分数阶粘弹性流体流动传热研究
发布时间：2021-02-09 14:21
分数阶粘弹性流体流动与传热研究为合理刻画复杂流体本构关系、改进生产和输运效率等应用领域提供了理论指导。本文分别研究了加速平板上和压强梯度驱动下矩形管道内的分数阶粘弹性流体流动传热问题。研究内容如下:1)研究了指数加速平板上不可压缩广义Burgers’磁流体的流动和热传递过程。基于粘性耗散项将Burgers’流体分数阶本构方程引入能量方程,利用改进的隐式有限差分方法与G1算法结合求解,得到了速度、温度和剪切应力的数值解,并构造算例对数值算法进行了误差分析。讨论了松弛时间、延滞时间、滑移参数以及分数阶导数的阶数等参数对流动速度、温度和应力的影响规律。2)建立了矩形管道内变压力梯度驱动的分数阶Maxwell流体二维流动模型。针对分数阶导数的阶数分布于区间（0,2）的多项偏微分方程,利用分数阶分离变量法,得到速度的解析解。采用分数阶预估-校正方法和有限差分方法得到方程数值解。证明了二维偏微分方程有限差分格式稳定性和收敛性。在数值结果的基础上,探讨了分数阶阶数、哈特曼数以及松弛时间系数对矩形管道内流体速度分布的影响规律。3)基于分数阶散度和分数阶Cattaneo传热模型,建立了拉伸板上分数阶Ma...
【文章来源】：北京建筑大学北京市
【文章页数】：70 页
【学位级别】：硕士
【部分图文】：
数值计算例子的两种方法结果对比
第 3 章 二阶滑移和粘性耗散效应下广义 Burgers’磁流体流动传热研究图 3-1 数值计算例子的两种方法结果对比Fig.3-1 Comparison of the example result of different method
图 3-1 数值计算例子的两种方法结果对比Fig.3-1 Comparison of the example result of different method图 3-2 不同 值情况下的速度分布Fig.3-2 Velocity distribution for different
【参考文献】：
期刊论文
[1]纳米Al2O3分布对Al2O3/PE-EVA复合材料导热性能与力学性能的影响[J]. 陈金,王春锋,王永亮,韩宝忠,韩志东. 复合材料学报. 2015(05)
[2]Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction[J]. Jing ZHU,Liu ZHENG,Liancun ZHENG,Xinxin ZHANG. Applied Mathematics and Mechanics（English Edition）. 2015(09)
[3]Stokes’first problem for a viscoelastic fluid with the generalized Oldroyd-B model[J]. Haitao Qi Mingyu Xu Department of Applied Mathematics and Statistics,Shandong University at Weihai,Weihai 264209,China School of Mathematics and System Science,Shandong University,Jinan 250100,China. Acta Mechanica Sinica. 2007(05)
[4]On the MHD flow of fractional generalized Burgers’ fluid with modified Darcy’s law[J]. T.Hayat,M.Khan,S.Asghar. Acta Mechanica Sinica. 2007(03)
[5]Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders[J]. H. Qi Department of Applied Mathematics and Statistics, Institute of Applied Mathematics,Shandong University at Weihai,Wcihai 264209, Shandong, China e-mail: htqi@sdu.edu.cn H. Jin School of Mathematics and Systematical Science, Shandong University, Jinan 250100, Shandong, China. Acta Mechanica Sinica. 2006(04)
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本文编号：3025769
【文章来源】：北京建筑大学北京市
【文章页数】：70 页
【学位级别】：硕士
【部分图文】：
数值计算例子的两种方法结果对比
第 3 章 二阶滑移和粘性耗散效应下广义 Burgers’磁流体流动传热研究图 3-1 数值计算例子的两种方法结果对比Fig.3-1 Comparison of the example result of different method
图 3-1 数值计算例子的两种方法结果对比Fig.3-1 Comparison of the example result of different method图 3-2 不同 值情况下的速度分布Fig.3-2 Velocity distribution for different
【参考文献】：
期刊论文
[1]纳米Al2O3分布对Al2O3/PE-EVA复合材料导热性能与力学性能的影响[J]. 陈金,王春锋,王永亮,韩宝忠,韩志东. 复合材料学报. 2015(05)
[2]Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction[J]. Jing ZHU,Liu ZHENG,Liancun ZHENG,Xinxin ZHANG. Applied Mathematics and Mechanics（English Edition）. 2015(09)
[3]Stokes’first problem for a viscoelastic fluid with the generalized Oldroyd-B model[J]. Haitao Qi Mingyu Xu Department of Applied Mathematics and Statistics,Shandong University at Weihai,Weihai 264209,China School of Mathematics and System Science,Shandong University,Jinan 250100,China. Acta Mechanica Sinica. 2007(05)
[4]On the MHD flow of fractional generalized Burgers’ fluid with modified Darcy’s law[J]. T.Hayat,M.Khan,S.Asghar. Acta Mechanica Sinica. 2007(03)
[5]Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders[J]. H. Qi Department of Applied Mathematics and Statistics, Institute of Applied Mathematics,Shandong University at Weihai,Wcihai 264209, Shandong, China e-mail: htqi@sdu.edu.cn H. Jin School of Mathematics and Systematical Science, Shandong University, Jinan 250100, Shandong, China. Acta Mechanica Sinica. 2006(04)
[6]PLANE SURFACE SUDDENLY SET IN MOTION IN A VISCOELASTIC FLUID WITH FRACTIONAL MAXWELL MODEL[J]. 谭文长,徐明瑜. Acta Mechanica Sinica. 2002(04)
本文编号：3025769
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