本研究擬以逆向三維計算流體動力學方法配合超定的實驗溫度數據及最小平方法來預測具等腰棱柱形屋頂之建築內的適當流動模型，熱傳及流體流動特性，入射至屋頂的總太陽熱及石蠟的吸收熱。透過對各種流動模型的測試發現，無論改變屋頂傾斜角或加裝抽風扇，零方程式的RMSE皆屬最小。因此在其他變因組別皆選擇零方程式作為運算的紊流模型。
在自然對流情況下，大傾斜角的熱對流係數比小傾斜角高約3.4%，導致散熱效益增加；相反，在混合對流情況下，大傾斜角的熱對流係數比小傾斜角低約8.2%，導致散熱效益下降。若加裝風扇，在30°傾斜屋頂的熱對流係數約提升4.32倍，而在45°傾斜屋頂的熱對流係數約提升3.72倍。若將相變化材料貼合於屋頂，在不同流動形式與傾斜角度狀況下，其吸熱效率 Q_pcm/Q_h 依序為63%、54%、39%及45%。此外，亦發現加裝相變化材料不會造成空氣溫度顯著上升。本研究對於被動式建築的設計提供節能與通風方法，藉以呼應全球關注的「能源危機」之相關議題。

In this study, a simulated attic building with an isosceles prismatic roof was used, where a silicone electric heater were attached to the left side of the roof to simulate sunlight. The research combines phase change materials, the installation of exhaust fans, and changes in roof angle to explore internal flow field trends and heat transfer characteristics.
Under natural convection, the steeper roof has higher heat convection efficiency, enhancing heat dissipation. However, in mixed convection, he steeper roof has lower heat convection efficiency, reducing heat dissipation efficiency.
If fans are installed, the heat convection coefficient on both 30° and 45° inclined roofs increases, resulting in an increase in heat dissipation efficiency. If phase change materials are applied to the roof, the heat absorption efficiency Q_pcm/Q_h under different convection conditions and inclination angles is 63%, 54%, 39%, and 45% sequentially. Additionally, it was found that installing phase change materials does not lead to a significant increase in air temperature.

1. Mlaouah, H., T. Tsuji, and Y. Nagano, A study of non-Boussinesq effect on transition of thermally induced flow in a square cavity. International Journal of Heat and Fluid Flow, 1997. 18(1): p. 100-106.
2. Shi, X. and J.M. Khodadadi, Laminar natural convection heat transfer in a differentially heated square cavity due to a thin fin on the hot wall. Journal of Heat Transfer, 2003. 125(4): p. 624-634.
3. Bilgen, E., Natural convection in cavities with a thin fin on the hot wall. International Journal of Heat and Mass Transfer, 2005. 48(17): p. 3493-3505.
4. Elatar, A., M.A. Teamah, and M.A. Hassab, Numerical study of laminar natural convection inside square enclosure with single horizontal fin. International Journal of Thermal Sciences, 2016. 99: p. 41-51.
5. Kadari, A., N.E. Sad Chemloul, and S. Mekroussi, Numerical investigation of laminar natural convection in a square cavity with wavy wall and horizontal fin attached to the hot wall. Journal of Heat Transfer, 2018. 140(7).
6. Sparrow, E.M., A. Haji-Sheikh, and T.S. Lundgren, The inverse problem in transient heat conduction. Journal of Applied Mechanics, 1964. 31(3): p. 369-375.
7. Chan, Y.L. and C.L. Tien, A numerical study of two-dimensional laminar natural convection in shallow open cavities. International Journal of Heat and Mass Transfer, 1985. 28(3): p. 603-612.
8. Chen, Q. and W. Xu, A zero-equation turbulence model for indoor airflow simulation. Energy and Buildings, 1998. 28(2): p. 137-144.
9. Prandtl, L., Bericht über untersuchungen zur ausgebildeten turbulenz. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1925. 5(2): p. 136-139.
10. Chen, H.T., M.C. Lin, and J.R. Chang, Numerical and experimental studies of natural convection in a heated cavity with a horizontal fin on a hot sidewall. International Journal of Heat and Mass Transfer, 2018. 124: p. 1217-1229.
11. Chen, H.T., et al., Prediction of 3D natural convection heat transfer characteristics in a shallow enclosure with experimental data. Progress in Nuclear Energy, 2022. 153: p. 104425.
12. Chen, H.T., et al., Experimental and numerical study of inverse natural convection-conduction heat transfer in a cavity with a fin. Numerical Heat Transfer, Part A: Applications, 2023. 84(6): p. 641-658.
13. Kurpisz, K. and A.J. Nowak, Inverse thermal problems. 1995: Computational Mechanics Publications.
14. Abdulrahman, R.S., F.A. Ibrahim, and S.F. Dakhil, Development of paraffin wax as phase change material based latent heat storage in heat exchanger. Applied Thermal Engineering, 2019. 150: p. 193-199.
15. Li, D., et al., Influence of glazed roof containing phase change material on indoor thermal environment and energy consumption. Applied Energy, 2018. 222: p. 343-350.
16. Khan, Z. and Z.A. Khan, Experimental investigations of charging/melting cycles of paraffin in a novel shell and tube with longitudinal fins based heat storage design solution for domestic and industrial applications. Applied Energy, 2017. 206: p. 1158-1168.
17. Kara, Y.A. and A. Kurnuç, Performance of coupled novel triple glass and phase change material wall in the heating season: an experimental study. Solar Energy, 2012. 86(9): p. 2432-2442.
18. Pomianowski, M., P. Heiselberg, and Y. Zhang, Review of thermal energy storage technologies based on PCM application in buildings. Energy and Buildings, 2013. 67: p. 56-69.
19. Chen, H.-T., et al., Natural convection heat transfer in isosceles prismatic roof with perforated partition and phase change material. Thermal Science and Engineering Progress, 2024. 48: p. 102428.
20. Chen, H.T., et al., Numerical and experimental study of inverse natural convection heat transfer for heat sink in a cavity with phase change material. International Journal of Heat and Mass Transfer, 2024. 224: p. 125333.
21. Launder, B.E. and D.B. Spalding, Paper 8 - the numerical computation of turbulent flows, in Numerical prediction of flow, heat transfer, turbulence and combustion, S.V. Patankar, et al., Editors. 1983, Pergamon. p. 96-116.
22. Orszag, S.A., Renormalisation group modelling and turbulence simulations. Near-wall turbulent flows, 1993.
23. Gasia, J., et al., Experimental evaluation of a paraffin as phase change material for thermal energy storage in laboratory equipment and in a shell-and-tube heat exchanger. Applied Sciences, 2016. 6(4): p. 112.
24. GmbH, A.P. Viscosity of paraffin wax. [cited 2024 March 20]; Available from: https://wiki.anton-paar.com/en/paraffin-wax/.
25. Patankar, S.V., W. Minkowycz, and E. Sparrow, Series in computational methods in mechanics and thermal sciences. McGraw Hill Book Company, New York, 1980: p. 1-197.
26. Arpaci, V.S., Kao, S.H., and Selamet, A., “Introduction to heat transfer”. Prentice Hall. 1999.
27. Chen, H.-T., et al., Numerical and experimental study of inverse natural convection-conduction heat transfer in an inclined rectangular cavity. Numerical Heat Transfer, Part B: Fundamentals, 2023: p. 1-18.
28. 四管於封閉空腔內之三維自然對流的熱傳特性研究. 2021: National Cheng Kung University Department of Mechanical Engineering.