temperature at which the hybrid fluid is allowed to enter and which is tested in the range from 5°C to 45°C. The aspect ratio is defined to be the ratio between the inlet height of the channel and the height of the channel. The aspect ratio is tested in the range from 0.5 to 1. In Figures 5(a)–5(d), the cell efficiency is calculated by increasing the inlet temperature and both aspect ratios by fixing the volume fraction of copper and the Reynolds number. It can be noted that the maximum accuracy is achieved at an inlet temperature of 5°C and an aspect ratio of 0.5. It is obvious that by increasing the inlet temperature, the cell efficiency is decreasing linearly for each volume fraction and the aspect ratio. Increasing the aspect ratio in the cavity produces a vortical region which might decrease the velocity and increase the temperature. Due to that consequence, the cell efficiency is decreasing by increasing the aspect ratio.

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Moreover, in Figures 5(a)–5(d), it can be seen the negative percentage for cell efficiency which means that the cell efficiency is decreasing concerning reference cell efficiency of the photovoltaic cell. For the current problem, the maximum cell efficiency can be achieved up to 6% when the inlet temperature is 5°C.

As stated in the previous article [15], when the inlet temperature of the flow channel of PV/T is increased, the electrical performance of the fluid will decrease, as evident from our figures. The decrease in the electrical performance of PV/T may be increasing because the inlet temperature will increase the fluid’s temperature. This increase in temperature will lead to more production of thermal energy, thereby reducing the production of electrical energy. We are observing a decrease in the performance of cell efficiency as a result. It has also been explained earlier that increasing the aspect ratio reduces electrical efficiency. The main reason for this is that increasing the aspect ratio increases the vertical region, which reduces the fluid’s velocity. As a result, the temperature increases, leading to a decrease in electrical efficiency.

4.2. Impact of Volume Fraction on Cell Efficiency

To analyze the impact of the volume fraction of copper on the cell efficiency, Figures 6(a)–6(d) and Figures 7(a)–7(d) are produced for varying the inlet temperature, Reynolds number, and aspect ratio. It is obvious from these graphs that for each aspect ratio and the inlet temperature, the cell efficiency is increased by increasing the volume fraction of copper. For a low Reynolds number Re= 100, the cell efficiency is boosted to 5.945% in Figure 6(a), and for a high Reynolds number, the cell efficiency is boosted to 5.97% which is about 6%, see Figure 7(a). Increasing the inlet temperature goes in favor of cell efficiency. It is almost a decline of 50% when the aspect ratio is 0.5, and the inlet temperature is changing from 5°C to 15°C. For a low Reynolds number, the rate of increment of cell efficiency against the volume fraction is almost the same for all aspect ratios. However, for high Reynolds numbers, the rate of increment is the same when the aspect ratio Ar = 0.7, 0.9, and 1. It is also discussed in the previous section that inlet temperature does not go in favor to enhance cell efficiency, but from Figures 6(a)–6(d) and Figures 7(a)–7(d), it can be understood that using nanofluid than the conventional fluid will go in favor to enhance the cell efficiency. It means the gap of deficiency in the cell can be improved by the use of nanofluids. Therefore, the nanofluid in this problem works as a cooling component. In this particular example, it is deduced that using a 10% volume fraction improved the cell efficiency to the maximum level.

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As mentioned in articles [5, 8, 9, and 12], the use of nanofluids as a coolant can help increase the electrical production of PV/T systems. This is because increasing the volume fraction of nanofluids leads to an increase in the thermal conductivity of the fluids, which results in a decrease in the temperature of the fluid. This decrease in temperature has the same effect that the article aims to achieve to increase the electrical performance of the PV/T system. Additionally, it can be said that increasing the concentration of nanofluids reduces the temperature gradient of the fluid, as most of the energy is transferred from the fluid to the nanosized particles. Therefore, we can see that the average temperature of the nanofluid is decreasing.

