Heat Transfer Model Predicts Solar Collector Efficiency With Remarkable Precision

Flat-plate solar collectors are among the simplest and most affordable devices for turning sunlight into useful heat, yet their performance depends on a delicate interplay of conduction, convection, and radiation occurring simultaneously across several thin layers. A research team in Oaxaca, Mexico, has now built a phenomenological mathematical model that captures this interplay in detail, validated it against real measurements, and identified exactly where the energy escapes. The work, published in Frontiers in Thermal Engineering, offers designers an accessible, open-source tool for squeezing more heat out of one of the world’s most widespread solar technologies.

The study, led by Ángel Alfonso García López and colleagues at the Tecnológico Nacional de México/Instituto Tecnológico de Oaxaca, together with researchers from the Instituto Politécnico Nacional, focused on a solar air collector consisting of three essential elements: a glass cover on top, an aluminum absorber plate beneath it, and wood insulation at the base. Air flows longitudinally through the channel between the glass and the plate, while energy moves perpendicular to that flow through the collector’s thickness. The team installed the device at a 20-degree tilt at coordinates in Oaxaca and instrumented it with thermocouples accurate to 0.01 °C, recording ambient temperature, glass temperature, absorber plate temperature, insulation temperature, and the final temperature of the working fluid throughout the day.

At the heart of the modeling approach lies a thermal resistance network, a conceptual map in which every pathway that heat can take out of the collector is represented as a resistance, much like resistors in an electrical circuit. Convection and radiation from the glass cover to the environment act in parallel, while conduction through the insulation acts in series below the absorber plate. The researchers combined empirical correlations widely used in the field, including the McAdams correlation for external convection and the linearized Stefan–Boltzmann equation for radiative exchange between gray surfaces and the sky, to quantify each pathway. The overall top loss coefficient, Ut, emerges from the series combination of the internal and external coefficients, while the bottom loss coefficient Ub depends directly on insulation thickness and inversely on its thermal conductivity.

What distinguishes this study is its insistence on experimental grounding. Rather than relying solely on textbook correlations, the team measured temperatures and air velocities to derive the heat transfer coefficients themselves. The sky temperature was first estimated using an empirical correlation by Zvirin and Aronov, then fed into the radiative equations. With glass and ambient temperatures in hand, the researchers computed the external radiative and convective coefficients. The internal convective coefficient, however, remained an unknown to be determined. By proposing an initial value, calculating the resulting glass temperature from an energy balance, and comparing it with the measured data, the team iteratively adjusted the coefficient until the sum of quadratic errors was minimized.

The experiments were run under two distinct flow regimes. Under natural convection, air entered the collector at 0.66 meters per second; under forced convection, the velocity rose to 4.5 meters per second. A pyranometer measured the incident solar radiation, and an optical efficiency of 86 percent was assumed for the glass, meaning that roughly 86 percent of the incoming short-wave radiation actually reaches the absorber plate. The glass cover acts as a selective filter in this arrangement: it transmits short-wave solar radiation while limiting long-wave infrared emissions from the hot plate, creating a greenhouse effect that enhances the collector’s performance.

To solve the resulting system of energy balances, the researchers turned to Scilab Xcos, an open-source graphical modeling environment. The model was implemented as a block architecture dividing the system into three interdependent subsystems representing the absorber plate, the working fluid, and the glass cover. Solar radiation and ambient temperature, recorded experimentally, were incorporated as time-dependent polynomial functions and fed into the calculation blocks. Ordinary differential equations for the plate and fluid temperatures were solved numerically using the Sundials/CVODE method with a backward differentiation formula and Newton iteration. The glass cover temperature, owing to its negligible thermal capacitance, was computed algebraically under a quasi-steady-state assumption, a simplification that dramatically speeds computation without sacrificing accuracy.

The validation results are striking. Comparing simulated and experimental temperatures yielded a root mean square error of just 0.19 °C under natural convection and an extraordinary 0.0089 °C under forced convection. The fitted internal heat transfer coefficient came out at 14.2 W/m²K for natural convection and 136.8 W/m²K for forced convection, values consistent with previous reports ranging from 2 to 15 W/m²K for natural convection and 100 to 150 W/m²K for forced convection, and in agreement with the Dittus–Boelter equation for internal flows. The overall top loss coefficient averaged 10.5 W/m²K under natural convection and 12.4 W/m²K under forced convection.

The efficiency numbers tell a compelling story about where the energy goes. Under forced convection, the collector achieved a thermal efficiency of 52.7 percent, while under natural convection it managed only 29.3 percent. The dramatic difference stems from the transition toward turbulent flow at higher air velocities, which promotes better mixing and a greater capacity for energy transport away from the absorber plate. Losses through the insulation on the sides and bottom accounted for 55.4 percent of incident energy under natural convection but dropped to 31.9 percent under forced convection. Optical losses from reflection and absorption in the glass cover remained constant at 15.4 percent, since they depend solely on the material’s optical properties rather than on flow conditions.

These findings point to clear design priorities. Because more than a third of the incident energy escapes through the bottom and sides, the researchers recommend replacing the wood insulation with polystyrene foam to reduce conductive losses. The glass cover, identified as the site of the most significant optical losses, could be swapped for a material with better optical and thermal properties, such as polycarbonate. Beyond material substitutions, the team notes that incorporating controlled textures, fins, or roughness on the absorber plate surface can modify the flow distribution pattern, promote turbulence, and raise the convective coefficient, further boosting thermal efficiency.

The modular block structure in Xcos makes the model a practical tool for parametric analysis, allowing rapid modification of variables such as mass flow rate and the absorber’s optical properties. Looking ahead, the researchers outline several avenues for strengthening the tool: transitioning to variable thermophysical properties that adjust dynamically with temperature, integrating computational fluid dynamics to refine the internal convection coefficients, and running sensitivity analyses on mass flow to identify the optimal balance between inlet air velocity and thermal performance. They also plan to implement optimization algorithms in Scilab to automatically determine geometric dimensions and flow rates that maximize energy gain under specific climate profiles, and to extend the framework toward thermal energy storage with phase change materials using dimensionless Fourier and Stefan numbers. For a technology that remains one of the most cost-effective ways to harvest solar heat for drying agricultural products and warming communities, this blend of rigorous measurement and accessible simulation offers a roadmap for designs that waste far less of the sun’s generous gift.

Subject of Research: Thermal modeling and experimental validation of heat transfer in a flat-plate solar air collector

Article Title: Thermal simulation of a flat-plate solar collector based on heat transfer coefficients

Article References: García López, Á. A., García-Montalvo, I. A., Sandoval Torres, S., Pérez-Santiago, A. D., Sánchez-Medina, M. A., Matías-Pérez, D., & Hernández-Bautista, E. (2026). Thermal simulation of a flat-plate solar collector based on heat transfer coefficients. Frontiers in Thermal Engineering, 6, Article 1734742. https://doi.org/10.3389/fther.2026.1734742

Image Credits: AI Generated

DOI: 10.3389/fther.2026.1734742

Keywords: flat-plate solar collector, heat transfer coefficients, thermal resistance network, solar thermal energy, Scilab Xcos, forced convection, natural convection, thermal efficiency, glass cover, absorber plate, insulation losses, numerical simulation