本文選題：Oldroyd-B流體 + 冪律流體��； 參考：《北京建筑大學》2017年碩士論文

【摘要】：納米薄膜的流動傳熱研究能夠為優(yōu)化材料加工工藝設計、改善產(chǎn)品性能提供理論指導。本文針對三種不同類型流體,分別研究了牛頓流體、粘彈性流體、冪律流體在拉伸平板上流動傳熱問題。研究工作如下:1)研究了拉伸平板上牛頓納米流體的邊界層流動傳熱問題,探討了牛頓流體薄膜的表面張力梯度所引發(fā)的Marangoni效應,利用相似變換理論將偏微分方程組轉化為非線性常微分方程組。通過同倫分析方法對方程組進行解析求解,通過打靶法對方程組進行數(shù)值求解,分析了邊界層速度以及溫度的分布特點,獲得了各類物理參數(shù)對邊界層速度、溫度以及薄膜厚度的影響規(guī)律。2)建立了非穩(wěn)態(tài)拉伸平板上Oldroyd-B流體的流動傳熱邊界層控制模型,探討了納米粒子的加入對原有流體導熱性能的影響。選取PVA水溶液為基液,加入Cu和Ag兩種納米粒子。通過相似變換將模型中偏微分方程組轉化為四階非線性常微分方程組,運用同倫分析方法得到解析近似解,分析了不穩(wěn)定參數(shù)、普朗特數(shù)以及納米粒子的體積分數(shù)對流體速度和溫度的影響規(guī)律。3)研究了變壁溫拉伸平板上冪律納米流體薄膜的流動傳熱問題,根據(jù)非牛頓流體速度場粘性擴散與溫度場熱擴散比擬原理,重構冪律非牛頓流體傅里葉導熱定律,探討了變磁場、冪律速度滑移、冪函數(shù)壁面溫度對流動傳熱的影響。選取熔融EVA作為基液,添加不同體積分數(shù)的Al2O3、Ti O2以及CuO納米粒子。采用微分變換方法,結合牛頓迭代法(DTM-NIM)對方程組進行求解,獲得各種參數(shù)對流體速度和溫度分布的影響規(guī)律。本文所進行的理論分析和解析求解方法,為納米流體薄膜的流動和傳熱研究奠定了基礎。同時,通過與其他學者研究成果的比較,說明了文中所用兩種解析方法的有效性,也為解決其他工程領域中的非線性微分方程問題提供了研究思路。
[Abstract]:The study of flow heat transfer of nanocrystalline films can provide theoretical guidance for optimizing material processing process design and improving product performance. In this paper, the flow heat transfer problems of Newtonian fluid, viscoelastic fluid and power-law fluid on a stretch plate are studied respectively for three different types of fluids. The research work is as follows: 1) the flow heat transfer problem of Newtonian nanoscale fluid on a stretch plate is studied, and the Marangoni effect caused by the surface tension gradient of Newtonian fluid film is discussed. The system of partial differential equations is transformed into nonlinear ordinary differential equations by using similarity transformation theory. The homotopy analysis method is used to solve the equations, and the target shooting method is used to numerically solve the equations. The distribution characteristics of boundary layer velocity and temperature are analyzed, and the physical parameters of the boundary layer velocity are obtained. The influence of temperature and film thickness on the flow heat transfer boundary layer control model of Oldroyd-B fluid on an unsteady tensile plate was established. The influence of the addition of nanoparticles on the thermal conductivity of the original fluid was discussed. PVA aqueous solution was selected as base solution and Cu and Ag nanoparticles were added. The partial differential equations in the model are transformed into fourth order nonlinear ordinary differential equations by similarity transformation. The analytical approximate solution is obtained by homotopy analysis method, and the unstable parameters are analyzed. The effects of Plantt number and volume fraction of nanoparticles on the velocity and temperature of the fluid are studied. According to the principle of viscous diffusion and thermal diffusion of non-Newtonian fluid velocity field, the Fourier law of thermal conduction of power law non-Newtonian fluid is reconstructed, and the influence of variable magnetic field, power law velocity slip and wall temperature of power function on flow heat transfer is discussed. Molten EVA was selected as base solution and Al _ 2O _ 3 TIO _ 2 and CuO nanoparticles with different volume fraction were added. The differential transformation method and Newton iterative method (DTM-NIMA) are used to solve the equations. The effects of various parameters on the velocity and temperature distribution of the fluid are obtained. The theoretical analysis and analytical solution in this paper lay a foundation for the study of flow and heat transfer in nanoscale fluid films. At the same time, by comparing with other scholars' research results, the effectiveness of the two analytical methods used in this paper is illustrated, and the research ideas for solving nonlinear differential equations in other engineering fields are also provided.
【學位授予單位】：北京建筑大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TB383.2

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本文編號：1794219