Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot

IF 1.8 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
Yanjun Sun, Jialu Wang, Beinan Jia, Long Chang, Yongjun Jian
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Abstract

The convection stability of Maxwell–Cattaneo fluids in a vertical double-diffusive layer is investigated. Maxwell–Cattaneo fluids mean that the response of the heat flux with respect to the temperature gradient satisfies a relaxation time law rather than the classical Fourier one. The Chebyshev collocation method is used to resolve the linearized forms of perturbation equations, leading to the formulation of stability eigenvalue problem. By numerically solving the eigenvalue problem, the neutral stability curves in the a–Gr plane for the different values of solute Rayleigh number RaS are obtained. Results show that increasing the double diffusion effect and Louis number Le can suppress the convective instability. Furthermore, compared with Fourier fluid, the Maxwell–Cattaneo fluids in a vertical slot cause an oscillation on the neutral stability curve. The appearance of Maxwell–Cattaneo effect enhances the convection instability. Meanwhile, it is interesting to find that the Maxwell–Cattaneo effect for convective instability becomes stronger as the Prandtl number rises. That means Prandtl number (Pr) also has a significant effect on convective instability. Moreover, the occurrence of two minima on the neutral curve can be found when Pr reaches 12.
麦克斯韦-卡塔尼奥流体在垂直槽中的双重扩散对流
研究了垂直双扩散层中 Maxwell-Cattaneo 流体的对流稳定性。Maxwell-Cattaneo 流体意味着热通量对温度梯度的响应满足弛豫时间法则,而不是经典的傅里叶法则。切比雪夫配位法用于解决线性化形式的扰动方程,从而提出了稳定特征值问题。通过对特征值问题进行数值求解,得到了不同溶质雷利数 RaS 值在 a-Gr 平面上的中性稳定曲线。结果表明,增加双重扩散效应和路易数 Le 可以抑制对流不稳定性。此外,与傅立叶流体相比,垂直槽中的麦克斯韦-卡塔尼奥流体会在中性稳定曲线上产生振荡。麦克斯韦-卡塔尼奥效应的出现增强了对流不稳定性。同时,有趣的是,对流不稳定性的 Maxwell-Cattaneo 效应会随着普朗特数的增加而增强。这说明普朗特数(Pr)对对流不稳定性也有显著影响。此外,当 Pr 达到 12 时,中性曲线上会出现两个最小值。
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来源期刊
Open Physics
Open Physics PHYSICS, MULTIDISCIPLINARY-
CiteScore
3.20
自引率
5.30%
发文量
82
审稿时长
18 weeks
期刊介绍: Open Physics is a peer-reviewed, open access, electronic journal devoted to the publication of fundamental research results in all fields of physics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind.
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