本論文研究首先針對部分限制散熱座在渠道內自然對流及強制對流下之熱流特性作一系列的理論與實驗探討。在自然對流實驗中，相關參數包括葛拉雪夫數(GrH)，上側旁通比(Htb / Hch)及側邊旁通比(Wsb / Wch)；其參數範圍則為GrH = 3.0X107 ~ 9.0X107, Wsb / Wch = 0.00 ~ 0.55及 Htb / Hch = 0.28 ~ 0.83。在強制對流中，相關參數分別為葛拉雪夫數(GrH)，雷諾數(Rech)，上側旁通比(Htb / Hch)及側邊旁通比(Wsb / Wch )；其參數範圍為GrH = 5.5X108 ~ 1.6X109, Rech = 20209 ~ 40073, Wsb / Wch = 0.00 ~ 0.55與Htb/Wch = 0.28 ~ 0.83。在研究中，則有系統地探討這些相關參數對於熱流特性的影響。
有關於流場及熱傳特性探討之內容及成果分別敘述如下：(一) 在流場特性方面，研究發現散熱座內平均流速與槽道入口流速之比值(Vs/Vin)受到Rech，Wsb / Wch 及Htb / Hch三個參數很顯著的影響；而上側旁通或側邊旁通內平均流速與槽道入口流速之比值(Vtb/Vin或Vsb/Vin)則只受到Rech顯著的影響，而Wsb / Wch 及Htb / Hch的影響並不顯著。經由此參數探討，研究中提出了上述三種流速比值與相關影響參數之新的經驗關係式。在本論文中更進一步地探討這三個參數對壓降及等效摩擦係數的影響；進而也提出準確估算壓降及等效摩擦係數之新的經驗公式。(二) 在熱傳特性方面，局部紐塞數在自然對流中由於在散熱座基部熱擴散效應影響，以致無論在垂直流體流動方向及沿著流體流動方向皆呈現均勻的分佈；但在強制對流中則在垂直流體流動方向呈現均勻的分佈，而在沿著流體流動方向則呈現不均勻的分佈，其局部紐塞數沿著流體流動方向逐漸降低。同時研究發現在局部的外界熱導分佈上亦有相同的趨勢。在自然對流中，平均紐塞數會隨著GrH上昇或Wsb / Wch 及Htb / Hch之比值下降而減少；但是在強制對流中則是隨著Rech上昇或Wsb / Wch 及Htb / Hch之比值下降而增加。根據這些相關影響參數之探討結果，本研究分別提出了平均紐塞數在自然及強制對流下的經驗公式；並且經與相同渠道內水平加熱平面之平均熱傳特性相比較，發現本研究之部分限制散熱座之平均熱傳在自然及強制對流中分別達到125% -236%與961%-4453%的熱傳增益。
此外，本論文研究成功地發展出一個連結散熱座與多孔性材質兩模型間新的相似性法則，並且針對熱流特性建立了此兩模型間之正向與逆向轉換方法。因此，部分限制散熱座在渠道中流體流動摩擦係數與熱傳效能除了可以使用散熱座模型直接計算外，還能使用正向與逆向轉換方法透過多孔性材質模型演算出來。在多孔性材質模型中，流體流動摩擦係數可由滲透率(permeability)及慣性係數(inertial coefficient)計算得到，並且可以渠道孔隙率( )及雷諾數(Rech)為參數建立其經驗公式。在熱傳方面，相關之熱傳係數(如 hwa，hws及hsa)會顯著地受到Rech及 的影響：當Rech上昇或 下降時，hws及hsa會增加；但hwa雖會隨著Rech上昇而增加，卻不會受 影響。在多孔性材質模型中的兩種平均紐塞數(Nui及Nueff)同樣會隨著Rech上昇或 下降而增加。依據此實驗結果，本研究針對Nui及Nueff分別提出含Rech及 影響參數的經驗公式；再經由與相同渠道內水平加熱平面之平均散熱效能相比較，在本研究的實驗參數範圍內其最高的熱傳增益可達4581%。同時根據實驗數據與計算流體力學軟體的模擬結果，本研究針對熱傳性能因子(j)及熱傳性能因子對等效摩擦係數之比值(feff)分別提出含Rech及 兩參數的經驗公式；接著再以多孔性材質模型計算得來的熱傳性能因子為基礎，透過逆向轉換法將多孔性材質模型參數 轉變成散熱座模型中最適當的幾何參數(Wsb / Wch 及Htb / Hch)。另外，本研究亦藉由統計上的參數敏感度分析，而得到散熱座模型之參數GrH、Rech、Wsb / Wch 及Htb / Hch對等效摩擦係數的貢獻度分別為1.6%、49.1%、23.3%及26.0%，而對於熱傳性能因子的貢獻度則分別為2.6%、51.1%、13.4%及32.9%；多孔性材質模型之參數GrH、Rech及 對等效摩擦係數的貢獻度分別為1.5%、57.7%及40.8%，對於熱傳性能因子的貢獻度則分別為4.3%、55.1%及40.6%。
最後，本研究利用反應曲面法分別針對散熱座模型與多孔性材質模型建立了等效摩擦係數與熱傳性能因子的經驗公式；進而成功地採用連續二次規劃法配合多起點方式有效地對此兩個模型尋找出全域熱傳最佳化的結果。依據這些方法，本研究分別採用散熱座模型與多孔性材質模型來針對部分限制散熱座在不同旁通限制條件下的最佳j 或j/feff 案例作有系統的探討。經由此兩模型一系列最佳化結果比對後，則成功地驗證了本研究所提出之相似性法則應用於多限制條件下對部分限制散熱座之j 或j/feff最佳熱傳演算之可行性與優異性。

In the present study, a series of theoretical and experimental investigations on fluid flow and heat transfer characteristics of partially-confined heat sinks in natural and forced convections have been performed. The relevant parameters in the experiments include Grashof number (GrH), top-bypass ratio (Htb / Hch), and side-bypass ratio (Wsb / Wch) in natural convection; and Grashof number (GrH), Reynolds number (Rech), top-bypass ratio (Htb / Hch), and side-bypass ratio (Wsb / Wch) in forced convection. The parametric ranges in natural convection are GrH = 3.0X107 ~ 9.0X107, Wsb / Wch = 0.00 ~ 0.55 and Htb / Hch = 0.28 ~ 0.83; those in forced convection are GrH = 5.5X108 ~ 1.6X109, Rech = 20209 ~ 40073, Wsb / Wch = 0.00 ~ 0.55 and Htb / Hch = 0.28 ~ 0.83. Their effects on fluid flow and heat transfer characteristics have been systematically explored.
