Renewable energy plays a crucial role in mitigating environmental impact and reducing dependence on fossil fuels. Solar thermal energy offers a clean and sustainable alternative. This study presents a phenomenological mathematical model for simulating heat transfer in a flat-plate solar collector. The model aims to optimize thermal efficiency and support the design of energy systems. The thermal analysis considers temperature gradients across the glass cover (GC), the air gap between the GC and the absorber plate (GC-AP), the aluminum absorber plate (AP), the airflow inside the tubes, and the wood insulation (WI) at the base. A thermal resistance network is developed that incorporates conduction, convection, and radiation mechanisms. Heat transfer coefficients are obtained from experimental measurements of temperature and air velocity, including ambient, GC, AP, insulation, and working fluid temperatures. These coefficients feed an energy balance model, producing differential equations that are solved numerically using Scilab Xcos to simulate the collector’s behavior. The GC acts as a selective filter, transmitting short-wave radiation and limiting long-wave emissions, contributing to a greenhouse effect that enhances performance. However, significant thermal losses occur through insulation and optical elements. Model validation against experimental data yields RMSE of 0.19 °C for natural convection and 0.0089 °C for forced convection. The thermal efficiency of 52.7% under forced convection and 29.3% under natural convection. Total energy losses amount to 35% via insulation and 15% due to optical inefficiencies. The results highlight the critical role of airflow and the importance of improving optical properties and insulation to enhance collector performance.
energy balanceheat exchangernon-commercial softwareparametric studytransient analysisThe author(s) declared that financial support was not received for this work and/or its publication.section-at-acceptanceHeat Transfer Mechanisms and ApplicationsIntroduction
At both the local and global levels, the transition to renewable energy sources is crucial for mitigating climate change and ensuring energy sustainability. Among the various alternatives, solar thermal energy is one of the available and economical solutions applied to local communities and startups in Mexico (Messina et al., 2022; Bedle and y Garneau, 2024). It enables the conversion of solar radiation into useful heat for drying agricultural products in the region (Méndez-Lagunas et al., 2025; Ndukwu et al., 2023).
Within this field, flat-plate solar collectors stand out as one of the most widely used and cost-effective technologies. Their operation is based on a simple principle: capturing as much solar energy as possible and transferring it to a working fluid, while reducing heat loss to the environment. However, their performance is limited by the low heat capacity of the fluid and the nature of the convective process, which depends directly on the available heat transfer area (Cengel and Ghajar, 2014). Additionally, there is a complex interaction of heat transfer mechanisms that coincide between the different components, such as the glass cover, the absorber plate, and the insulation.
To optimize the design and improve the thermal efficiency of these collectors, it is essential to thoroughly understand how each component and physical phenomenon contributes to the overall system performance. Mathematical modeling and numerical simulation are indispensable tools that allow these interactions to be analyzed in detail. This is the case with the model developed by Luna et al. (2010), which optimizes solar thermal collectors. It formulates a classic model based on linearized energy balances, which serves as a reference. Next, reduced models are developed where the efficiency of the collector is expressed directly as a function of the design variables (length and width of the collector), the operating variable (air flow), and auxiliary variables such as air velocity. The main result is that the model offers the same accuracy as the classical model, with deviations of less than 3%, but with far fewer equations and variables, making it more precise and efficient for the preliminary design of collectors.
Bracamonte and Baritto (2013) Optimize the design of flat solar collectors for air heating using a dimensionless model by minimizing entropy generation. They identify the optimal relationships between length/width and width/spacing of the collectors, using numerical simulations and equation fitting. The results show that, for low mass flows, optimal solar collectors tend to be short and wide, as friction losses are negligible. On the other hand, for high mass flows, they must be designed longer and narrower to balance friction losses and heat transfer. This analysis is complemented by the calculation of heat transfer coefficients, both inside the duct and to the outside, which are determined using empirical correlations widely used in the literature: in internal convection, those of Dittus–Boelter and its variants for parallel plates predominate. In external convection, the McAdams correlation is employed, and for radiation, the linearized Stefan–Boltzmann equation is applied between gray surfaces and the sky.
