為探討矩形空腔中自然對流之熱傳特性，以3D CFD逆向方法經由實驗量測數個特定溫度點，搭配CFD商業模擬軟體ANSYS Icepak 15.0，選取適當之流動模型，再以最小平方法修正空腔中未知熱源之Q值，以接近實驗量測值，最後，利用後處理系統將模擬結果以溫度分布圖、速度向量圖與流線圖等等，使流場可視化並配合實驗數據分析其熱傳特性。
本研究透過改變空腔高度與傾斜角度，探討高度與傾角對空腔中之自然對流的影響。而結果指出，當空腔傾斜角度θ = 0˚及30˚時，流動模型選用零方程式模型與實驗結果較為吻合，而傾斜角度θ = 60˚及90˚為選擇層流則較為適當。當空腔H = 10 mm時，其空腔內幾乎由熱傳導所主宰，隨著空腔高度逐漸增加時，Bénard Cell的尺寸也會隨之增加，而當RaH上升時，("Nu" ) ̅也會同時上升，雖然實驗配合經驗公式與CFD所求得之("Nu" ) ̅趨勢相同，但整體而言，經驗公式所求得之("Nu" ) ̅較大。而當改變空腔傾斜角度下，雖然其流場之變化非常大，但由於不同角度下RaH皆幾乎相同，("Nu" ) ̅並不會有太大之變化。

To study the heat transfer characteristics of natural convection in the enclosure rectangular cavity, a 3D CFD inverse method which combined experiments and numerical simulation was used to select an appropriate flow model, and then used the least square method to correct the unknown heat source Q to close to the actual value. Finally, the post-processing program was used to convert the numerical results to temperature distribution diagrams, velocity vector diagrams, streamline diagrams, etc. to visualize the flow field and analyze the heat transfer characteristics in accordance with the experimental.
This study discussed the influence of height and inclination on the natural convection in the cavity by changing the height and inclination angle of the cavity. The results indicated that when the cavity inclination angle θ = 0˚ and 30˚, the zero-equation model for the flow model is more consistent with the experimental results, and the inclination angle θ = 60˚ and 90˚ is more appropriate for laminar flow. When the cavity H = 10 mm, the cavity is almost dominated by heat conduction. As the height of the cavity gradually increasing, the size of the Bénard cell also increased, and when the RaH rising, ("Nu" ) ̅ also increased at the same time. Although the ("Nu" ) ̅ received by the experiment and the empirical formula has the same trend with the results obtained by CFD, overall, the ("Nu" ) ̅ received by the empirical formula were larger. Although the flow field changes greatly, the ("Nu" ) ̅ were not change much, because the RaH were almost the same at different angles when the inclination angle of the cavity was changed.

[1] A. Baudoin, D. Saury, and C. Boström, Optimized distribution of a large number of power electronics components cooled by conjugate turbulent natural convection, Appl. Therm. Eng., vol. 124, pp. 975-985, 2017.
[2] R. Bessaih and M. Kadja, Turbulent natural convection cooling of electronic components mounted on a vertical channel, Appl. Therm. Eng., vol. 20(2), pp. 141-154, 2000.
[3] D. A. Vasco, C. Zambra, and N. O. Moraga, Numerical simulation of conjugate forced turbulent heat convection with induced natural laminar convection in a 2D inner cavity, Int. J. Therm. Sci., vol. 87, pp. 121-135, 2015.
[4] M. H. Anderson, L. E. Herranz, and M. L. Corradini, Experimental analysis of heat transfer within the AP600 containment under postulated accident conditions, Nucl. Eng. Des., vol. 185(2), pp. 153-172, 1998.
[5] M. M. Swartz and S. C. Yao, Experimental study of turbulent natural-convective condensation on a vertical wall with smooth and wavy film interface, Int. J. Heat Mass Transfer, vol. 113, pp. 943-960, 2017.
[6] Y. Wang, X. Meng, X. Yang, and J. Liu, Influence of convection and radiation on the thermal environment in an industrial building with buoyancy-driven natural ventilation, Energy Build., vol. 75, pp. 394-401, 2014.
[7] I. V. Miroshnichenko, M. A. Sheremet, and A. A. Mohamad, Numerical simulation of a conjugate turbulent natural convection combined with surface thermal radiation in an enclosure with a heat source, Int. J. Therm. Sci., vol. 109, pp. 172-181, 2016.
