**4. Conclusions**

This work investigates a compound parabolic concentrator (CPC) design for air heating with a double U-pass configuration. The double pass is incorporated to recover part of the heat lost by the flat plate receiver inside the CPC cavity. Overall, four configurations have been studied, and they are differentiated by the position of the air inlet into the cavity and the position of the air outlet of the cavity towards the receiving duct that constitutes the second pass of the collector.

In general, adding the first pass through the CPC cavity significantly increases the air temperature. Hence, by making the air circulate first through the CPC cavity, instead of a conventional manner where it only circulates through the duct, an increase in temperature is accomplished before entering the receiving duct. As a result, an average increase in air temperature of 11.8 K at a mass flow rate of 0.01 kg/s and 6.2 K at a mass flow rate of 0.02 kg/s was achieved. This represents a minimum temperature rise of 36% (0.01 kg/s) and 40% (0.02 kg/s) when only the first pass is used.

In addition, the analysis showed that the positions of the air inlet and outlet in the cavity do not influence the outlet temperature of the U-shape double pass CPC solar heater due to an efficiency difference of up to 3.5% being achieved. The Down–Down configuration is the one that provides slight outlet temperature and thermal efficiency increases. With this configuration, an air temperature increase from the U-shape double-pass CPC inlet to the outlet of 28.9 K and an efficiency of 77.3% are obtained when the airflow rate is 0.01 kg/s, and 15.1 K and 80.5% when the flow rate is 0.02 kg/s. This is because the air heated in the cavity is transported more effectively, as it is a more homogeneous flow and the heat transfer coefficient in the flat-plate receiver is high.

The first pass allows an extraction between 36% and 45% of the total heat, justifying its inclusion into the solar collector. Although configuration (a) Down–Down presents a slightly higher efficiency with both studied flows, the difference between the values of configurations (b), (c), and (d) seems irrelevant. Therefore, the decision of the configuration should be based on other aspects such as the manufacture of the collector, air pumping requirements, and the design of the collectors' array, which are highly dependent on the application conditions and needs.

In the case of the (a) Down–Down configuration, including elements that restrict air circulation from the cavity to the area near the flat-plate receiver could be explored to encourage contact with the hot surface. Strategies to accomplish this are to add a second cover close to the receiver inside the cavity or to increase the truncation of the collector reflectors. Finally, the structural design and financial analysis remain as future work to determine the potential application of this technology.

**Author Contributions:** Conceptualization, I.A.C.-B., E.V.-R. and N.O.-A.; Data curation, I.A.C.-B.; Formal analysis, I.A.C.-B., N.A.R.-M., L.V. and N.O.-A.; Funding acquisition, N.O.-A.; Investigation, I.A.C.-B.; Methodology, I.A.C.-B. and N.A.R.-M.; Project administration, N.O.-A.; Resources, N.A.R.- M. and L.V.; Software, I.A.C.-B.; Supervision, N.A.R.-M., E.V.-R. and N.O.-A.; Validation, I.A.C.-B., L.V. and N.A.R.-M.; Visualization, I.A.C.-B., N.A.R.-M. and N.O.-A.; Writing—original draft, I.A.C.-B., N.A.R.-M. and N.O.-A.; Writing—review & editing, I.A.C.-B., N.A.R.-M., E.V.-R., L.V. and N.O.-A. All authors have read and agreed to the published version of the manuscript.

**Funding:** The APC was funded by the Centro de Investigacion en Materiales Avanzados (CIMAV) through project number PI-22-24/2022.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors wish to thank the Mexican National Science Council (CONACYT) for the financial support through scholarship 698432. To Durango Science and Technology Council (COCYTED) for the financing of the annual ANSYS software license. Also, to the Laboratorio de Computo Cientifico of FCQ-UJED and the Academic Group UJEDCA129 for the use of software and computational facilities.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the decision to publish the results.

#### **Nomenclature**