Recent studies have underscored the significance of accurate thermal modeling and experimental validation in solar air collectors. Both experimental and numerical investigations have demonstrated that precisely estimating convective heat transfer coefficients is essential for accurately predicting collector efficiency and temperature distributions (Rony et al., 2024). Furthermore, comprehensive energy and exergy analyses have been utilized to assess performance under various operating conditions, confirming that optimized geometric configurations and flow parameters can greatly enhance thermal efficiency while minimizing irreversibilities (Yahya, 2023). Recent research has further expanded this focus to the use of advanced heat transfer fluids, such as mono- and hybrid-ceramic nanofluids (e.g., Titanium diboride and Boron carbide), which have demonstrated energy efficiency improvements of 26%–27% in flat plate solar collectors (FPSC). Simulations using tools like ANSYS have demonstrated that hybrid nanofluids can achieve an optimal balance between enhanced thermal conductivity and manageable pressure drop, thus optimizing the overall energy and exergy efficiency of the collector at varying inlet temperatures (Alsabagh et al., 2025).
Numerical studies in thermal systems highlight the importance of precise heat transfer modeling for solar radiation. Recent research shows that solar irradiation significantly affects indoor air temperature, airflow patterns, and humidity. Validated computational fluid dynamics (CFD) models indicate that increased solar irradiance leads to higher indoor temperatures and thermal discomfort. This underscores the need to integrate solar radiation models with convective heat transfer and airflow simulations for accurate thermal predictions (Verma et al., 2024). Recent advancements have enhanced the modeling of thermal absorber coatings essential for high-temperature applications. By utilizing NURBS-based extended isogeometric analysis (XIGA), we can more accurately simulate the coatings’ stress response, crack initiation, and heat transfer. This improves our understanding of their durability and effectiveness in extreme conditions. Overall, these developments highlight the significance of detailed numerical methods in capturing heat transfer, material behavior, and fluid-thermal interactions in solar energy systems (Thappa et al., 2024).
Therefore, the main objective of this work is to develop a mathematical model that represents heat transfer in a flat-plate solar collector. This model is conceived as a handy tool for design optimization, as it allows the most appropriate dimensions and geometric proportions of its components to be established, such as the separation between the cover and the absorber or the sizing of the tubes, to maximize heat exchange and, consequently, the overall efficiency of the collector. It also includes the experimental determination of the fluid’s heat transfer coefficients, providing an indispensable empirical basis for validating the model’s robustness. Finally, the model will be implemented in Scilab’s Xcos open-source environment, which not only promotes its reproducibility and accessibility but also opens up the possibility of its improvement and application in future studies.
Methods
The solar collector addressed in this study consists of three main elements: a glass cover (GC), an absorber plate (AP), and a thermal insulation system (WI). Air, which acts as the working fluid, flows longitudinally through the duct between the cover and the absorber plate (y-direction). Simultaneously, energy transfer occurs perpendicular to this flow, through the thickness of the collector (in the z-direction).
Data collection was carried out at coordinates 17°03′35.28“ N and 96°53′51.84” W. The solar collector was installed at an angle of 20°, as shown in Figure 1. Temperatures were recorded throughout the day using Vaisala Veritec thermocouples with an accuracy of 0.01 °C, measuring the following parameters: ambient temperature (Ta), temperature at the glass cover (Tc), temperature at the absorber plate (Tp), insulation temperature (Tb), and final fluid temperature (Tf). The experiments were conducted under both natural and forced convection conditions. The air velocity at the collector inlet was 0.66 m/s for natural convection and 4.5 m/s for forced convection, measured with an anemometer. A pyranometer was used to calculate the incident solar radiation, and an optical efficiency of 86% was assumed for the glass, just like the one used by Tiwari and Tiwari (2016).