4.3. Impact of Reynolds Number on the Cell Efficiency

We analyze the modeling and simulation of the cell efficiency of a thermal photovoltaic cell via the transport of nanofluids. The flow is allowed to enter with a certain inlet velocity which is the function of the Reynolds number. To analyze the cell efficiency, the range of Reynolds number is chosen from 100 to 1000 assuming that the flow is laminar. Figures 8(a)–8(d) are produced to check the impact of the Reynolds number on the cell efficiency. It can be seen from these four graphs that the cell efficiency is improving via increasing the Reynolds number for each volume fraction, inlet temperature, and aspect ratio. It can also be deducted that for a low Reynolds number, the rate of increment of cell efficiency is higher than the higher Reynolds number. The cell efficiency against the Reynolds number can be further improved by increasing the volume fraction whereas increasing the inlet temperature does not give favor cell efficiency against the Reynolds number. The reason behind this increase in Reynolds number means increasing the rate of the volume flow of a nanofluid inside the cavity. Therefore, a cooling environment is created in the region, and temperature decreases along the absorber. Also, using the high Reynolds number of 1000 the cell efficiency is maximum and almost improved by 5.97% for a 10% volume fraction of copper and a low inlet temperature of 5°C. Figure 8(a) shows that when the volume fraction of copper is 0.1, the Reynolds number increases from 100 to 1000, and the cell efficiency increases from 5.94% to 5.97%. This means that the cell efficiency is improving by 0.5%. Similarly, in Figures 5(a)–5(d), it can be seen that when Re = 1000 and the volume fraction of copper are increased from 0.01 to 0.1, the cell efficiency also increases from 5.95% to 5.97%, resulting in a total improvement of 0.3%. Note that in Figure 5(a), the inlet temperature is 5°C, which can be considered a cool temperature.

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4.4. Impact of Average Nusselt Number on Cell Efficiency

The average Nusselt number is a ratio to measure the convection over the conduction process. It is said that an increasing Nusselt number indicates the dominancy of convection over conduction or vice versa. In this section, we evaluate graphically the cell efficiency against the average Nusselt number at the outlet, see Figures 9(a)–9(d). It can be understood that by increasing the Nusselt number, the convection process is improved, and hence, the cell efficiency is improved. Also, using nanofluid as the transport material will give a further improvement to the cell efficiency when plotted against the average Nusselt number. It can be concluded that actually, it is the convection process that is sufficient to improve the cell efficiency. By increasing the cell temperature, the conduction process becomes faster than the convection; therefore, the cell efficiency is declining. Also, cell efficiency against the average Nusselt number is evaluated at the single aspect ratio, because we think an increase in the height of the cavity cannot give a further improvement to cell efficiency against the Nusselt number.

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(d)

5. Conclusion

In this study, we investigated the electrical efficiency of a thermal photovoltaic cell with the transport of hybrid nanofluids. The photovoltaic cell is assumed to be two-dimensional and composed of a silicon cell absorber and a rectangular flow channel attached to a deep cavity for simplicity. The hybrid mixture is composed of Cu-alumina water-based nanofluid. The modeling and simulation were carried out using COMSOL Multiphysics 5.6, which implements the finite element approach in the governing Navier and energy equations. Constant sun irradiation is assumed as heat flux on the silicon cells. The article aimed to measure the enhancement in cell efficiency by altering the aspect ratio, inlet temperature, volume fraction of copper, Reynolds number, and the average Nusselt number. We have succeeded in demonstrating the following points in the study:(i)The percentage cell efficiency decreases by increasing both the aspect ratio and the inlet temperature. The maximum percentage cell efficiency achieved was about 6% by using an inlet temperature of 50°C with an aspect ratio of 0.5.(ii)For any particular inlet temperature and aspect ratio, the percentage cell efficiency increases by increasing the volume fraction of copper.(iii)Enhancement in the inlet velocity or the Reynolds number goes in favor of increasing the cell efficiency. It can be seen that for low-volume fractions and moderate Reynolds numbers, the enhancement in cell efficiency is very quick.(iv)It is determined that increasing the Nusselt number increases the percentage of cell efficiency. It can be said that only a faster convection process (heat transfer from liquid to solid) can enhance cell efficiency.(v)It was also concluded that when the volume fraction of copper is 0.1, the increase in Reynolds number from 100 to 1000 improves the cell efficiency by 0.5%. On the other hand, when increasing the volume fraction of copper from minimum to maximum at Re = 1000, the cell efficiency increases by 0.3%.(vi)Since this photovoltaic thermal system was analyzed based on the applications of nanofluids, we intend to analyze it in the future using the applications of ternary hybrid nanofluids. Furthermore, as the construction of this PV/T system was two-dimensional, we aim to analyze it in three dimensions to further validate the obtained results. Additionally, we plan to examine the impact of magnetic effects on the flow channel of the system. Moreover, we are interested in investigating the effects of fitting a rectangular or circular cylinder inside the flow channel to observe its influence on the electrical efficiency of the system.

Data Availability

No data were required to perform this research.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

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Copyright © 2023 Abid A. Memon et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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