Abstract
The present study uses three mathematical approaches to analyze the dual-purpose solar collector, making it a novel contribution. Three MATLAB codes (C1, C2, and C3), each with its mathematical model, are developed. The effectiveness- number of transfer unit method is used in C1. The heat removal term is used in C2. In C3, the effectiveness term of the parallel flow heat exchanger is used. Mathematical modeling, simulation, and experimental validation are conducted for each code. The calculated numerical-experimental errors revealed excellent convergence. The root mean square error and the mean absolute error for C3 are 1.8 and 1.5, respectively, which are less than for C2 and C3. This indicates that C3 is a reliable approach and can assist researchers in future analysis of the dual-purpose solar collector.
1 Introduction
Solar collectors are critical for absorbing renewable energy for various applications, including space heating, water heating, and electricity generation [1]. A solar thermal collector is a type of heat exchanger that transforms solar radiation energy into internal energy in the transport medium [2]. Typically, three categories of flat-plate solar heating collectors may be found: water-heating, air-heating, and dual-purpose collectors [3]. The bi-fluid thermal collector, also known as a Dual-Purpose Solar Collector (DPSC), consists of two separate sections: one for air heating and the other for water heating [4]. This hybrid system is a strategic approach that deals with the trade-offs between the lower efficiency of air-based heating collectors and the better performance of water-based ones in the domain. By using this cutting-edge technology, customers may simultaneously save expenses, optimize installation space, improve operational effectiveness, and have access to both heated air and water for a range of household or industrial uses [5], providing a comprehensive and effective solution for exploiting solar energy.
Like other solar collector types, evaluating DPSC is a crucial endeavor that aims to maximize their efficacy and validate their practical applicability. Researchers worldwide widely employ the Effectiveness- Number of Transfer Unit (ε-NTU) method for conducting comprehensive performance assessments of the DPSC. Researchers choose this technique because of its simplicity and versatility, which allows it to reliably forecast collector performance regardless of the system's design. Assari et al. [6] employed the ε-NTU approach to develop a mathematical model that assessed the thermal performance of a DPSC in various air channel designs. Significant factors were thoroughly examined, like how the DPSC's heat exchange efficiency fluctuates by the water inlet temperature, air flow rate, and air duct design. After prolonged testing, the model has demonstrated its suitability for both liquid and air collectors of any shape. Jaffari et al. [7] thoroughly examined the DPSC, considering its energetic and energetic aspects. Their investigation employed the ε-NTU approach, emphasizing triangular-shaped air channels. The results demonstrate that the DPSC has higher energy and exergy efficiency than individual collectors. Zhang et al. [8] constructed a mathematical model to explain the functioning of a DPSC in three distinct modes: air heating, water heating, and air-water combination heating. The mathematical representation of the DPSC has been derived by applying the principles of the effectiveness-NTU method. Various experiments were carried out to assess the collector's performance in real-world situations. The findings suggest that dual-purpose systems can improve efficiency while reducing heat dissipation. More and Pole [9] enhanced the thermal performance of the DPSC by making changes to the design proposed by earlier researchers. Furthermore, they constructed a mathematical model utilizing the ε-NTU technique and validated its correctness through actual observations. The results were confirmed against experimental data, demonstrating the model's ability to make exact predictions.
Other scholars have used the energy balance equation as one of their techniques for building the DPSC mathematical model. This approach creates an energy balance equation for each component of the solar collector and solves it numerically. Ma et al. [10] developed a mathematical model specifically for the behavior of DPSCs in air heating mode. This model combines the energy balance equations governing the collector's components: the cover, back plate, and absorber plate. The mathematical framework's ability to appropriately represent the collector's behavior in air heating mode was verified via rigorous development and experimental validation. In addition, a theoretical analysis was carried out to assess how the flow rate and structural characteristics affect the collector's performance. Shemelin and Matuska [11] constructed an intricate theoretical framework for DPSCs, validated by experimental testing. This model calculates the one-dimensional energy balance equations of the solar collector under steady-state circumstances, taking into account two distinct designs. In addition, they utilized the model within the TRNSYS software simulation environment to evaluate the collector's energy efficiency. The results showed that the DPSC produced more solar energy than the control group, which might lead to more efficient solar systems. In their numerical study, Venu and Arun [12] assess the performance of an improved DPSC that uses a porous material under the absorber plate. Their fluid flow model used the incompressible Navier-Stokes equation with ANSYS 13 software simulation assistance. The modified DPSC significantly outperforms the conventional DPSC in temperature rise for both the air and water streams. Another mathematical model of a novel DPSC was developed by Somwanshi and Sarkar [13]. Using the energy balance equation, they created a simple mathematical model for each component. They applied the energy balance equation and validated it against the experiments conducted in Raipur, India. They developed a model in their study that can predict the system's performance under various climatic conditions. A DPSC embeddable in a hybrid solar drying system was suggested and built by Hao et al. [14]. They develop a mathematical model for every component using the energy balance concept. They also numerically solve the energy balance equations using the finite difference method, and simultaneously solve them using an implicit technique with MATLAB 2014a software. The experimental measurements examining its operating strategy, thermal performance, and economic analysis agree with this work's numerical simulation findings. Rao and Somwanshi [15] meticulously crafted a comprehensive mathematical model for the V-corrugated double-glazed dual-purpose air-water heater, taking into account the energy balances of the top and bottom glass covers, air flow, absorber plate, water, and basin. Furthermore, they conducted an experimental validation to confirm the accuracy and reliability of their mathematical framework.
