# Numerical Study of Mixed Convection and Heat Transfer in Arc-Shaped Cavity with Inner Heat Sources
## 4 Conclusions  
Aiming at the problem of mixed convection in a curved cavity with an internal heat source, the transient characteristics of the fluid flow and heat transfer characteristics at the fully developed stage under different Re are studied by using a two-dimensional numerical simulation technique. The following conclusions can be drawn:  
* When Ra is fixed (Ra = 2.36 \(\times\) 10\({}^{12}\)), with the increase in Re, the flow in the arc cavity experiences a transition from turbulent flow to periodic flow and then to a steady flow. The flow period and amplitude decrease with the increase in Re, and the main frequency increases with the increase in Re. The critical Re of transition from weak turbulence to periodic flow is about 6.14 \(\times\) 10\({}^{6}\) and 6.15 \(\times\) 10\({}^{6}\), and the critical Re of transition from periodic flow to constant flow is between 1.38 \(\times\) 10\({}^{7}\) and 1.39 \(\times\) 10\({}^{7}\). The flow structure changes from asymmetric and multiple convection cells to symmetric double convection cells. * There is a linear positive correlation between the heat flux and Re, \(q_{t}\)-4.9 Re, \(q_{cv}\)-4.89 Re, \(q_{cd}\)-0.001 Re. Increasing the number of Re increases the heat convection in the curved cavity structure, and the gap between heat convection and heat conduction also increases with the increase in Re. Nu increases first and then gradually decreases with Re. We found that for 1.75 \(\times\) 10\({}^{6}\)\(\leq\) Re \(\leq\) 6.14 \(\times\) 10\({}^{6}\), Nu\(\leftarrow\)\(-\)0.0059 Re, for 6.15 \(\times\) 10\({}^{6}\)\(\leq\) Re \(\leq\) 1.1 \(\times\) 10\({}^{7}\), Nu\(\leftarrow\)\(-\)0.017 Re and for 1.31 \(\times\) 10\({}^{7}\)\(\leq\) Re \(\leq\) 4.38 \(\times\) 10\({}^{7}\), Nu\(\leftarrow\)\(-\)0.001 Re. * The average temperature \(T_{m}\) in the middle region of the two heat sources is similar to Nu, while the effective heat coefficient \(m\) generally conforms to the rising trend. After the steep rise of Re in the range from 1.14 \(\times\) 10\({}^{7}\) to 1.18 \(\times\) 10\({}^{7}\), the continued increase in Re has little effect on the removal of waste heat. As the Reynolds number increases, the heat removal capacity in the middle region of the double heat sources is not always enhanced, which is due to the sudden change in flow structure and flow state around Re = 1.18 \(\times\) 10\({}^{7}\). In practical engineering problems,  
Figure 10: The change of effective heat coefficient \(m\) with Re number. the inlet wind speed can be controlled in the most appropriate Re to achieve a better heat removal effect. Conceptualization, H.C., F.X. and S.C.S. ; Methodology, H.C., H.A. and W.W.; Validation, Z.H. ; Formal analysis, H.A. and B.H. ; Resources, Z.H. and B.H. ; Data curation, W.W.; Writing--original draft, H.C.; Writing--review & editing, H.A., W.W., Z.H., B.H., F.X., Q.L. and S.C.S. ; Visualization, H.C.; Supervision, F.X., Q.L. and S.C.S. ; Project administration, Q.L. All authors have read and agreed to the published version of the manuscript. This research was funded by [Programs of Natural Science Foundation of Hebei Province of China] grant number [E2022210069, E2019210026], [National Natural Science Foundation of China] grant number [11802186], [Innovation research group project of Natural Science Foundation of Hebei Province of China] grant number [E2022210078], [Science and Technology Winter Olympics Special Project] grant number [21475402D] and [High-end Talents Project of Hebei Province of China] grant number [(2019) 63]. All data produced from the simulations are used in this paper as the form of Tables and Figures. The authors declare no conflict of interest.