CFD Analysis of Heat Transfer Enhancement in a Flat-Plate Solar Collector with Different Geometric Variations in the Superficial Section

— Nowadays, there is an increasing need for improving the inefficient ways for obtaining thermal energy from renewable sources to fulfil the industrial and typical needs in heat transfer processes that may be covered using solar assisted heat pumps due to their appropriate performance in the thermal energy transfer process. To improve the efficiency of the collector/evaporator by increasing the heat flux to the refrigerant, in this research, a numerical and computational fluid dynamics (CFD) analysis is conducted with geometrical variations in the surface section of a collector/evaporator. The performance was compared to the results of a base case, replicating its limit and environmental conditions such as the initial temperature of 5.5 °C, incident solar radiation of 464.1 W·m - 2 , the operating temperature of 17.6 °C and other parameters. The surface geometrical variations involved in this study show a surface area similar to the base case. However, different lengths of the fluid path were considered due to the new geometrical shapes represented with less thermal resistances and correct distribution of the fluid in the collector/evaporator, obtaining temperature variations of 3.78, 5.47, 5.56 °C and a maximum value of 5.63 °C, including the corresponding variation of the heat flux. Considering the geometric changes in the superficial section of a flat-plate solar collector, it is possible to implement these variations in different kinds of heat exchangers in order to analyze the efficiency in these devices and the impact in the global systems where the heat exchangers are used.


I. INTRODUCTION
Due to the increment in energy consumption in the development of different sectors, an increase in the consumption of fossil energy sources has been generated, and this has produced a negative effect on the environment [1], [2]. Due to this situation, different technologies that employ solar energy are currently analyzed to improve efficiencies and reduce carbon dioxide (CO2) generation [3]. The directexpansion solar-assisted heat pump (DX-SAHP) system is used in heating applications of different fluids that employ refrigerants as working fluids in the vapor compression refrigeration cycle because they have a series of thermodynamic, physicochemical and environmentally acceptable (low flammability and toxicity) properties [4].
The DX-SAHP systems can be utilized in different fields with reduced energy consumption, as stated by Ji et al. [5]. They consider different design and operation factors, such as the relative humidity, which, when increased from 70 to 90 %, causes an increment of 16.3 % in the COP of the uncovered flat plate device. Combariza et al. [6] state that different parameters influence the performance of a heat pump using numerical models that consider continuity, momentum and energy conservation equations to vary values of pressure, velocity, heat flux, among others, despite exhibiting errors smaller than 6 %. These values show their validity when being contrasted with experimental results achieving a reduction of 60.2 % in electrical consumption when the temperature of sanitary water increases from 25 a 32 °C, compared to the same process with electrical resistances.
To improve the performance in devices that use solar radiation, such as flat-plate collectors, investigations using new materials with experimental and numerical validation are being carried out as can be appreciated in the research of Zhou et al. [7] used this method in a conventional solar collector and achieved an increase of 11.3 % in the efficiency of the device, considering 20 °C as ambient temperature.
The research conducted is focused on improving the use of solar energy. It involves handling the heat flux, where the temperatures achieved are validated through the use of a CFD software such as the analysis performed by Panchal and Patel [8], where the geometry and meshed of the construction model are carried out using software for different applications such as solar collectors, drying chambers, agricultural domes, among others. In further studies, the CFD validation is developed with software, which achieves acceptable results in the design and generates an improvement in compact heat exchangers, as shown in the study by Abeykoon [9], where it is observed that this type of validation may be used for different design options without requiring to build prototypes that employ working fluids with different thermodynamic properties.
In order to improve the efficiency of a solar collector (flatplate), which absorbs energy in a solar-assisted directexpansion heat pump, this component uses the incident solar radiation to complete the working fluid phase change into superheat vapor, Ma et al. [10] carried out a simulation in which the COP of a DX-SAHP is larger than the corresponding to a conventional heat pump system. To reach the superheated state, the refrigerant temperature increases from 2 to 3 °C.
Saffarian et al. [11] modified the flow direction in a flatplate solar collector to increase the convection heat transfer coefficient. They apply three geometries, namely U-shaped, wavy, and spiral, and solve the steady-state continuity, momentum, and energy equations; they use water with copper oxide and aluminum nanofluids as working fluids. Results show an increase of 78.25 % in the heat transfer coefficient when using wavy pipelines and the water with copper oxide nanofluid. In the research conducted by Yao et al. [12], uncovered flat-plate collector/evaporator is studied at -10 °C and with solar irradiation of 500 W·m -2, reaching a value of 4 as a coefficient of performance.
The objective of the present investigation is to investigate the effect of different surface shapes that may be implemented for the path of the pipeline through which the refrigerant will circulate in a collector/evaporator constituent of a DX-SAHP system. For this purpose, a mathematical description of the system governed by various equations is presented, and a CFD analysis is conducted about the effect of new configurations on the surface area of the pipeline.

