Modification of heat transport by finitely-extensible polymers in boundary layer flow.

• Other Authors: Wang, Yiqu.
• Format: Others
• Language: English; Chinese
• Published: 2012
• Subjects: Heat > Transmission; Polymers > Thermal properties; Boundary layer
• Online Access: http://library.cuhk.edu.hk/record=b5549149; http://repository.lib.cuhk.edu.hk/en/item/cuhk-328728

長期以來，人們知道壁面受限湍流中的聚合物添加劑將顯著降低摩擦阻力，但是對聚合物在熱對流熱傳輸的影響還沒有太多研究。作為第一步，一項最近的工作[1]研究了在穩態邊界層流中熱量傳輸是怎樣被聚合物添加劑所影響的。在這項工作中[1]，聚合物是用Oldroyd-B模型來描述，這個模型允許聚合物無限伸展而沒有限制。 === 在這篇論文中，我們用一個更加真實的聚合物模型來研究聚合物在穩態邊界層流中對熱量傳輸的影響。我們採用FENE-P（有限擴展非線性彈性Peterlin）模型，在這個模型中，聚合物僅可以被伸展到一個最大的長度。聚合物的有限伸展性由參數L來衡量，它是聚合物最大長度與平衡長度的比例。基於該模型，我們發現，相對於與聚合物溶劑在底板處粘度相同的牛頓流體，熱量傳輸可以被提高或者被降低，這取決於聚合物不同的L值。而在不同的L值下，流場中底板的阻力始終加強。在早期的工作中，可以用一個隨位置改變的有效粘度來理解聚合物的效果。我們探討了聚合物的有效粘度和流速場是怎樣被聚合物改變的，以理解這個問題。我們也對熱量傳輸與不同參數的依賴關係進行了研究，這些參數包括威森博格數，普朗特數和聚合物對零剪切下溶劑粘度作出的貢獻的比例。 === It has long been known that friction drag will be reduced signicantly due to polymer additives in turbulent wall-bounded flows, but the effect of polymers on heat transport in thermal convection has not been studied much. As a rst step, a recent work [1] has studied how heat transport in a steady-state boundary layer flow might be influenced by the addition of polymers. In this work [1], polymers are modeled by the Oldroyd-B model, in which they can be extended innitely without a limit. === In this thesis, we study the effect of polymers on the heat transport in steady-state boundary layer flow using a more realistic model of polymers. We apply the FENE-P (nite extensible nonlinear elastic-Peterlin) model, in which the polymers can only be extended up to a maximum length. The nite extensibility of the polymers is measured by the parameter L, which is the ratio of the maximum length to the equilibrium one. Based on the model, we nd that compared to a Newtonian flow with the same viscosity as that of the polymer solution at the plate, heat transport can be enhanced or reduced depending on L. The fraction drag is always enhanced by the polymers for all different L. In the earlier work, the effect of the polymers has been understood to produce an effective viscosity that is position-dependent. We have explored the effective viscosity of the polymers and how the velocity eld is modied by the polymers to understand our results. We have also studied how the results depend on the different parameters, including Weissenberg number, Prandtl number and the ratio of polymer contribution to the total zero-shear viscosity. === Detailed summary in vernacular field only. === Detailed summary in vernacular field only. === Wang, Yiqu = 有限伸展的聚合物對邊界層流中熱量傳輸的改變 / 王異曲. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. === Includes bibliographical references (leaves 68-69). === Abstracts also in Chinese. === Wang, Yiqu = You xian shen zhan de ju he wu dui bian jie ceng liu zhong re liang chuan shu de gai bian / Wang Yiqu. === Chapter 1 --- Introduction --- p.1 === Chapter 2 --- Prandtl-Blasius boundary layer flow --- p.7 === Chapter 3 --- Earlier work with Oldroyd-B polymers --- p.13 === Chapter 4 --- Theoretical formulation of the problem with polymers of finite extensibility --- p.20 === Chapter 4.1 --- Equations of motion --- p.20 === Chapter 4.2 --- Quantities of interest --- p.30 === Chapter 5 --- Checking validity of fixed angle approximation --- p.34 === Chapter 6 --- Results and Discussion --- p.42 === Chapter 6.1 --- Calculations --- p.42 === Chapter 6.2 --- The effect on heat transport --- p.45 === Chapter 6.3 --- The effect on drag --- p.48 === Chapter 6.4 --- The velocity field due to polymers --- p.49 === Chapter 6.5 --- Effective viscosity --- p.55 === Chapter 6.6 --- Dependence on Weissenberg number --- p.58 === Chapter 6.7 --- Dependence on Prandtl number --- p.61 === Chapter 6.8 --- Dependence on the ratio of polymer contribution to the total zero-shear viscosity --- p.64 === Chapter 7 --- Conclusion --- p.66