本研究利用暫態之數值方法探討水平鰭片熱沉在多通道情形下的自然對流特性，著重探討側向氣流之三維流場對於各通道與整體熱沉散熱量的影響。模擬之鰭片尺寸為L=80 ~254 mm，H=6.4~25 mm，S=6.4 mm、8 mm。全文共分為四個部分，第一部分利用無限通道之模擬結果與實驗數據進行比對以驗證模擬的可靠度；第二部分探討L=127 mm下鰭片高度H對於多通道流場以及散熱效果的影響，結果顯示H=6.4 mm時由於側向氣流會嚴重壓制熱沉外部通道中上浮之氣流，且僅有內側通道能順利產生滑移煙囪流，因此內側通道的散熱效果將優於外側通道；隨著高度增加至H=25 mm，各通道的流場行為會趨近單一煙囪流，側向氣流將無法壓制各通道上浮之氣流，反而還會增加外側通道上方空氣之浮力，因此外側通道的散熱效果反而優於內側通道；第三部分討論L=127 mm時不同型式的側板條件對於側向氣流與整體熱傳效果的影響，結果發現熱沉外側有無添加保護鰭片(guard fin)對於高鰭片(H=25 mm)而言影響不大；然而對於矮鰭片(H=6.4 mm)而言卻能大幅增加外側通道的散熱效果，使得多通道熱沉平均各通道之 h ̅ 接近於無限通道模擬之結果。此外若將矮鰭片(H=6.4 mm)最外側的鰭片增添6.6 mm高的絕熱段或是改為13 mm高之等溫鰭片皆能有效的阻隔側向氣流對於內部通道的壓制行為。其中最外側為13 mm高等溫鰭片的熱沉，平均內部各通道之h ̅可高出標準十六通道之熱沉21.9%；第四部分則探討鰭片長度對於多通道流場之影響，模擬結果發現短鰭片(L=80 mm)熱沉，在任何鰭片高度下各通道之流場型態皆為單一煙囪流，此外側向氣流幾乎不會對內部通道造成影響，因此採用無限通道所求出之h ̅ 與多通道(平均通道1~8)之間差異不超過1.2%；反觀長鰭片(L=254 mm)在三種高度下(H=6.4~25 mm)，側向氣流皆會被引入熱沉中段上方影響內部通道之熱傳效果。即便在H=25 mm之情況下，利用無限通道模擬所求出之h ̅仍會高估11.4%。另外模擬結果還發現矮鰭片(H=6.4 mm)熱沉之側向氣流在z方向上會產生大週期左右振盪行為，這現象導致熱沉部分通道之h ̅甚至會低於穩態解hss。因此多通道長鰭片之熱沉須同時考量長度方向上流場的振盪行為、側向氣流帶來的三維效應還要顧及側向氣流是否會發生左右振盪的情形。

This study investigates the transient natural convection characteristics of horizontal multi-channel plate-fin heat sinks, focusing on the impact of the three-dimensional side flow on the heat dissipation of each individual channel and the overall heat sink. The simulated fin dimensions are L=80~254 mm, H=6.4~25 mm, S=6.4~8 mm. The full text is divided into four parts. The first part compares the simulation results of the infinite channel heat sink with the experimental data to verify the reliability of the simulation. The second part discusses the effect of the fin height H under L=127 mm on the multi-channel flow field and heat dissipation. The results show that when H=6.4 mm, the side flow will seriously suppress the upward airflow in the outer channel of the heat sink, and only the inner channel can smoothly generate the sliding chimney flow. Consequently, the heat dissipation ability of the inner channels is better than that of the outer channels. As the fin height increases to H=25 mm, the flow field behavior of all channels approximates a single chimney flow. The side flow does not suppress the upward airflow, but increase the buoyancy for the outer channels. Therefore, in this case, the heat dissipation of the outer channels is better than of the inner channels. The third part discusses the influence of different types of side plate conditions on the side flow and the overall heat transfer effect at L=127 mm. It is found that whether there are guard fins on the outer sides of the heat sink has little effect on the high-fin heat sink (H=25 mm). But for a short-fin heat sink (H=6.4 mm), the heat dissipation of the outer channels is significantly increased and the h ̅ in each individual channel of the multi-channel heat sink approximates the result of infinite-channel simulation. Besides, if both outermost fins of the short-fin heat sink (H=6.4 mm) are added with a 6.6 mm-high insulation section or are changed to 13 mm-high isothermal fins, the suppression of the side flow to internal channels can be effectively avoided. Also, if the outermost are 13 mm- high elongated isothermal fins, the average of h ̅ in internal channels can be 21.9% higher than the standard 16-channel heat sink. The last part mainly discusses the effect of fin length on the multi-channel flow field. The simulation results indicate that for the short-fin (L=80 mm) heat sink, the flow field pattern of each channel at any fin height is a single chimney flow. The side flow hardly affects the internal channels, so the difference of h ̅ between the infinite channel and multi-channel heat sink (average of channels 1~8) does not exceed 1.2%. In contrast, for the long-fin heat sink (L=254 mm) at three fin heights (H=6.4~25 mm), the side flow will penetrate above the heat sink to affect the heat transfer effect of the internal channels. Even in the case of H=25 mm, the h ̅ obtained by simulation with the infinite channel will still be over-estimated by 11.4%. Also, the simulation results indicate that the side flow of the low fin (H=6.4 mm) heat sink will oscillate left and right in the transverse direction with a larger period, which will cause the h ̅ of part of the heat sink channels to be even lower than the steady-state solution hss. Therefore, the analysis for multi-channel long-fin heat sinks must consider the oscillation behavior of the flow field in the longitudinal direction, the three-dimensional effect brought by the side airflow, and whether the lateral airflow will oscillate.

