分?jǐn)?shù)階粘彈性流體流動(dòng)與傳熱研究為合理刻畫(huà)復(fù)雜流體本構(gòu)關(guān)系、改進(jìn)生產(chǎn)和輸運(yùn)效率等應(yīng)用領(lǐng)域提供了理論指導(dǎo)。本文分別研究了加速平板上和壓強(qiáng)梯度驅(qū)動(dòng)下矩形管道內(nèi)的分?jǐn)?shù)階粘彈性流體流動(dòng)傳熱問(wèn)題。研究?jī)?nèi)容如下:1)研究了指數(shù)加速平板上不可壓縮廣義Burgers’磁流體的流動(dòng)和熱傳遞過(guò)程�；谡承院纳㈨�(xiàng)將Burgers’流體分?jǐn)?shù)階本構(gòu)方程引入能量方程,利用改進(jìn)的隱式有限差分方法與G1算法結(jié)合求解,得到了速度、溫度和剪切應(yīng)力的數(shù)值解,并構(gòu)造算例對(duì)數(shù)值算法進(jìn)行了誤差分析。討論了松弛時(shí)間、延滯時(shí)間、滑移參數(shù)以及分?jǐn)?shù)階導(dǎo)數(shù)的階數(shù)等參數(shù)對(duì)流動(dòng)速度、溫度和應(yīng)力的影響規(guī)律。2)建立了矩形管道內(nèi)變壓力梯度驅(qū)動(dòng)的分?jǐn)?shù)階Maxwell流體二維流動(dòng)模型。針對(duì)分?jǐn)?shù)階導(dǎo)數(shù)的階數(shù)分布于區(qū)間（0,2）的多項(xiàng)偏微分方程,利用分?jǐn)?shù)階分離變量法,得到速度的解析解。采用分?jǐn)?shù)階預(yù)估-校正方法和有限差分方法得到方程數(shù)值解。證明了二維偏微分方程有限差分格式穩(wěn)定性和收斂性。在數(shù)值結(jié)果的基礎(chǔ)上,探討了分?jǐn)?shù)階階數(shù)、哈特曼數(shù)以及松弛時(shí)間系數(shù)對(duì)矩形管道內(nèi)流體速度分布的影響規(guī)律。3)基于分?jǐn)?shù)階散度和分?jǐn)?shù)階Cattaneo傳熱模型,建立了拉伸板上分?jǐn)?shù)階Ma... 

【文章來(lái)源】：北京建筑大學(xué)北京市

【文章頁(yè)數(shù)】：70 頁(yè)

【學(xué)位級(jí)別】：碩士

【部分圖文】：

數(shù)值計(jì)算例子的兩種方法結(jié)果對(duì)比

第 3 章 二階滑移和粘性耗散效應(yīng)下廣義 Burgers’磁流體流動(dòng)傳熱研究圖 3-1 數(shù)值計(jì)算例子的兩種方法結(jié)果對(duì)比Fig.3-1 Comparison of the example result of different method

圖 3-1 數(shù)值計(jì)算例子的兩種方法結(jié)果對(duì)比Fig.3-1 Comparison of the example result of different method圖 3-2 不同 值情況下的速度分布Fig.3-2 Velocity distribution for different

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