热对流与卡塔尼奥热通量模型

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-01-31 DOI:10.1098/rspa.2023.0771
M. Gentile, B. Straughan
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引用次数: 0

摘要

分析了粘性不可压缩流体层中的热对流问题。热通量定律被认为是卡塔尼奥类型的定律。热通量的时间导数可以是物质导数,也可以是一般的客观导数。结果表明,只有一种客观导数会导致与现实生活中预期一致的结果。这种客观导数导致卡塔尼奥-克里斯托夫理论,线性不稳定性理论的结果与物质导数的结果一致。研究进一步表明,这些理论都无法进行标准的非线性能量稳定性分析。P.M. Mariano 提出的热通量被进一步添加,然后对静止对流、振荡对流和完全非线性理论进行了分析。对于材料导数情况,分析继续进行,并实现了全局非线性稳定性。对于卡塔尼奥-克里斯托夫理论,似乎有必要在热通量方程中添加正则化项,即使这样,分析也只能在两个空间维度上进行,并且以初始数据的大小为条件。对于三维空间的情况,我们展示了如何利用纳维-斯托克斯-沃伊特流体而不是纳维-斯托克斯流体实现非线性稳定性分析。
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Thermal convection with a Cattaneo heat flux model
The problem of thermal convection in a layer of viscous incompressible fluid is analysed. The heat flux law is taken to be one of Cattaneo type. The time derivative of the heat flux is allowed to be a material derivative, or a general objective derivative. It is shown that only one objective derivative leads to results consistent with what one expects in real life. This objective derivative leads to a Cattaneo–Christov theory, and the results for linear instability theory are in agreement with those for a material derivative. It is further shown that none of the theories allow a standard nonlinear, energy stability analysis. A further heat flux due to P.M. Mariano is added and then an analysis is performed for stationary convection, oscillatory convection, and fully nonlinear theory. For the material derivative case, the analysis proceeds and global nonlinear stability is achieved. For Cattaneo–Christov theory, it appears necessary to add a regularization term in the equation for the heat flux, and even then the analysis only works in two space dimensions, and is conditional upon the size of the initial data. For the three-dimensional situation, it is shown how a nonlinear stability analysis may be achieved with a Navier–Stokes–Voigt fluid rather than a Navier–Stokes one.
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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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