The literature review indicates two primary methods for analyzing the DPSC. The first method involves using the energy balance equation, where a system of equations is derived for each component of the DPSC, and these equations are solved numerically. The second method is the effectiveness-NTU method, which can be applied to any design of DPSC. This method defines the heat removal factor (FR), a pivotal parameter that computes the beneficial heat acquisition of solar collectors as a function of the effectiveness equation. This study proposes an alternative approach to analyzing the DPSC by defining the effectiveness equation for a parallel flow heat exchanger. This allows us to use the effectiveness equation directly for calculating heat gain instead of relying on the heat removal factor. This study seeks to develop a mathematical framework for the DPSC by employing multiple analytical approaches. Three methodologies are utilized to formulate the heat removal factor equation, which is essential for calculating the beneficial heat acquisition of solar collectors. The first method derives the heat removal factor as a function of the effectiveness found in the literature. The second method employs the heat removal factor specifically for the DPSC when operating as a single-purpose collector. The third novel approach considers the DPSC as a parallel flow heat exchanger, using the effectiveness equation instead of the heat removal factor. To the best of available knowledge, previous research has yet to conduct three distinct analyses of the DPSC simultaneously. These methodologies have been numerically investigated using three MATLAB codes to simulate the thermal performance of the DPSC. The models were validated against experimental research conducted by [16]. Additionally, the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE) were calculated to assess the accuracy of the proposed models in relation to one another. Based on the estimated percentage error values, the optimal model is identified. This research is considered novel in the field, as it employs three different analytical procedures that have yet to be previously utilized in this context. The new and optimal model could significantly aid researchers in future studies analyzing the DPSC. This multidimensional analysis aims to enhance understanding of the collector's behavior and identify the most appropriate analytical approach for accurate prediction.
2 Mathematical model
The mathematical model described in this work applies to the DPSC systems, including a straight air channel devoid of fins (see Fig. 1).
Schematic layout of the DPSC used in the present study
Citation: Pollack Periodica 2025; 10.1556/606.2024.01244
The novelty of the current study lies in developing the effectiveness-NTU method, a widely employed approach found in existing literature and research papers. In this research, the effectiveness term given in Eq. (13) is directly implemented into Eq. (6) to figure out the useful heat gain of DPSC instead of using the term FR. To the best of the authors' knowledge and thorough examination of the literature in this domain, no other researchers have employed this particular method. The heat removal factor
3 Numerical simulation and error metrics
In this context, n,
4 Results and discussion
The DPSC used in the current simulation is identical to the one employed by Saleh and Jasim [16]. The system is comprised of two distinct sections: water and air section. The air portion is a rectangular duct that lacks fins, whereas the water section consists of risers and two primary headers (see Fig. 1). The current numerical simulation utilized identical input values, including climatic and operational parameters, as those employed in [16]. In accordance with the previous debate in Section 3, the analysis includes three numerical simulation models, each employing a distinct analytical approach. The numerical outlet fluid temperatures yielded from these programs contrasted with the experimental work of Saleh and Jasim [16]. The air outlet temperature obtained from the three MATLAB codes C1, C2, and C3 along with the experimental results is illustrated in Fig. 3. The predicted results and experimental data coincide extremely well during the first three hours. The variations begin around eleven o'clock and persist until five o'clock in the afternoon.
The variation of air outlet temperature with time for the three codes
Citation: Pollack Periodica 2025; 10.1556/606.2024.01244
It is worth mentioning that the gap between our ingenious code C3 and experimental findings is only one and a half to three degrees Celsius, while it exceeds five degrees Celsius for both C1 and C2. However, the error values between the output numerical results and the measured data are then calculated. The RMSE values for C1, C2, and C3 are 3.4%, 3.8%, and 1.8%, respectively. The MAE values for C1, C2, and C3 were 3%, 3.3%, and 1.5%, respectively. It is crucial to emphasize that the RMSE and MAE values of our mathematical model C3 reveal superior temperature prediction competencies compared to mathematical models C1 and C2. Figure 4 plainly shows the tremendous capability of our innovative and proposed mathematical model C3 for forecasting the water outlet temperature. It is obvious that the predicted values of the outlet water temperature obtained from the simulation codes highly reflect the experimental results. While the predicted temperatures are relatively consistent with the actual temperature, the temperature yielded from code C3 remains superior due to the relatively lower error values compared to the remaining codes C1 and C2. Nevertheless, the RMSE values for C1, C2, and C3 are 0.8%, 1.7%, and 0.3%, respectively. The MAE values for C1, C2, and C3 were 0.7%, 1.4%, and 0.3%, respectively.
The variation of water outlet temperature with time for the three codes
Citation: Pollack Periodica 2025; 10.1556/606.2024.01244
5 Conclusion
The development of highly accurate prediction models has been investigated extensively in the present work to enhance the performance of DPSC. To develop the theoretical analysis of the DPSC, the mathematical equation of the heat removal factor
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