From the aspect of fluid flow behavior, the ratio of average velocity in the heat sink region to average channel inlet velocity (Vs/Vin) is significantly affected by Rech, Wsb / Wch or Htb / Hch . The ratio of average velocity in the top-bypass or side-bypass region to average channel inlet velocity ( Vtb/Vin or Vsb/Vin ) is significantly affected by Rech, but insignificantly affected by Wsb / Wch or Htb / Hch . New correlations of Vs/Vin, Vsb/Vin and Vtb/Vin in terms of relevant influencing parameters are proposed. The effects of Rech, Wsb / Wch and Htb / Hch on pressured drop and effective friction factor (feff) are explored. New correlations for evaluating the pressure drop and the effective friction factor in terms of relevant influencing parameters are also presented.
From the aspect of heat transfer behavior, a uniform distribution of local effective Nusselt number in natural convection is achieved either in the spanwise or in the streamwise direction due to the spreading effect of the heat conduction within the heat sink; while, the distributions of local effective Nusselt number in the spanwise and streamwise directions are uniform and non-uniform, respectively, in forced convection. The local effective Nusselt number (Nueff) in forced convection gradually decreases along the streamwise direction. A similar trend can be found for the distribution of local external thermal conductance. In natural convection, the average effective Nusselt number (Nueff) decreases with increasing GrH or decreasing Wsb / Wch and Htb / Hch ; while, it increases with increasing Rech or decreasing Wsb / Wch and Htb / Hch in forced convection. Two new correlations of Nueff in terms of relevant influencing parameters in natural and forced convections are presented, respectively. As compared with the average Nusselt number on a heating horizontal flat surface confined in a channel, the average heat transfer performances of partially-confined heat sinks in natural and forced convections can be enhanced in the range of 125% -236% and 961%-4453%, respectively.
Furthermore, a novel parametric similarity method to effectively link the relationship between the heat sink and the porous medium models has been successfully developed. Both the direct and inverse transformations on the fluid flow friction and thermal performance with relevant influencing parameters in these two models have also been established. The fluid flow friction and thermal performance for partially-confined heat sinks can be directly evaluated in the heat sink model. With the proposed direct and inverse transformations, those can be indirectly and effectively determined in the porous medium model. The effective friction factor in the porous medium model is evaluated from the permeability and the inertial coefficient, and the correlation in terms of Rech and porosity is presented. All the heat transfer coefficients such as hwa, hws and hsa in the porous medium model are significantly affected by Rech and porosity. The hws and hsa increase with increasing Rech or decreasing porosity; hwa increases with increasing Rech, but is almost independent of porosity. Both the average Nusselt number of Nui and average effective Nusselt number of Nueff in the porous medium model increase with increasing Rech or decreasing porosity. Based on the experimental data, two new correlations of Nui and Nueff in terms of Rech and porosity are presented. The maximum heat transfer enhancement defined as can be achieved up to 4581% in the present parametric range studied. Based on both the experimental data and the CFD results, two new correlations of j and j/feff in terms of Rech and porosity in the porous medium model are reported. With the Colburn factor obtained in the porous medium model, the most suitable geometric parameters such as Wsb / Wch and Htb / Hch in the heat sink model can be effectively determined by porosity used in the porous medium model by using the proposed parametric inverse transformations. From the statistical sensitivity analysis, the contributions of GrH, Rech, Wsb / Wch and Htb / Hch on the effective friction factor in the heat sink model are 1.6%, 49.1%, 23.3%, and 26.0%, respectively; and those on the Colburn factor are 2.6%, 51.1%, 13.4%, and 32.9%, respectively. The contributions of GrH, Rech and porosity on the effective friction factor in the porous medium model are 1.5%, 57.7%, and 40.8%, respectively; and those on Colburn factor are 4.3%, 55.1%, and 40.6%, respectively.
Finally, in either the heat sink model or the porous medium model, two empirical response formulas with a quadratic RSM model for evaluating the effective friction factor and the Colburn factor are established for each model, respectively. An effective sequential quadratic programming with a multi-start-point method has been successfully employed to automatically and efficiently seek the global thermal optimization in both the heat sink and the porous medium models. Accordingly, three cases of thermal optimization on j or j/feff in a partially-confined heat sink under different bypass ratio constraints have been explored for either the heat sink model or the porous medium model; and a series of optimal thermal evaluations on j and j/feff for partially-confined heat sinks under multi-constraints with the novel heat sink/porous medium similarity method presented in the study have been successfully performed and verified.

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