[8] M. Yasuo and U. Yutaka, Forced convective heat transfer between horizontal flat plates, Int. J. Heat Mass Transfer, vol. 9(8), pp. 803-817, 1966.
[9] A. Srivastava, A. Phukan, P. K. Panigrahi, and K. Muralidhar, Imaging of a convective field in a rectangular cavity using interferometry, schlieren and shadowgraph, Opt. Lasers Eng., vol. 42(4), pp. 469-485, 2004.
[10] D. Goluskin, Internally Heated Convection and Rayleigh-Bénard Convection (SpringerBriefs in Applied Sciences and Technology). 2016.
[11] A. Pandey, J. D. Scheel, and J. Schumacher, Turbulent superstructures in Rayleigh-Bénard convection, Nat Commun, vol. 9(1), p. 2118, 2018.
[12] M. J. Tummers and M. Steunebrink, Effect of surface roughness on heat transfer in Rayleigh-Bénard convection, Int. J. Heat Mass Transfer, vol. 139, pp. 1056-1064, 2019.
[13] A. Rincón-Casado, F. J. Sánchez de la Flor, E. Chacón Vera, and J. Sánchez Ramos, New natural convection heat transfer correlations in enclosures for building performance simulation, Eng. Appl. Comput. Fluid Mech., vol. 11(1), pp. 340-356, 2017.
[14] W. J. Hiller, S. Koch, and T. A. Kowalewski, Three-dimensional structures in laminar natural convection in a cubic enclosure, Exp. Therm Fluid Sci., vol. 2(1), pp. 34-44, 1989.
[15] Y. S. Tian and T. G. Karayiannis, Low turbulence natural convection in an air filled square cavity: Part I: the thermal and fluid flow fields, Int. J. Heat Mass Transfer, vol. 43(6), pp. 849-866, 2000.
[16] Y. S. Tian and T. G. Karayiannis, Low turbulence natural convection in an air filled square cavity: Part II: the turbulence quantities, Int. J. Heat Mass Transfer, vol. 43(6), pp. 867-884, 2000.
[17] J. L. Wright, H. Jin, K. G. T. Hollands, and D. Naylor, Flow visualization of natural convection in a tall, air-filled vertical cavity, Int. J. Heat Mass Transfer, vol. 49(5), pp. 889-904, 2006.
[18] R. F. Bergholz, Instability of steady natural convection in a vertical fluid layer, J. Fluid Mech., vol. 84(4), pp. 743-768, 1978.
[19] V. Kishor, S. Singh, and A. Srivastava, Investigation of convective heat transfer phenomena in differentially-heated vertical closed cavity: Whole field experiments and numerical simulations, Exp. Therm Fluid Sci., vol. 99, pp. 71-84, 2018.
[20] H. Karatas and T. Derbentli, Natural convection in differentially heated rectangular cavities with time periodic boundary condition on one side, Int. J. Heat Mass Transfer, vol. 129, pp. 224-237, 2019.
[21] F. J. Hamady, J. R. Lloyd, H. Q. Yang, and K. T. Yang, Study of local natural convection heat transfer in an inclined enclosure, Int. J. Heat Mass Transfer, vol. 32(9), pp. 1697-1708, 1989.
[22] R. A. Kuyper, T. H. Van Der Meer, C. J. Hoogendoorn, and R. A. W. M. Henkes, Numerical study of laminar and turbulent natural convection in an inclined square cavity, Int. J. Heat Mass Transfer, vol. 36(11), pp. 2899-2911, 1993.
[23] A. K. Sharma, K. Velusamy, and C. Balaji, Interaction of turbulent natural convection and surface thermal radiation in inclined square enclosures, Heat Mass Transfer, vol. 44(10), pp. 1153-1170, 2008.
[24] D. Saury, A. Benkhelifa, and F. Penot, Experimental determination of first bifurcations to unsteady natural convection in a differentially-heated cavity tilted from 0° to 180°, Exp. Therm Fluid Sci., vol. 38, pp. 74-84, 2012.
[25] R. B. Yedder and E. Bilgen, Turbulent natural convection and conduction in enclosures bounded by a massive wall, Int. J. Heat Mass Transfer, vol. 38(10), pp. 1879-1891, 1995.
[26] G. V. Kuznetsov and M. A. Sheremet, Numerical simulation of turbulent natural convection in a rectangular enclosure having finite thickness walls, Int. J. Heat Mass Transfer, vol. 53(1), pp. 163-177, 2010.
