本文利用三維CFD逆向方法，針對以往一項研究為封閉空腔內壁貼附之鰭片，配合冷熱等溫壁產生空氣自然對流進行探討，並重新隨機給定一熱源Q值配合最小平方法收斂之新方法，與舊有的實驗與模擬結果進行比對。本文使用ANSYS Fluent 18.0套裝軟體進行模擬，透過等熱傳率與先前實驗量測之溫度以及等溫壁模擬結果進行比較，並將結果透過方均根誤差計算，得到適合之流動模型與網格，再利用溫度分布圖及速度流線圖分析系統熱傳特性。結果顯示，零方程式為適合之流動模型，本研究亦發現利用等熱傳率進行模擬，能較以往之等溫壁模擬更加準確。針對鰭片的分析，主要改變鰭片1與鰭片2之間距以及鰭片2長度，探討對空腔內熱傳的影響。透過模擬結果可發現，當兩鰭片間距增加時，因渦漩逐漸消散使流體速度上升，鰭片1之熱傳係數也會跟著上升。當鰭片2逐漸伸長時，雖能增加冷壁吸收之熱量，但阻塞效應(block effect)也隨之產生，導致空腔內流體速度下降，使鰭片1熱傳係數下降。

This study employs a three-dimensional CFD inverse method to investigate the natural convection heat transfer of fins involving hot and cold isothermal walls in a cavity.By randomly assigning a new heat source value Q and utilizing the Least Square Method (LSM), the results are compared with previous experimental and simulation data.This study utilizes ANSYS Fluent 18.0 for simulations, comparing results with previous experimental temperature measurements and isothermal wall simulation results through equivalent heat transfer rates. The root mean square error is calculated to determine the most suitable flow model and mesh. System heat transfer characteristics are analyzed by using temperature distributions and velocity streamlines. The results indicate that the zero-equation model is the most appropriate flow model. It’s also found that simulations using equivalent heat transfer rates are more accurate than previous isothermal wall simulations.For the fin analysis, the primary focus was on changing the spacing between fin 1 and fin 2, as well as the length of fin 2, to study the impact on heat transfer within the cavity. The simulation results show that as the spacing between the two fins increased, the fluid velocity rise due to the gradual dissipation of vortices, leading to an increase in the heat transfer coefficient of fin 1. However, as fin 2 is lengthened, it absorbed more heat from the cold wall, but the blocking effect caused a decrease in fluid velocity within the cavity, resulting in a lower heat transfer coefficient of fin 1.

[1] 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 and Building , vol. 75, 2014, pp. 394-401.
[2] I. V. Miroshnichenko and M. A. Sheremet,“Turbulent natural convection heat transfer in rectangular enclosures using experimental and numerical approaches: A review,”Renewable and Sustainable Energy Reviews, vol. 82, 2018, pp. 40-59.
[3] H. T. Chen and Y. H. Chen,“Experimental And Numerical Study on natural convection heat transfer of fins on a hot wall and cold wall in a cavity, ”2020.
[4] F. Harahap, H. Lesmana and I. A. S. Dirgayasa,“Measurements of heat dissipation from miniaturized vertical rectangular fin arrays under dominant natural convection conditions,” Heat and mass transfer, vol. 42, 2006, pp. 1025-1036.
[5] A. Kadari, 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, vol. 140(7), 2018, pp. 072503.
[6] X. Shi and J. M. Khodadadi,“Laminar natural convection heat transfer in a differentially heated square cavity due to a thin fin on the hot wall,”J. Heat Transfer, vol. 125(4), 2003, pp. 624-634.
[7] A. Ben-Nakhi and A. J. Chamkha,“Conjugate natural convection in a square enclosure with inclined thin fin of arbitrary length,” International journal of thermal sciences, vol. 46(5), 2007, pp. 467-478.
[8] T. K. Ibrahim, M. N. Mohammed, M. K. Mohammed, G. Najafi, N. A. C. Sidik, F. Basrawi, A. N. Abdalla and S. S. Hoseini,“Experimental study on the effect of perforations shapes on vertical heated fins performance under forced convection heat transfer,”International Journal of Heat and Mass Transfer, vol. 118, 2018, pp. 832-846.
[9] A. K. Sharma, K. Velusamy and C. Balaji,“Interaction of turbulent natural convection and surface thermal radiation in inclined square enclosures,”Heat and mass transfer, vol. 44, 2008, pp. 1153-1170.
[10] 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,”International Journal of Heat and Mass Transfer, vol. 36(11), 1993, pp. 2899-2911.
[11] 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°,”Experimental thermal and fluid science, vol. 38, 2012, pp. 74-84.
[12] I. V. Miroshnichenko and M. A. Sheremet,“Numerical simulation of turbulent natural convection combined with surface thermal radiation in a square cavity ,”International Journal of Numerical Methods for Heat & Fluid Flow, vol. 25(7), 2015, pp. 1600-1618.
[13] M. A. R. Sharif and W. Liu,“Numerical study of turbulent natural convection in a side-heated square cavityat various angles of inclination,”Numerical Heat Transfer: Part A: Applications , 43(7), 2003, pp. 693-716.
[14] 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), 2012, pp. 492-504.
[15] H. Sajjadi and R. Kefayati,“Lattice Boltzmann simulation of turbulent natural convection in tall enclosures,”Thermal science, vol. 19(1), 2015, pp. 155-166.
[16] Y. Wei, H. S. Dou, Z. Wang , Y. Qian and W. Yan,“Simulations of natural convection heat transfer in an enclosure at different Rayleigh number using lattice Boltzmann method,”Computers & Fluids, vol. 124, 2016, pp. 30-38.
[17] M. A. Sheremet,“Mathematical simulation of conjugate turbulent natural convection in an enclosure with local heat source,” Thermophysics and Aeromechanics, vol. 18(1), 2011, pp. 107-121.
[18] A. Ben-Nakhi and M. A. Mahmoud,“Conjugate turbulent natural convection in the roof enclosure of a heavy construction building during winter,”Applied Thermal Engineering, vol. 28(11-12), 2008, pp. 1522-1535.
[19] 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,”International Journal of Heat and Mass Transfer, vol. 124, 2018, pp. 1217-1229.
[20] H. T. Chen, W. X. Ma and P. Yu. Lin,“Natural convection of plate finned tube heat exchangers with two horizontal tubes in a chimney: experimental and numerical study,”International Journal of Heat and Mass Transfer, vol. 147, 2020, pp. 118948.
[21] M. N. Özişik and H. R. B. Orlande, Inverse Heat Transfer: Fundamentals and Applications, Taylor & Francis, 2000.
[22] O. M. Alifanov, Inverse Heat Transfer Problem, Springer-Verlag, 2012.
[23] J. B. Bell, Solutions of Ill-Posed Problems, 1978.
[24] J. V. Beck, B. Blackwell and C. R. S. Clair, Inverse heat conduction: Ill-posed problems, James Beck, 1985.
[25] Q. Chen and Xu. Weiran,“A zero-equation turbulence model for indoor airflow simulation,”Energy and buildings, vol. 28(2), 1998, pp. 137-144.
[26] H. Heidary and M. J. Kermani,“Heat transfer enhancement in a channel with block(s) effect and utilizing Nano-fluid,”International Journal of Thermal Sciences, vol. 57, 2012, pp. 163-171.