[1] G.-J. Huang, S.-C. Wong, Dynamic characteristics of natural convection from horizontal rectangular fin arrays, Appl. Therm. Eng. 42 (2012) 81–89.

[2] S.-C. Wong, G.-J. Huang, Parametric study on the dynamic behavior of natural convection from horizontal rectangular fin arrays, Int. J. Heat Mass Transfer 60 (2013) 334–342.
[3] W. Elenbaas, Heat dissipation of parallel plates by free convection, Physica 9(1942) 1–28.

[4] Bar-Cohen, W.M. Rohsenow, Thermally optimum spacing of vertical, natural convection cooled, parallel plates, J. Heat Transfer 106 (1984) 116–123.

[5] J.R. Bodoia, J.F. Osterle, The development of free convection between heated vertical plates, ASME J. Heat Transfer 84 (1962) 40–44.

[6] C.F. Ketteborough, Transient laminar free convection between heated vertical plates including entrance effects, Int. J. Heat Mass Transfer 15 (1972) 883–896.

[7] H. Nakamura, Y. Asako, T. Naitou, Heat transfer by free convection between two parallel flat plates, Numerical Heat Transfer 5 (1982) 95–106.

[8] D. Naylor, J.M. Floryan, J.D. Tarasuk, A numerical study of developing free convection between isothermal vertical plates, J. Heat Transfer 113 (1991) 620–626.

[9] L. Martin, G.D. Raithby, M.M. Yovanovich, On the low Rayleigh number asymptote for natural convection through an isothermal, parallel-plate channel, J. Heat Transfer 113 (1991) 899–905.

[10] B. Morrone, A. Campo, O. Manca, Optimum plate separation in vertical parallel-plate channels for natural convection flows: incorporation of large spaces at the channel extremes, Int. Heat Mass Transfer 40 (1997) 993–1000.

[11] J.M. Floryan, M. Novak, Free convection heat transfer in multiple vertical channels, Int. J. Heat and Fluid Flow 16 (1995) 244–253.

[12] S.-C. Wong, S.-H. Chu, Revisit on natural convection from vertical isothermal plate arrays-effects of extra plume buoyancy, Int. J. Therm. Sci. 120 (2017) 263–272.

[13] S.-C. Wong, S.-H. Chu, M.-H. Ai, Revisit on natural convection from vertical isothermal plate arrayⅡ–3-D plume buoyancy effects, 126 (2018) 205–217.

[14] A.G. Staatman, J.D. Tarasuk, J.M. Floryan, Heat transfer enhancement from a vertical, isothermal channel generated by the chimney effect, J. Heat Transfer 115 (1993) 395–402.

[15] A. Auletta, O. Manca, B. Morrone, V. Naso, Heat transfer enhancement by the chimney effect in a vertical isoflux channel, Int. J. Heat Mass Transfer 44 (2001) 4345 –4357.

[16] A. Auletta, O. Manca, Heat and fluid resulting from the chimney effect in a symmetrically heated vertical channel with adiabatic extensions, Int. J. Thermal Sciences 41 (2002) 1101 –1111.

[17] A. Andreozzi, B. Bernardo, O. Manca, Thermal management of a symmetrically heated channel-chimney system, 48 (2009) 475 –487.

[18] K.E. Starner, H.N. McManus Jr., An experimental Investigation of Free-Convection Heat transfer from Rectangular-Fin Arrays, ASME J. Heat Transfer 85 (1963) 273–278.

[19] T. Aihara, Natural convection heat transfer in vertical parallel fins of rectangular profile, Jap. Soc. Mech. Eng. 34 (1968) 915–926.

[20] A. De Lieto Vollaro, S. Grignaffini, F. Gugliermetti, Optimum design of vertical rectangular fin arrays, Int. J. Therm. Sci. (1999) 525–529.

[21] J.R. Welling, C.B. Wooldridge, Free convection heat transfer coefficients from rectangular vertical fins, ASME J. Heat Transfer 87 (1965) 439–444.

[22] D.W. Van de Pol, J.K. Tierney, Free convection Nusselt number for vertical u-shaped channels, ASME J. Heat Transfer 95 (1973) 542–543.

[23] F. Harahap, H.N. McManus Natural convection heat transfer from horizontal rectangular fin arrays, ASME J. Heat Transfer 89 (1967) 32–38.

[24] C.D. Jones, L.F. Smith, Optimum arrangement of rectangular fins on horizontal surfaces for free-convection heat transfer, ASME J. Heat Transfer 92 (1970) 6–10.

