Temperature evolution within a solar panel using a cooling source of varying sizes and shapes in the

Abstract

Keywords: Hybrid Nanofluid; Circular Cold Cylinder; Square Cold Cylinder; Temperature Solar Panel; Natural Convection; Finite Element Method; Triangular Cavity

Introduction

The field of heat transfer is a significant focus of this study. Hybrid nanofluids, known for their superior thermal conductivity compared to conventional fluids, are gaining prominence in this area. This research provides valuable insights for engineers and researchers aiming to optimize cooling systems for electronic devices, such as solar panels [1]. The performance of solar panels in hot climates has been extensively studied [2-4]. Furthermore, investigations into laminar natural convection through various cavity shapes can enhance our understanding and improvement of various engineering applications, including solar collectors [5-7]. Free convective heat transfer is commonly utilized in electrical systems to provide efficient heat dissipation. Convective liquid metal cooling is one method; its special thermal characteristics provide excellent performance [8]. Recent developments in the electronic sector have raised interest in convective heat transfer in different limited enclosures with heat sources. Natural convection has been the subject of numerous investigations about heat transfer in cavities filled with nanofluids when a heat source is present [9–14]. The use of natural convection to transfer heat from a heat source to a nanofluid-filled cavity has been the subject of numerous studies. Various numerical techniques, including the finite volume method and the Boltzmann lattice method, were employed to solve heat transport via natural convection in the submitted work [15–17]. The natural convection of nanofluids has been experimentally examined by various researchers [18–20]. Researchers Rao et al. [21], P. M. Sankar et al. [22] and Dogonchi et al. [23] have also looked into the function of nanofluids in natural convection within porous containers. An emerging area of study, known as a “hybrid” nanofluid, is steadily expanding in tandem with the ever-expanding capabilities of conventional nanofluids. This sort of nanofluid is created by suspending many types of nanoparticles in a base fluid. Several industrial applications rely heavily on hybrid nanofluids and materials. These include heat transfer [24-31], renewable energy technology [32], chemical engineering [32], solar energy devices [33, 34] and heat exchangers [35]. A.M. Rashad [36] looked into the transmission of thermal energy through the convection of two nanoparticles (Al2O3-Cu) from a scientific perspective that was heated from below by a continuous heat flux contained in an enclosure in a magnetic field. He found that increasing the volume percentage of the hybrid nanofluid has a substantial effect when the natural convection is very minimal. In addition, as compared to conventional nanofluid, the hybrid nanofluid made of equal parts Cu and Al2O3 nanoparticles in a water-based fluid does not significantly improve the average Nusselt number. S. Manjunatha et al. [37] focused on thermal flow. Thermogravimetric and viscosity-dependent hybrid nanofluid boundary layer flows with improved heat transmission. Furthermore, the impact

of the Laurentz force on the flow is taken into account. Significant discovery: when certain conditions are present, the thermal conductivity of hybrid nanofluids is higher than that of normal nanofluids. A reduction in the variable viscosity causes the boundary layer thickness of both normal and hybrid nanofluids to drop. Both conventional nanofluid and hybrid nanofluid flow and temperature are proportional to the volume fraction. A triangular annular hollow was filled with a hybrid nanofluid of Al2O3/Cu and water. Fatih Selimefendigil et al. [38] statistically investigated the cavity’s free convection. They discovered that the Nusselt number was improved with an increase in the Rayleigh number and an aperture ratio. The opening ratio’s impact on heat transmission is amplified as the Rayleigh numbers rise. There is a straight line connecting the increase in average heat transfer and the volume fraction of solid nanoparticles; the more thermally conductive the solid, the steeper the hill on the linear curve. For their study, A.I. Alsabery et al. [39] used a vertically undulated surface cavity with a heat source block at the base to examine natural convection within the cavity. The method utilizes the use of a nanofluid that is a combination of water, copper, and aluminum oxide. The results indicate that the Nusselt number is proportional to the heat source’s length. Also, compared to regular nanofluids and pure water, the Nusselt number of the water-Cu-Al2O3 hybrid is larger. Compared to pure water and other nanofluids, the hybrid nanofluid achieves average heat transfer percentages that are 13.7% and 5% greater, respectively, at φ = 0.02. The impact of impediments and their placement inside the square hole (L = H) on heat transfer is the primary subject of Farid Hachichi et al. [40]. Mixed nanofluid movement and heat exchange are greatly affected by the value of square barriers within the square-shaped cavity, according to the data. According to their findings, the hybrid nanofluid heat transmission is enhanced when the obstruction reaches Y = 0.25H. In recent years, a number of research projects have made use of various geometries of enclosures housing heat sources [41-46]. The computational and empirical research on internal and external factors influencing natural convection in sealed spaces has been compiled in a bibliographical review by Pandey [47]. In this review, many forms were considered, including elliptical, square, and circular cylinders as internal bodies. To enhance the flow’s hydrodynamic and thermal behavior, he outlined the many approaches taken in the literature. Additional research on natural convection using hybrid nanofluids can be found in the cited works [48-54]. The present work explores convective heat transport involving computational analysis with a tilted wall design and a nanofluid mixture (Al2O3-Cu/water). It is essential to determine the optimal cold source size and the fractions of copper and aluminum oxide nanoparticles to enhance convective heat transfer. Situated in a dry border region (southwest Algeria), the solar panel is efficiently cooled.

