## 6 Conclusions  
The flat plate solar collector (FPSC) performance depends on contributing factors such as \(\dot{m}\), \(Re\), \(Nu\), \(h_{fi}\), \(F_{R}\), \(Q_{u}\), and \(\mu_{Th}\). In this paper, the heat transfer characteristics of the flat plate solar thermal collectors with circular and elliptical serpentine designs, using water as the working fluid, were theoretically investigated in detail under the standard test conditions (\(S=\)1000 Wm\({}^{-2}\), \(T_{a}=25\)\({}^{\circ}\)C). It was concluded that:  
* The lower manufacturing costs and high efficiency even at low flow rates of circulating fluid are principal advantages of serpentine designs compared to their counterparts. However, they require pumping systems at higher flow rates. * The greatest values of \(Q_{u}\) were obtained for elliptical and circular cross-sections (493.8 W and 493 W, respectively) under turbulent flow (\(\dot{m}=\) of 0.05 kg s\({}^{-1}\)), even though the lowest values were 420.4 W and 412.4 W for circular and elliptical design  
Figure 10: Schematic diagram of governing parameters affecting \(\mu_{Th}\). under laminar flow (\(\dot{m}=0.01\) kg s\({}^{-1}\)), respectively. The maximum thermal efficiency (56%) is achievable under turbulent flow for the elliptical cross-section. * The highest values of \(F_{R}\) corresponded to elliptical and circular design under turbulent flow with 0.538 and 0.539, respectively, and \(F_{R}\) was the minimum for circular and elliptical designs with 0.458 and 0.450, respectively, under laminar flow. * At various mass flow rates, the tubes with different cross-sections lead to various values for \(Re\), \(Nu\), \(h_{fj}\), \(F_{R}\), \(Q_{u}\), and \(\mu_{Th}\), while the \(Pr\) remains constant as it does not depend on the geometry of the tube. * All heat transfer governing parameters increased notably by changing laminar to non-laminar flow rates for both cross-sections. It was due to the cooling effect of water showing better performance under non-laminar flow rates. * It was concluded that at the same area, the cross-section geometry with lower values of hydraulic diameter (12 mm for elliptical design) had higher heat transfer characteristics in comparison to a cross-section with a greater hydraulic diameter (13 mm for circular design). * At the same area, the elliptical tube increased the heat transfer rate (\(Q_{u}\)) by approximately 2% in comparison to a circular tube due to a larger contact area between the working fluid and the solid surface of tubes. In summary, it is essential to conduct an analytical study on the heat transfer parameters of a solar thermal collector in the primary stage of its design to fabricate a highly efficient system and save time as well as manufacturing costs. The authors suggest that employing nanofluids and phase change materials alongside effective cross-sections might significantly enhance the thermal characteristic of a solar thermal system. Conceptualization, K.S., H.J. and A.I. ; methodology, S.R. and H.J. ; software, S.R., H.J. and A.B. ; validation, K.S. and H.J. ; formal analysis, S.R. and A.B. ; investigation, S.R. ; resources, H.J. ; data curation, S.R. and H.J. ; writing--original draft preparation, S.R., H.J. and A.B. ; writing--review and editing, S.R. and H.J. ; visualization, H.J. and A.I. ; supervision, K.S., H.J. and A.I. ; project administration, A.S.A.H., K.S. and A.I. ; funding acquisition, A.S.A.H. and A.I. All authors have read and agreed to the published version of the manuscript. This research was funded by the FRGS/1/2019/TK07/UKM/02/4 (Fundamental Research Grant Scheme-Universiti Kebangsaan Malaysia) and SPBK-UMS phase 1/2022 (SBK0518-2022-Universiti Malaysia Sabah) research grants. The APC was funded by Universiti Malaysia Sabah. Not applicable. The authors would like to thank the Solar Energy Research Institute, Universiti Kebangsaan Malaysia (UKM) and Faculty of Science and Natural Resources, Universiti Malaysia Sabah (UMS) for the lab facilities.