[27] M. A. Sheremet, Mathematical simulation of conjugate turbulent natural convection in an enclosure with local heat source, Thermophys. Aeromech., vol. 18(1), pp. 107-121, 2011.
[28] I. V. Miroshnichenko and M. A. Sheremet, Numerical simulation of turbulent natural convection combined with surface thermal radiation in a square cavity, Int. J. Numer. Methods Heat Fluid Flow, vol. 25(7), pp. 1600-1618, 2015.
[29] M. A. R. Sharif and W. Liu, Numerical study of turbulent natural convection in a side-heated square cavity at various angles of inclination, Numerical Heat Transfer; Part A: Applications, vol. 43(7), pp. 693-716, 2003.
[30] A. Ben-Nakhi and M. A. Mahmoud, Conjugate turbulent natural convection in the roof enclosure of a heavy construction building during winter, Appl. Therm. Eng., vol. 28(11), pp. 1522-1535, 2008.
[31] S. K. Choi, S. O. Kim, T. H. Lee, Y. I. Kim, and D. Hahn, Computation of Turbulent Natural Convection in a Rectangular Cavity with the Lattice Boltzmann Method, Numerical Heat Transfer Part B-Fundamentals, vol. 61(6), pp. 492-504, 2012.
[32] C. S. Zhuo and C. W. Zhong, LES-based filter-matrix lattice Boltzmann model for simulating turbulent natural convection in a square cavity, Int. J. Heat Fluid Flow, vol. 42, pp. 10-22, 2013.
[33] H. Sajjadi and R. Kefayati, Lattice Boltzmann Simulation of Turbulent Natural Convection in Tall Enclosures, Thermal Science, vol. 19(1), pp. 155-166, 2015.
[34] Y. K. Wei, H. S. Dou, Z. D. Wang, Y. H. Qian, and W. W. Yan, Simulations of natural convection heat transfer in an enclosure at different Rayleigh number using lattice Boltzmann method, Comput. Fluids, vol. 124, pp. 30-38, 2016.
[35] C. H. Huang, I. C. Yuan, and H. C. Ay, A three-dimensional inverse problem in imaging the local heat transfer coefficients for plate finned-tube heat exchangers, Int. J. Heat Mass Transfer, vol. 46(19), pp. 3629-3638, 2003.
[36] C. H. Huang, I. C. Yuan, and H. Ay, An experimental study in determining the local heat transfer coefficients for the plate finned-tube heat exchangers, Int. J. Heat Mass Transfer, vol. 52(21-22), pp. 4883-4893, 2009.
[37] H. T. Chen, J. P. Song, and Y. T. Wang, Prediction of heat transfer coefficient on the fin inside one-tube plate finned-tube heat exchangers, Int. J. Heat Mass Transfer, vol. 48(13), pp. 2697-2707, 2005.
[38] H. T. Chen and W. L. Hsu, Estimation of heat transfer coefficient on the fin of annular-finned tube heat exchangers in natural convection for various fin spacings, Int. J. Heat Mass Transfer, vol. 50(9), pp. 1750-1761, 2007.
[39] H.-T. Chen, 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, Int. J. Heat Mass Transfer, vol. 124, pp. 1217-1229, 2018.
[40] H. T. Chen, W. X. Ma, and P. Y. Lin, Natural convection of plate finned tube heat exchangers with two horizontal tubes in a chimney: Experimental and numerical study, Int. J. Heat Mass Transfer, vol. 147, p. 118948, 2020.
[41] B. E. Launder and D. B. Spalding, Lectures in mathematical models of turbulence, 1972.
[42] S. Orszag, V. Yakhot, and W. Flannery, Renormalization group modeling and turbulence, in international conference on near-wall turbulent flows, 1993.
[43] T. H. Shih, W. W. Liou, A. Shabbir, Z. Yang, and J. Zhu, A new k-ϵ eddy viscosity model for high reynolds number turbulent flows, Comput. Fluids, vol. 24(3), pp. 227-238, 1995.
[44] W. Reynolds, Fundamentals of turbulence for turbulence modeling and simulation, 1987.
[45] B. E. Launder and D. B. Spalding, The numerical computation of turbulent flows, Computer Methods in Applied Mechanics and Engineering, vol. 3(2), pp. 269-289, 1974.
[46] K. G. T. Hollands, Multi-prandtl number correlation equations for natural convection in layers and enclosures, Int. J. Heat Mass Transfer, vol. 27(3), pp. 466-468, 1984.