II. MATERIALS AND METHOD
The present study conducts a comparative analysis of the increment of the heat transfer in a collector/evaporator using R600a refrigerant as a working fluid. This study considers as reference the experimental parameters of a base model of the heat exchanger presented in the investigation of Quitiaquez et al. [13], [14], which are shown in Table 1. A numerical and CFD analysis is conducted, generating proposals that consider changes in the pipeline arrangement to obtain better results regarding heat transfer, using an output temperature more extensive than the initial model shown in Fig. 1.

A. Experimental parameters
The results obtained with the initial case to analyze the different models proposed and compared, it is necessary to consider the conditions under which the base model was developed to use them as parameters in the proposed analyses, as seen in Table 1.  The analysis was conducted in a collector/evaporator that has a horizontal collector plate and a conduit that passes through it in the central region in model 1, as can be seen in Fig. 2 in a central cut view; however, its distribution changes in models 2, 3 and 4.

B. CFD Analysis
To conduct simulations with different parameters and their influence in the movement of fluids, the software for CFD analysis performs calculations that are governed by equations that represent the conservation of continuity (mass), energy, and momentum (when there is heat flux), described in (1), (2) and (3), respectively [1], [7].
In the case of conducting analyses that involve fluids with phase change, the required calculations are governed by equations specific for these models that similarly represent the conservation of mass, energy, and momentum considering the phases related, as it is seen in 4, 5, and 6, respectively, which represent the equations of the Eulerian model used in the present research [16], [17].
1) Turbulence model: The flow regime in the CFD analysis is considered when involving the required turbulence models in the simulation. In the case of turbulent flows, the most widely used models are k-Ɛ, with its governing 7 and 8 and k-ω, which exhibit high fidelity in their results for the development of the fluid. In the particular case of the k-Ɛ model, it requires a smaller computational expense [18].
2) Mesh: Due to the variety of models proposed, it is required to carry out an independent meshed in each case to validate its modeling. However, since the heat fluxes in the interface are calculated by integration, it is required a refined meshed in this zone in all models proposed, as can be seen in Fig. 3, obtaining an average value of skewness smaller than 0.25 and average orthogonal quality of 0.8 [19].

III. RESULTS AND DISCUSSION
The results obtained in this investigation come from a numerical analysis that considered parameters such as mass flow, fluid quality, incident solar radiation, input, and ambient temperature, among others. The purpose is to generate a comparative analysis of the influence of different surface sections and how they can increase the heat flux in a collector/evaporator.

A. Validation
In order to validate the numerical analysis with the mathematical algorithm generated and the CFD models. The experimental results were obtained with a built model [13] that employed conditions similar to the ones considered in the numerical studies, like the research work by Duarte et al. [20] and Ma et al. [10]. It obtained errors of 0.11 and 1.12 % respectively, comparing the outlet temperature obtained in the experimental process. The simulated result in the base case is subject to the divergence of the values, with the data presented in Table 2 [12]. Besides, as presented in some research, CFD analyses can be realized in steady and transient states or with steady considerations to obtain useful values in the investigation processes [20], [21]. The output temperature in the CFD analysis for validation considers the value in the central region of a circular pipe, as shown in Fig. 4. The maximum values of 9.5 °C in the region of the interface with the wall. The temperature change generated in the proposed models improves the heat exchange process, visible when compared with the output temperature of the base case (O) with a value of 9.5 °C. It results in the central region of 9.28, 10.9, 11.07 and 11.13 °C in models 1, 2, 3, and 4, respectively, leading to the comparative analysis shown in Table 3.
Similarly, this increase may be seen along with the heat exchanger in a region close to the fluid, within the conduit at 0.1 mm of the refrigerant interface wall, as shown in Figures  6, 7, and 8. Fig. 6 shows the temperature increase for Model 1. Similarly, the increasing temperature trend may be seen in model 2, where there is a temperature variation of 5.47 °C between the inlet and outlet of the heat transfer device, as seen in Figure 7. The increase in heat flux visible in models 3 and 4 results in various temperatures along with the collector/evaporator of 5.56 and 5.63 °C, respectively, revealing a greater heat flux in the heat exchanger, as shown in Fig. 8 (A and B).

IV. CONCLUSIONS
In the present research work, a numerical simulation was carried out utilizing the application of a mathematical algorithm generated and a CFD analysis of a collector/evaporator, obtaining a relative error between experimental and simulated results smaller than 1.5 % in the validation process, from which the following conclusions were obtained. The temperature increase present in the refrigerant that circulates in the collector/evaporator represents the increase in the heat flux with temperature variations in the central region of the collector/evaporator of 3.78, 5.4, and 5.57 °C in models 1, 2, and 3, respectively, where it is seen how a more considerable heat flux to the R600a refrigerant is generated when increasing the length of the conduit along with the collector plate. The direction of the heat flux in the heat transfer device is seen with the temperature difference in the heat exchanger with minimum values in the central region of the conduit, and maximum surface temperatures of 13.39, 11.81, 12.32, and 13.46 °C for models 1, 2, 3 and 4, respectively, at the most distant regions of the collector plate. The larger output temperature in the R600a refrigerant appears in model 4, with 11.13 °C in the central region of the conduit, resulting in a temperature increase of 5.63 °C along with the collector/evaporator, with a ring-shaped distribution of the conduit in the device and a more considerable length compared to the first model analyzed.