Problem And Theoretical Method

The geometry that was investigated is shown in 2D in Figure 1(a) and in 3D in Figure 1(b). The major component is a mixed nanofluid made of water and (Al2O3-Cu) that flows across a triangle-shaped cavity with a height of H and a base of L. Our solar panel, which has dimensions of Lp=1.7m and Hp=1.15m, is heated by means of the slanted wall. Adiabatic describes the vertical wall. The temperature Tc of the cold generating cylinder and the horizontal wall remains constant. Assuming all physical properties, except density, which is represented using the Boussinesq approximation, are constant, Table 1 displays the Cu-Al2O3 mixed nanofluid physical attributes. Newtonian, homogeneous, incompressible, laminar, two-dimensional, stationary flow is presumed for the (Cu-Al2O3)-water hybrid nanofluid. The solar panel thickness is presumed to be insignificant. The size of the cold source is mentioned by SL (see Figure 1). The three cases studied are obtained by varying this dimension in: SL=0.04 (case 1), SL=0.06 (case 2) and SL=0.08 (case 3). The following is an example of a non-dimensional representation of the conservation equation that is reached by using the variables below [57]:

(4) With T* representing the dimensionless temperature and P* the dimensionless pressure, with u* and v* denoting the x- and y-direction velocity components, respectively. The Rayleigh number Ra and the Prandtl number Pr are the distinguishing parameters.

The properties of mixed nanofluid using different models in literature are grouped in Table 2. When describing the thermo-physical characteristics of hybrid nanofluid, the volume fraction is a crucial metric. This is determined using the following formula, which takes into account the proportions of the two nanoparticle kinds distributed in the basic fluid: (5)

Table 1. The thermo-physical properties of hybrid nanofluid components [52, 55-56]. (1) (2)

Figure 3. Optimal mesh for: (a) SL=0.04, (b) SL=0.06 and (c) SL=0.08. The dimensionless temperature and velocity boundary conditions to the enclosure as shown in Figure 1 are grouped in Table 3. The Nusselt number relations at the tilted surface, both local and average, can be obtained using the following formulas: (6) (7)

Numerical Simulation And Validation CODE

Numerical Simulation To get accurate results rapidly, verifying the solution grid dependency is necessary before drawing any conclusions on its findings. Computing the non-linear ordinary differential equations within the stated boundary conditions is done using computational grids that have been partitioned into two-dimensional spatial domains using the Galerkin FEM. Triangular elements and Lagrange-quadratic interpolation are used in this process. The finite element approach is applied to discretize

2. Perform complementary functions,

combinations, interpretations, interpolations, animation, etc.

the system of mass, momentum, and energy conservation that regulate hydrodynamic and thermal flow. The velocities, temperatures, and pressures were calculated using the flowchart of finite element analysis. In order to record the temperature and velocity gradients, we finetuned the mesh adjacent to the boundary. The equation system yielded a solution. This approach uses the profiles between nodes in integral computations based on differential equations integrated over the control grid. When the relative error of the supplied variables meets the following convergence requirements, we say that this approach has stable solution convergence:

Validation Code The graphical results of Keramat et al.’s [63] have been compared with the current results. A cavity in the form of an H-shaped, filled with a nanofluid, is considered for this purpose. Both the highest and lowest walls are actually heated. The remaining surfaces are insulated, whereas the two vertical walls stay cold. For varying Rayleigh numbers, we found the Nuavr as a function of φ of nanofluid. Our findings for the values of the Rayleigh number 105 and 106 agree well with those of Keramet, as can be seen in Figure 4. A margin of error of less than 4% is displayed in the results. Because the two authors used different numerical methods,

(8) In which i and j stand for the ith and jth mesh cells of the I×J structured computational domain, respectively. The process used to analyze a physical model is shown schematically in Figure 2. For dependable and useful outcomes, examining the grid dependency of the solution is a vital operation to do before making decisions about the findings. With SL=0.04, Ra=106, and j=0.03, we averaged the Nusselt numbers of the inclined walls for several meshes in order to accomplish this. Table 4 gives the mesh test of our problem. We notice that the average Nusselt number stabilizes from grid 19185. The different optimal meshes for the three cases, SL=0.04, SL=0.06 and SL=0.08 of the problem, are summarized in Table 5 and Figures 3(a), 3(b) and 3(c). In case 01, we used a mesh of 19185 domain elements and 777 boundary layer elements.