Solar collector with transfer mechanisms and thermal resistance diagram.
Diagram illustrating heat transfer in a solar collector. Components include a glass cover, absorber plate, and insulation. Processes shown are convection, radiation, conduction, and solar radiation, with labeled thermal resistances and heat flows. Arrows indicate heat movement from inlet to outlet.
The various heat transfer mechanisms in the system are modeled as a network of thermal resistances, as shown in Figure 1, the analysis of which is presented below (Table 1). The development of the model is based on the following assumptions: the heat transfer through the collector components is considered one-dimensional; the system is analyzed under transient conditions in order to account for its thermal inertia over time (Sala et al., 2020); the thermophysical properties of the materials and the working fluid are assumed to be constant throughout the simulation; the thermal capacitance of the glass cover (GC) is neglected due to its relatively low energy storage capacity compared to that of the absorber plate (AP) and the fluid; the temperature is assumed to be spatially uniform across the absorber plate and within the fluid cross-section at any given time (Al-Tabbakh, 2022); the mass flow rate of the working fluid is considered steady and constant; and heat losses to the environment are modeled using global heat transfer coefficients that lump the combined effects of convection and radiation.
Summary of heat transfer coefficients and their description.
Term
Flow regime/Mechanism
Equation
Description
h2c
Laminar/Convective
1
Convective heat transfer coefficient from the glass cover to the ambient air, calculated using a correlation
h2r
Radiative
2
Radiative heat transfer coefficient from the glass cover to the ambient, calculated using a correlation
h2
Convective and radiative
-
Parallel sum of the heat transfer coefficients h2c (convection) and h2r (radiation)
h2c
Radiative
9
Calculated from experimental temperatures
h2r
Radiative
3
Radiative heat transfer coefficient from the glass cover to the absorber plate, calculated using a correlation
h2
Convective + radiative
-
Parallel sum of the heat transfer coefficients for conduction, convection, and radiation
Ut
Convective + radiative
4
Total overall top heat transfer coefficient between the plate and the environment. It is the series sum of h1 and h2 coefficients
Ub
Conductive
5
Overall bottom heat transfer coefficient between the plate and the insulation
UL
Convective, radiative and conductive
6
Total overall heat transfer coefficient between the plate, the insulation, and the environment
Heat transfer coefficients
The heat transfer phenomena between the glass cover (GC) and the environment are described by two parallel mechanisms: convection and radiation, shown in Figure 1, where the convective coefficient by radiation h2r in Equation 1 depends on the difference to the fourth power between the temperature of the GC and the temperature of the sky. For its part, the convective coefficient h2c in Equation 2 is determined mainly by the outside wind speed V (McAdams, W. H. 1954).h2r=εcσTc4−Tsky4Tc−Tah2c=2.8+3V
Where T is in K, σ is the Stefan-Boltzmann constant, and ε is the emissivity of the CG, the sum of these two coefficients in parallel gives us the coefficient h2 (Duffie, et al, 2020).