[25] K.D. Mannan, An experimental investigation of rectangular fins on horizontal surfaces, Ph.D. Thesis. Ohio State University.

[26] C.W. Leung, S.D. Probert, M.J. Shilston, Heat exchanger design: thermal performances of rectangular fins protruding from vertical or horizontal rectangular bases, Appl. Energy 20 (1985) 123–140.

[27] C.W. Leung, S.D. Probert, M.J. Shilston, Heat transfer performances of vertical rectangular fins protruding from rectangular bases: effect of fin length, Appl. Energy 22 (1986) 313–318.

[28] C.W. Leung, S.D. Probert, Heat exchanger design: optimal length of an array of uniformly-spaced vertical rectangular fins protruding upwards from a horizontal base, Appl. Energy 30 (1988) 29–35.

[29] C.W. Leung, S.D. Probert, Heat exchanger design: optimal thickness (under natural convective conditions) of vertical rectangular fins protruding upwards from a horizontal base, Appl. Energy 29 (1988) 299–306.

[30] C.W. Leung, S.D. Probert, Thermal effectiveness of short-protrusion rectangular, heat-exchanger fins, Appl. Energy 34 (1989) 1–8.

[31] S. Baskaya, M. Sivrioglu, M. Ozek, Parametric study of natural convection heat transfer from horizontal rectangular fin arrays, Int. J. Therm. Sci. 39 (2000) 797–805.

[32] C.B. Sobhan, S.P. Venkateshan, K.N. Seetharamu, Experimental analysis of unsteady free convection heat transfer from horizontal fin arrays, W"a" ̈rme-Stoff"u" ̈bertragung 24 (1989) 155–160.

[33] C.B. Sobhan, S.P. Venkateshan, K.N. Seetharamu, Experimental studies on steady free convection heat transfer from fins and fin arrays, W"a" ̈rme-Stoff"u" ̈bertragung 25 (1990) 345–352.

[34] H. Y"u" ̈nc"u" ̈, G. Anbar, An experimental investigation on performance of rectangular fins on a horizontal base in free convection heat transfer, Heat Mass Transfer 33 (1998) 507–514.

[35] M. Mobedi, H. Y"u" ̈nc"u" ̈, A three dimensional numerical study on natural convection heat transfer from short horizontal rectangular fin array, Heat Mass Transfer 39 (2003) 267–275.

[36] L. Dialameh, M. Yaghoubi, O. Abouali, Natural convection from an array of horizontal rectangular thick fins with short length, Appl. Therm. Eng. 28 (2008) 2371–2379.

[37] G.-J. Huang, S.-C. Wong, C.-P. Lin, Enhancement of natural convection heat transfer from horizontal rectangular fin arrays with perforations in fin base, Int. J. Therm. Sci. 84 (2014) 164–174.

[38] M. Dogan, M. Sivrioglu, O. Yılmaz, Numerical analysis of natural convection and radiation heat transfer from various shaped thin fin-arrays placed on a horizontal plate-a conjugate analysis, Energy Conver. Manage. 77 (2014) 78–88.

[39] R. Charles, C.-C. Wang, A novel heat dissipation fin design applicable for natural convection augmentation, Int. Commun. Heat Mass Transfer 59 (2014) 24–29.

[40] S. Feng, M. Shi, H. Yan, S. Sun, F. Li, T.-J. Lu, Natural convection in a cross-fin heat sink, Appl. Therm. Eng. 132 (2018) 30–37.

[41] D. Jeon, C. Byon, Thermal performance of plate fin heat sinks with dual-height fins subject to natural convection, Int. J. Heat Mass Transfer 113 (2017) 1086–1092.

[42] G. Mittelman, A. Dayan, K. Dado-Turjeman, A. Ullmann, Laminar free convection underneath a downward facing inclined hot fin array, Int. J. Heat Mass Transfer 50 (2007) 2582–2589.

[43] I. Tari, M. Mehrtash, Natural convection heat transfer from inclined plate-fin heat sinks, Int. J. Heat Mass Transfer 56 (2013) 574–593.

[44] M. Mehrtash, I. Tari, A correlation for natural convection heat transfer from inclined plate-finned heat sinks, Appl. Therm. Eng. 51 (2013) 1067–1075.

[45] I. Tari, M. Mehrtash, Natural convection heat transfer from horizontal and slightly inclined plate-fin heat sinks, Appl. Therm. Eng. 61 (2013) 728–736.

[46] Z.Y. Zong, K.T. Yang, J.R. Lloyd, Variable property effects in laminar natural convection in a square enclosure, J. Heat Transfer 107 (1985) 107–133.

[47] J. Hernández, B. Zamora, Effects of variable properties and non-uniform heating on natural convection flows in vertical channel, Int. J. Heat Mass Transfer 48(2005) 793–807.

[48] R.I. Issa, Solution of the implicitly discretized fluid flow equations by operator-splitting, J. Computational Physics 62 (1985) 40–65.

[49] H.K. Versteeg, W. Malalasekera, An introduction to computational fluid dynamics, Pearson education (2007).

[50] Handbook of Fluent, ANSYS, Inc.