Figure 4. Validation of numerical code for average Nusselt number.

Figure 5. Average Nusselt evolution (a) and the histogram (b) at Ra=106 for various cold sources as a function of nanoparticle volume percentage.

there is a 10% discrepancy between the 0 and 2% fractions for the Rayleigh number Ra=104.

Result And Discussion

Isothermal patterns, streamlines, Nusselt numbers, and temperature fluctuations will all be presented here as findings for the three cases that were investigated. For a Rayleigh number of 106, we offer calculations regarding an interval of nanoparticle portions values, from 0 to 0.03. A variety of geometric shapes, including square, circular, triangular, rectangular, and star, as well as the influence dimension, are investigated. Influence of Cold Source Geometry on Mean Nusselt Number For different cold source geometries, Figures 5(a) and 5(b) show the variation of Nuavr and its histogram as a function of the nanoparticle fraction, respectively. We see that Nusselt’s values grow to the concentration of nanoparticles in the fluid influencing all forms. We find that compared to the other shapes, the cylindrical source allows a far higher convective transfer. As an example, when we compare the geometric shapes of cylinders and rectangles for a fraction of 0.05, we see a convective regime increase of about 14%, which is great for cooling the solar panel absorber. Consequently, the most efficient and effective design for the panel is a cylindrical one, which allows for the reduction of pressure losses. Our observations are validated by the histogram. Streamlines and Isotherms for Different Nanoparticles Fraction For different percentages of nanoparticle volume and Ra values, Figures 6 and 7 show the dispersion of the

stream function (6.a), (7.a) and isotherms (6.b), (7.b) of circular and square shapes respectively. As the nanoparticle concentrations vary, the streamline distribution (Figure 6.a) is always defined by a central cell that rotates clockwise and has a vortex at its center, which grows stronger. The strength of the convective regime’s flow is amplified by this amplification. A thermal boundary layer at the inclined wall and thermal stratification on the lower portion of the panel are always features of the isothermal field distribution, which we also remark (Figure 6.b). An increment in convective transfer and a reduction in thermal conductivity of the hybrid nanofluid are both made feasible by the impact of changing the nanoparticle volume fractions on the thermal field and velocity field values. The structure is maintained in Figure 7.a’s streamlines for the square shape, with the exception that the vortex is smaller compared to the circular shape. This indicates that the convective mode flow is becoming weaker. Additionally, tiny cells have emerged, indicating the presence of load losses. Compared to Figure (6.b), Figure 7.b exhibits a broader boundary layer and substantial thermal stratification. Therefore, a pseudo-conductive regime becomes dominant. The findings demonstrate that heat evacuation is enhanced by adjusting the concentration of the nanoparticles in the hybrid nanofluid, which impacts its thermal performance Figure (7.a). Contrasting the two shapes, we find that the square one has a wider boundary layer and a smaller vortex, suggesting that the convective transfer mode is more advantageous in the circular one. The circular shape is used for a number of reasons, including:

Figure 6. Streamlines (a) and Isotherms (b) of circular shape of numerous nanoparticles volume fraction for Ra=106.

Figure 7. Streamlines (a) and Isotherms (b) of square shape of numerous nanoparticles volume fraction for Ra=106.

2. It is easy to construct the design

Streamlines and Isotherms for Different Cold Cylinder Size With Ra and volume fraction held constant, Figure 8 illustrates how the circulation (8.a) and thermal changes

(8.b) are affected through the cold generating cylinder dimensions. Isotherms are defined by a thermal boundary layer along the slanted top wall, which stands in for the absorber, and thermal stratifications on the lower half of the panel, which provide a pseudo-conductive transmission

Figure 8. Streamlines (a) and Isotherms (b) of different cold source sizes for Ra=106 and jhnf=3%.