Similar to the interaction between the GC and the environment, convective and radiative heat transfer mechanisms also occur between the glass cover (GC) and the absorber plate (AP). The convective coefficient h1c can be estimated using the Dittus-Boelter correlation; however, in this study it will be considered as an unknown to be determined. On the other hand, heat transfer by radiation (Equation 3) between the surfaces of the GC and the AP is calculated using the following equation (Tiwari, 2011; Tiwari and Tiwari, 2016).h1r=εeffσTP4−Tc4TP−Tc
The parallel sum of the radiation coefficient h1r and convection coefficient h1c gives us the coefficient h1 (Hegazy, 1999). By adding the two coefficients h1 and h2 in series, we obtain an overall heat transfer coefficient, Ut (Equation 4), that shows us the heat losses from the AP to the environment.Ut=1h1+1h2−1
Resistance below the AP is directly proportional to the thickness of the insulating material and inversely proportional to its thermal conductivity. It is in series with the convection and radiation received by the insulating material on its surface. Given that the air velocity below the collector is 0, and the solar radiation received is negligible, this energy loss depends solely on conduction, as represented in Equation 5.Ub=LiKi+1hb≈LiKiUL=Ut+Ub+Ue
The thermal losses of the collector are quantified using overall heat loss coefficients for the lower surface, as shown in Equation 5 (Ub), and for the edges, as shown in Equation 6 (Ue). The Ue coefficient is a function of the conductive resistance of the base and is directly proportional to the area ratio between the edges and the collector (Ae/Ac). The combination of heat loss to the top, bottom, sides, and to the fluid itself is included in an overall loss coefficient (UL). The rate of sound energy transferred to the fluid is determined by the energy balance at the absorber plate, as shown in Equation 7. This balance considers the rate of solar energy absorbed per unit area, ατI(t), minus the rate of energy lost by the plate to the environment. This same value can be calculated using the sensible heat equation, which requires knowledge of the mass flow and heat capacity of the air, as well as the temperature differential of the fluid at the collector outlet and inlet (Ta).q˙u=α·τ·It−ULTpt−Tat=m˙·CpaTf−TaAc
Experimental calculation of heat transfer coefficients
To calculate the transfer coefficients, the sky temperature was first determined using the empirical correlation by Zvirin and Aronov (1998) shown in Equation 8, and its value was then substituted into Equation 1. Using the experimental data for the glass temperature (Tc) and the ambient temperature (Ta), the radiation transfer coefficient on the outer surface of the glass was obtained. Subsequently, using the wind velocity outside the collector and Equation 2, the convective coefficient h2c was calculated. Finally, both coefficients were combined in parallel to determine the overall coefficient h2 (He et al., 2021).Tsky=Ta−6
Similarly, based on temperature in the plate (Tp) and the glass temperature (Tc), the radiation transfer coefficient h1r was calculated using Equation 3. The convective coefficient h1c remains unknown, as it is the value of interest in this analysis. Both coefficients were combined in parallel, and the overall heat transfer coefficient, Ut, was then obtained using Equation 4.
When performing an energy balance, it is established that the amount of heat flowing from the environment (Ta) to temperature in the plate (Tp) is equivalent to that flowing from the glass (Tc) to temperature in the plate (Tp), considering the path of thermal resistances. Thus, Equation 9 is proposed:h1Tp−Tc=UtTp−Ta
By substituting AP´s Temperature (Tp), the ambient temperature (Ta), and the previously calculated coefficients, together with an initial proposal for the convective coefficient h1c in the collector, the glass temperature is determined from Equation 9. This value is then compared with the experimental data, adjusting h1c until the sum of the quadratic errors is minimized.
Methodology for the development and implementation of the model in xcos scilabEnergy balance in the absorption plate
Solar radiation I(t) first passes through the GC. Part of it is reflected, part is absorbed, and the rest passes through the GC. The product of this is called optical efficiency. This means that approximately 86% of the radiation reaches the AP. In Equation 1, this is expressed in the first term of the equation in brackets. The second term represents the loss of energy due to convection, as the AP loses heat when in contact with the working fluid. Newton’s law of cooling represents this. The behavior of the last term is because, as the AP heats up, it emits infrared radiation into the environment, most of which is radiated to the GC, which is expressed by an equation in the third term in brackets. And all this is equal to the cumulative or differential term.dTpdt=1ρ·d·Cp·α·τ·It−hc·Tp−Tf−hrad·Tp−TcTp0=Tpi
There is a slight spatial variation in temperature in the AP, as solar radiation ⍺τI(t) is distributed evenly across its surface (Al-Tabbakh, 2022). Furthermore, the high thermal conductivity of aluminum suggests that the temperature in the AP is practically homogeneous.
