Combining Thermal and Optical Modeling to Optimize the Performance of a Flat Plate Absorber at Various Locations in a Solar Air Collector

Increasing the absorber plate surface in a solar air heater system (SAHs) can increase thermal efficiency, heat transfer coefficient, and Nusselt number. This paper includes the development of a 3-dimensional computational fluid dynamics (3-D CFD) model for predicting the location of the absorber plate from the bottom of the collector, followed by its validation using experimental data. Various geometrical types are investigated to determine optimal design features, such as Type I, Type II, Type III, Type IV, and Type V. A comprehensive analysis is performed to achieve this goal, including thermal efficiency, heat transfer coefficient, and Nusselt number analyses. Results indicate that Type V has better performance than other geometries. When the absorber plate location Type V with a distance (dis) of 0.012 m far from the bottom of the collector. As a result, increases in the average thermal efficiency, heat transfer coefficient, and Nusselt number of the system are 19 %, 53%, and 268.8%. Compared to Type I, when the absorber plate was lying on the collectors without a gap between the absorber and collector bottom. This is an open-access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY 4.0) license.


Solar Energy and the Demand for Clean Energy Resources
Global economic progress and industrialization have become increasingly dependent on various forms of energy, including solar energy, an essential energy source in light of climate change and sustainable development. Light and heat are both forms of solar energy. A significant advantage of this renewable energy is that it is one of the most significant and promising energy sources. It is estimated that the sun's energy that falls on the surface of the Earth is about ten thousand times our current energy requirements [1].
In recent years, there has been an essential change in the adaptation of solar energy because of the global efforts to improve access to and ensure energy security and mitigate climate change [2][3][4]. As solar Journal of Studies in Science and Engineering. 2022, 2(3), 31-51. https://doi.org/10.53898/josse2022233 https://engiscience.com/index.php/josse radiations produce a large amount of energy, making it a valuable and limitless resource that can be collected by Solar Air Heaters (SAH), Solar Water Heaters (SWH) and Photo Voltaic (PV) collectors. SAHs are the most basic method of converting solar energy into thermal energy and are one of the most popular types of solar thermal systems due to their ease of use and low cost [5].
Solar radiation, both direct and diffuse, is absorbed in the absorber plate, which transfers this energy to the air flowing through the absorber plate. The beneficial heat gain by the collector fluid determines the thermal efficiency of solar air heaters [6]. There are a variety of applications for SAHs, including solar drying [7][8][9][10], solar thermal power [11][12][13], concentrated solar power [14,15], solar ponds [16,17], solar space heating and cooling [18][19][20], solar furnaces [21], and solar water heating [18,22]. Many researchers have tested the effectiveness of the SAH systems through the use of various geometries. In addition, baffles, slotted absorbers, and filled absorbers are among these improvements. In all of these methods, heat is transferred from the absorber plate to the air [23][24][25][26][27][28].

Solar Air Heaters, Literature Review
The use of various types of SAHs has been reported in several studies. Kumar et al. [29] experimentally investigated the thermal energy and outlet temperatures of a channel with winglet-shaped ribs roughened surface. The experimental results showed an increased thermal efficiency from 17 % to 46 % compared to the smooth channel.
Aboghrara et al. [30] tested corrugated absorber jet impingement through circular jets in a duct flow of solar air heaters plates and compared them with flat plate absorbers. They found that the inflow jet impingement on corrugated plating absorbers has a substantial heat transfer enhancement effect. It is observed that the proposed design duct has almost 14% higher thermal efficiency compared with the smooth duct. Luan et al. [31] experimentally analyzed inclined baffles with angles from 60° to 120° that caused the most significant turbulence due to increasing degree of blockage and obtained higher efficiencies.
Singh et al. [32]  Esen et al. [42]. proposed a Wavelet Neural Network (WNN), a neural network (ANN) modeling of SAHs, and an optimization method based on WANs. Based on predictions and experimental results for variations in airflow rates and ambient conditions of an absorbing surface SAH, the proposed WNN model allowed them to estimate the efficiency of SAHs more accurately.

Research Gap, Challenges, and Novelties
An analysis of solar heaters' shortcomings in the presence of an air absorber plate is presented here, Validation of the model is based on experimental evidence produced from a system with the same components and dimensions under various operating conditions. After simulation validation, the model was modified for various absorber plate locations, and the system thermal efficiency analysis was carried out.
Finally, the efficiency of the air heater from the viewpoints of outlet temperatures, thermal efficiency, heat transfer coefficient, and Nusselt number was evaluated. The simulation was done using COMSOL Multiphysics 5.6, which is versatile and can perform the simulation of multi-physics problems very well.

Experimental Conditions
A clean daytime environment was used for testing Esen [42]. was coated with black chrome. This absorber has a dimension of 0.84, 2.14 m, and a thickness of 1 mm.
The glass was 5 mm thick. The collector used a single cover glass. After installation, the collector ran for many days under normal weather conditions. Evenly spaced thermocouples on the absorber plate measured the collector's inlet and outlet temperatures using two thermocouples with well-insulated leads.
The environment temperature was measured with a mercury thermometer behind the collector. To determine whether Collectors are exposed to a total amount of solar radiation, a Kipp and Zonen CM 11 Pyranometer was used. The meter is adjacent to the glazing cover and on the same plane.   Pyranometers. A series of tests were administered between 9:00 to 16:00.

Optical Modeling
The  In Wavefront Ray Tracing, the ray directions and incidence angles are determined using the Fresnel equation and Snell's law. Each ray's propagation can be described by first-order equations coupled together.
q represents the position vector The model shows that the glass cover is transparent, allowing solar radiation to pass through it. A very slight diffuse and specular reflection is visible from the surface, as shown in Figure 2.a. Next is the black absorber plate, which is more thermally conducting, as shown in Figure 2.b.