mode. As the SL ratio increases, the boundary layer gets narrower, which is good news for the convective transfer mode up top. A huge vortex-filled center convective cell defines the streamline distribution, and its size grows in relation to the SL ratio. Consistent with this distribution, the convective flow regime is favored in the enclosure’s central region as the SL aspect ratio of the cylindrical source grows, leading to an intensification of the flow. The transfer mode and flow regime of the panel are directly affected by an increase in the aspect ratio of the cylindrical source SL, as we may deduce in the conclusion. Distribution of Temperature Along the Cold Generating Cylinder Figure 9 displays the temperature range for SL = 0.04, 0.06, and 0.08, φ = 0.03 and Ra = 106, as well as the position of the line below the cold source. As we get closer to the cool source, the temperature drops in all three cases. While there is a small fall in temperature between 0 and 0.3 m, the decrease is substantial between 0.3 and 0.5 m, particularly for a source size of SL=0.08. This indicates that the fluid is being accelerated, leading to better evacuation of the convective mode in this region. Looking at the final temperature values across all three dimensions, we find that the temperature drops by 50% between SL=0.08 and SL=0.04, and by 16.67% between SL=0.08 and SL=0.06. This suggests that our solar panel cooling is improving, but only to a certain extent, and that we must incorporate ventilation into our system immediately. Solar Panel Temperature Figure 10 illustrates the temperature distribution along the solar panel without the presence of the cold generating cylinder (10.a) and with the source (10.b) for Ra=106. The temperature grows at an exponential rate, as seen in Figure 10.a. Clearly, the vast upper portion of the panel is

Figure 9. Temperature distribution near the lowest point of the cold source for Ra=106. un-irradiated. As we see with natural convection, the fluid settles to the top of the panel as heat rises and cold falls. The cooling of the panel is impeded by this. Adding a cold source causes a temperature drop in a tiny top section of the panel, as shown in figure 10.b. Therefore, the fluid’s flow was enhanced by the source’s presence. To get the most out of the convective mode of evacuation, it is crucial to do an optimization study on the source size. Evolution of Nuav as Function as Ra and j Figure 11 shows that critical parameters for heat transfer include the number of Rayleigh and the nanofluid volume portions. Ra sees the increasing trend of the Nuavr rises in

Figure 10. Temperature distribution along the solar panel without the cold generating cylinder (a) and with the presence of the cold generating cylinder (b) for Ra=106.

As the regression coefficient indicates R2=0.99, the mathematical correlation requires on an exponential form.

Conclusion

Figure 11. Nuavr at different Ra and nanoparticles volume fraction for circular form. all curves. Also, heat transmission is improved when the nanofluid volume percentage is increased. The enhanced heat transfer is the reason behind the change in fluid properties caused by injecting of Al2O3 and Cu nanoparticles directly into water. Variation of Nuav as Function as SL The average Nusselt number plotted against the magnitude of the cold cylinder is shown in Figure 12 for Ra=106 and φ=0.03. As the heat source dimension improves, numerical simulations disclose the fact that both convective heat transport and Nusselt values increase.

This research investigates how the size and geometry of cold cylinder impacts the hydrodynamic and thermal flow in a triangular cavity full of hybrid nanofluid, aiming to optimize cooling conditions for solar panels. The results obtained in isothermal form, streamline, mean Nusselt number and temperature profile at various Rayleigh values; allow us to deduce the following points: o Raising the volume fraction concentrations of nanoparticles in water enhances the convective transfer regime, while increasing the aspect ratio intensifies the flow. o As the aspect ratio increases, solar panel cooling becomes more dependable. o A rise in the Rayleigh number and the volume percentage of the nanoparticles enhances the average Nusselt evolution, which grows exponentially with the cold generating cylinder size. o An ideal cold source would have a cylindrical shape with an aspect ratio of SL=0.08, which would greatly improve the efficiency and performance of the solar panel. Considering the thermal stratification of the hybrid nanofluid, our analysis indicates that the majority of our solar panels lack sufficient cooling. This does not bode well for our semi-arid climate. This is why we’re going to build ventilation to improve our cooling system.

Nomenclature

Rayleigh number Prandtl Number Nusselt number Gravitational acceleration, m.s-2 Cartesian coordinates, m Pressure, N.m-2 Temperature [K] Thermal conductivity, W.m-1.K-1 Components of velocity fields, m.s-1 Dimensionless coordinates, m Dimensionless velocity components, m.s-1 Dimensionless pressure The coled source size Height of cavity Base of cavity source’s height

Greec Symbol Α Thermal diffusivity, m-2.s-1 Β Coefficient of thermal expansion, K-1

Dynamic viscosity, kg.m-1.s-1 Density, kg.m-3 Heat capacity, J.m-3.K-1 Volume fraction

Subscripts f Fluid properties hnf Hybrid nanofluid properties s Solid properties c Cold wall h Hot wall eff Effective * Dimensional properties avr Average FEM Finite element method L Local

Data Availability Statement

The authors confirm that the data that supports the findings of this study are available within the article. Raw data that support the finding of this study are available from the corresponding author, upon reasonable request.

Conflict Of Interest

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethics

There are no ethical issues with the publication of this manuscript.

Statement On The Use Of Artificial Intelligence

Artificial intelligence was not used in the preparation of the article.

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