Energy balance in the fluid
Heat loss by convection in the AP-fluid occurs when the AP exchanges heat with the fluid. The GC is also subject to this phenomenon at the bottom. In the fluid, this represents an energy gain. However, due to the different arrangement of the absorber plate and the glass, the convective heat transfer coefficients between the fluid-glass and fluid -Ap in Equation 11 (h1c1 and h1c2) can be considered different, since one is the heat transfer coefficient between the fluid and the glass at the bottom and the other is the coefficient between the AP and the fluid at the top. Another consideration is that the fluid temperature varies along the collector, and this variation depends on its initial temperature and the sensible heat transferred per unit area (A) from the AP, as reflected in the last term in brackets in Equation 11.dTfdt=1ρf·Cpf·Df·h1c1·Tp−Tf+h1c2·Tc−Tf−mf·CpfTf−TaAcTf0=Tfi
Energy balance the glass cover
Due to its low absorptivity and heat capacity, the glass cover absorbs and retains negligible heat. Therefore, heat accumulation in it is minimal and can be disregarded in the analysis. Although the glass cover does not absorb direct solar radiation, it transmits it. However, GC is heated by two mechanisms: convection from the working fluid and environmental conditions. In addition, it also receives thermal radiation emitted by the absorption plate. The energy balance is as follows.hc2·Tf−Tc+hrad·Tp−Tc=Ut·Tc−Ta
Implementation of the model
The heat transfer model was implemented in the Scilab Xcos environment using a block architecture that divides the system into three interdependent subsystems, as shown in Figure 2. The dynamic variables considered are solar radiation I(t) and ambient temperature Ta, obtained from experimental data. These variables were incorporated into the model as time-dependent polynomial functions and fed to the calculation blocks corresponding to the absorber plate, the fluid, and the glass cover.
Information flow diagram of the model.
Diagram illustrating a mathematical model with equations for thermal processes involving variables such as density, heat capacity, and temperatures. Inputs include \(\rho\), \(d\), \(C_p\), \(\alpha \tau\), \(h_c\), \(h_r\), \(\rho_f\), \(C_{pf}\), \(D_f\), \(m_f\), \(A\), \(h_{c2}\), and \(U_t\). Equations describe changes in temperatures \(T_p\), \(T_f\), and \(T_c\) over time, with initial conditions specified. Arrows indicate flow and influence of parameters on equations within separate rectangular sections.
The remaining model parameters, such as the fluid and plate properties, heat transfer coefficients, and collector dimensions, are considered constant. For the absorber plate and the fluid, numerical integration blocks were used to solve the ordinary differential equations using the Sundials/CVODE (BDF–Newton) method, which allows the temporal evolution of temperatures Tp and Tf to be obtained from their initial conditions.
The interconnection between blocks incorporates feedback loops that link the outlet temperatures with the inputs of adjacent subsystems, representing heat exchange by convection and radiation. In contrast, the temperature of the glass cover (Tc) was calculated using an algebraic operations block, assuming a quasi-steady state, which simplifies the model without significantly affecting overall accuracy. Finally, this modular structure in Xcos facilitates parametric analysis by enabling rapid modification of variables, such as mass flow and the absorber’s optical properties.
Results of simulation test
The following figure shows the evolution of the temperature in the GC, both the experimental and the adjusted with Equation 9, yielding RMSE values of 0.19 °C for natural convection and 0.0089 °C for forced convection. Based on the difference between experimental and simulated temperatures, the average heat transfer coefficient h1 was determined. This coefficient was used to calculate the overall heat transfer coefficient, Ut, as described in sections 2.1 and 2.2 of this paper Figure 3.
Temperature of the glass cover and overall heat transfer coefficient under natural and forced convection conditions.