Optical-thermal model combined
To understand the related phenomena within a system, it is critical to examine the impacts of the essential parameters on its performance. Developing an accurate and helpful model requires being comprehensive, straightforward, and able to describe and predict behavior under conditions similar to the real world. An optical system model is proposed, and then a thermal and fluid flow model is constructed using the heat flux distribution from the optical model. To determine whether solar flux distributions on absorbing plates are not uniform, we used the geometric optics module in COMSOL Multiphysics.

Modeling of Energy and Fluid Flow
As ambient and time variations in solar radiation affect incoming solar radiation, it is evaluated as the system is operated to estimate its energy balance under unsteady-state conditions. As a result of energy balance across the entire system, the following equation can be expressed: Thermal capacity is expressed by p C density  , and thermal conductivity by k in this formula. Additionally, u represents the airflow velocity field through the box.
The ε parameter measures how much light the absorber absorbs and provides this Stefan-Boltzmann constant. Collectors have thermally insulated sides and bottoms.
In this study, the inlet air mass flow rate ranges between 0.02 and 0.08 kg/s. Thus, the Reynolds number of the air should be used to select the fluid flow model module. The purpose is to determine the velocity field inside the SAHs. The equation is as follows: .
The momentum formula describes how air moves in the collector: Time-dependent governing equations determine the thermal efficiency of the SAHs.

 
Nu is determined as follows: h the heat transfer coefficient in the SAHs determined as follows: Dh is a hydraulic diameter calculated as follows:

Defining the boundary and the initial conditions
A heat absorber plate displays the amount of heat absorbed as follows: When solving time-dependent governing equations, the absolute ambient temperature at the time the system was started is assumed.
In amb TT =

Grid validation independently
The mesh elements in the CFD modeling were created using a free tetrahedral grid in COMSOL Multiphysics. When a mesh control custom mesh generation defines this parameter, highly dense meshes are generated for the absorber plate, solar air heater, and air within the collector. Provides qualitative insight into how the mesh was shaped for modeling the system shown in Figure 3. A margin of error below 3% estimates the input solar energy due to developing independence criteria for meshes. Air running through the collector absorbs the sum of heat. Table 2. provides information on the number of grids. With the increase in the number of cells, outlet temperatures remained unchanged due to the mesh study. It is evident from Table 2. that a total of 803819 cells were independent.

Model verification
As part of this validation, experimental results were compared to the model's predictions to ensure that the proposed model is accurate. Various operating conditions are compared in Table 3. The average air temperature in the system is estimated by comparing models with experimental data (T1, T2, T3, T4, and  Table 3. It is also parametrically suitable, in addition to being reliable. Therefore, the system's heat losses can be considered when evaluating the model.

Solar Fluxes and Ray Trajectory Distributions
Solar air collectors are predicted to have ray trajectories and flux distributions. The collector surface interferes with reflections on the absorbing surface and concentrates them in irregular patterns. To show how rays cross a collector, a ray is focused on an absorbing surface shown in Figure 5. a., A surface with a distributed solar flux. A collector surface's solar flux distribution is also shown in Figure 5. b.    Type I=0 mm, Type II= 3mm, Type III= 6mm, Type IV= 9 mm, and Type V=12mm

Analyzing Thermal Data
Several distances between the absorber and base of the collector in the same conditions are chosen for the model simulation to compare the outcomes of the SAHs with various absorb position distances. In   . On a typical day in July, in Yasouj, Iran, ambient air temperature and solar irradiation [43].

The Results and Discussion
The use of plate Type V is the measure to enhance the heat transfer by providing more heat transfer area to air in the same length of the absorber plate compared to plate Type I, Type II, Type III, and Type   Also, compared with the case without distance, heater efficiency increases by 8.2% when choosing a suitable location for absorber plates.

Figure 8. The variation in thermal efficiency
Heat flows through the insulation of the collector mainly by conduction, which is the reason for energy loss through the bottom and edges. Absorbers' plate location affects local convective heat transfer coefficients when the airflow through the top and bottom absorbers' surfaces is shown in Figure 9. Heat transfer coefficients are higher with increased surface area. Compared with mornings and evenings, the values decrease during the middle of the day. At midday, there are more heat losses because the system's primary components are at a higher temperature. The heat transfer coefficient is higher than at the beginning.    Affect the system's thermal efficiency and air outlet temperature. This is shown in Figure 11. The temperatures at the outlet should determine the type of inlet air flow rate to use. When air is introduced at a higher rate, it reduces the system's average temperature, and as a consequence, the overall performance is improved. Due to reduced heat losses, the system achieves higher thermal efficiency. The system's thermal efficiency can be near 100% in some cases during evening hours. Therefore, this variation from the steady state represents the heat absorbed

Conclusion
This paper investigated using an array of SAHs as a new type of solar air heater. The system's simultaneous optical and thermal analysis was conducted using coupled ray tracing and FEM simulation techniques. In the presence of non-uniform heat flux on the absorber plate surfaces, the system's thermal performance was analyzed under different operational conditions. A 3D CFD simulation was created as a model for the entire system as well as the temperature and flow rate of inlet air affected the temperature of hot air produced. There was an analysis of the thermal efficiency, heat transfer coefficient, and Nusselt number of the absorber plate at various locations in the SAHs. Due to variation in heat flux distribution, the location of the absorber plate in the collectors significantly impacts the system efficiency. To achieve the highest thermal efficiency of the system, a d of 0.012 m was determined as the most appropriate location for the absorber plate. Under specified operating conditions, Type V caused increased thermal efficiency, heat transfer coefficient, and Nusselt number compared with other types of flat plate locations.

Declaration of Competing Interest:
The authors declare that they have no known competing interest