Graph showing temperature \(T_C\) in degrees Celsius and thermal transmittance \(U_t\) in watts per square meter Kelvin over time in seconds. It includes curves for both natural and forced conditions. The red and blue lines represent \(T_C\), and the black and gray lines represent \(U_t\). Each line shows varying trends over time, with \(T_C\) generally increasing and stabilizing, while \(U_t\) shows smaller variations.
The coefficient h1 was found to be 14.2 W/m2K for natural convection and 136.8 W/m2K for forced convection. By combining it in series with the coefficient h2, using Equation 4, the value of Ut was obtained. Figure 4 shows the average values of Ut: 10.5 W/m2K for natural convection and 12.4 W/m2K for forced convection.
Comparison of simulated and experimental temperature kinetics in solar collectors.
Two line graphs compare experimental and simulated temperature data over time. The left graph shows temperatures from 40 to 75 degrees Celsius, and the right graph from 30 to 55 degrees Celsius, over 18,000 seconds. Lines represent experimental (Tp exp, Tf exp, Tc exp) and simulated (Tp sim, Tf sim, Tc sim) data in red, blue, and green, showing similar trends and patterns between experimental and simulated results.
Figure 4 compares the experimentally obtained temperatures with those calculated by the mathematical model over time. The model, described in detail in sections 2.3 and 2.4, considers the temporal evolution of the temperature in three fundamental elements of the solar collector: the absorber plate, the working fluid, and the glass cover. To this end, the energy balances formulated in Equations 10–12 are used to establish the thermal interactions between the components and quantify heat transfer in the system. In this figure, the solid line represents model-simulated data, while the markers represent the experimental data. The experimental data for the AP (red), the fluid (blue), and the GC were compared, obtaining the respective RMSE values for each. Subsequently, an average value was calculated from these comparisons, resulting in an average RMSE of 0.19 °C for natural convection and 0.0089 °C for forced convection.
Discussion
The heat transfer model is considered unidirectional along the collector thickness, with energy balances formulated for the fluid, the absorber plate (AP), the glass cover (GC), and the insulating material. These domains are interconnected by a network of thermal resistances in that direction. In this way, the model allows the geometry of the collector thickness to be optimized and, at the same time, can be integrated into 2D and 3D CFD simulations solved using FEM, significantly reducing the computational complexity of the solution (Rani and Tripathy, 2020).
The heat transfer coefficients were determined from experimental temperature measurements at different points across the collector thickness. The values determined were 15 W/m2K for natural convection and 136 W/m2K for forced convection, in agreement with previous reports under similar conditions Rani and Tripathy (2020). These results are compared with the coefficients reported by Hollands et al. (1976) of 2–15 W/m2K for natural convection, and by Tiwari and Tiwari (2016) of 100–150 W/m2K for forced convection. They are also consistent with the Dittus-Boelter equation for internal flows.
Simulations show that losses due to reflection and absorption in the glass cover reach 15.4%, and remain constant, as they depend solely on the material’s optical properties. In contrast, losses associated with insulation on the sides and bottom of the collector account for 55.4% in natural convection and 31.9% in forced convection. As a result, the collector’s overall efficiency is higher under forced convection (52.7%) than under natural convection (29.3%), due to reduced losses on the outer surface.
Improvements to the collector design should focus primarily on thermal insulation, since more than a third of the incident energy is lost through the bottom and sides of the system. This can be achieved by replacing the wood insulation with polystyrene foam to reduce energy losses further.
The instantaneous thermal efficiency was evaluated through tests conducted under both natural and forced convection in quasi-dynamic conditions. This is calculated as the difference between the inlet temperature Ta and the fluid’s outlet temperature, multiplied by its heat capacity and mass flow rate, giving the amount of heat absorbed by the air in the plate (Equation 7). This value is divided by the incident solar radiation I(t), yielding the instantaneous collector efficiency. The performance results obtained from these two operating modes were subsequently averaged to derive an overall efficiency value representative of the collector’s behavior. The testing procedure and the calculation of the efficiency curve were carried out in strict accordance with the protocols established by ISO 9806 (International Organization for Standardization, 2017; Obstawski et al., 2020).
However, the most significant losses occur in the glass cover, so it is recommended that this component be replaced with a material with better optical and thermal properties, such as polycarbonate. In addition, it has been shown that the collector’s efficiency is higher under forced convection conditions, due to the increased heat transfer coefficient in the fluid. This increase can be attributed to the transition from laminar to turbulent flow, which promotes better mixing and, consequently, greater energy transport capacity. Several studies have shown that the flow distribution pattern can be modified by incorporating roughness into the absorber plate surface, thereby promoting turbulence and increasing the convective coefficient (Murmu et al., 2022; Bensaci et al., 2020; Bakari, 2018). Thus, the introduction of controlled textures, fins, or roughness into the design not only improves the collector’s thermal efficiency but also opens the possibility of optimizing its performance.
Conclusions and future perspective
Based on the thermal simulation of the flat plate solar collector, the following conclusions were drawn:
The thermal model effectively simulates the collector’s transient behavior using a system of differential and algebraic equations implemented in Scilab Xcos.
The simulation results demonstrate the significant influence of solar irradiation and ambient temperature on the evolution of the absorber plate and fluid temperatures.
Neglecting the glass cover’s thermal inertia proved a valid simplification, enabling faster computational resolution without compromising the accuracy of the fluid’s temperature profile.
Calculating the average hydraulic diameter and including convection and radiation coefficients provided a precise representation of energy exchange between the system’s layers.
The modular block diagram architecture in Xcos facilitates the analysis of different physical parameters and design configurations, making it a robust tool for solar thermal optimization
The current model provides a solid basis for the thermal analysis of solar collectors; however, several lines of research have been identified to strengthen the tool. One of the priorities is transitioning to a model with variable thermophysical properties, where parameters such as fluid viscosity and conductivity are dynamically adjusted to temperature fluctuations, thereby improving accuracy. Likewise, the methodology can be strengthened by integrating CFD, which would allow for refining the calculation of fluid convection coefficients (hc1).
A critical advance will be the execution of a sensitivity analysis on mass flow; this study will quantify how variations in the flow regime affect heat removal efficiency and outlet temperature, identifying the optimal balance between air inlet velocity and thermal performance. Finally, the implementation of optimization algorithms in the Scilab environment is planned to determine the optimal geometric dimensions automatically, and mass flows that maximize the collector’s energy gain under specific climate profiles.
Similarly, for future applications involving thermal energy storage with phase change materials (PCM), the integration of the dimensionless Fourier (Fo) and Stefan (Ste) numbers will be essential. The use of the Fourier number will allow for the dimensionless characterization of the transient response and heat diffusion in the storage tank. In contrast, the Stefan number facilitates analysis of the melting front velocity relative to the material’s latent heat (Yadav and Sahoo, 2019; Yadav and Sahoo, 2021).
Data availability statement
The datasets presented in this article are not readily available because they contain proprietary information. Requests to access the datasets should be directed to Emilio Hernández Bautista, Bautistahe@gmail.com.
Author contributions
ÁG: Conceptualization, Software, Writing – review and editing, Writing – original draft. IG-M: Writing – original draft, Writing – review and editing, Supervision. SS: Writing – original draft, Supervision, Validation, Writing – review and editing. AP-S: Writing – original draft, Visualization, Writing – review and editing, Data curation. MS-M: Writing – original draft, Writing – review and editing, Supervision. DM-P: Visualization, Writing – original draft, Validation, Writing – review and editing. EH-B: Writing – original draft, Writing – review and editing, Software, Conceptualization.
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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Edited by:Boxiang Wang, Chinese Academy of Sciences (CAS), China
Reviewed by:Xue Chen, Harbin Institute of Technology, China
Chandrmani Yadav, Sandip Institute of Technology and Research Centre, India
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