The linear natural convection of a Maxwell viscoelastic fluid with Cattaneo–Christov heat flux constitutive equation, between two thick walls with finite thermal conductivity is investigated. The viscoelastic fluid and the heat flux have different relaxation times. The main interest is on the curves of criticality for different thicknesses ratio D and thermal conductivities ratio X. In the middle range of log X the curves of criticality stabilize depending on the other parameters of the problem. It is revealed that for some Prandtl numbers the curves of criticality remain higher for small X and lower for large X. However, increasing the Prandtl number this behavior is reversed. It is shown that this has important consequences in the order of the criticality curves when the heat flux relaxation time is increased. Depending on the Prandtl number, an increase of this relaxation time may decrease (destabilize) the curves of criticality until a minimum is reached, after which the curves start to increase (stabilize) again. For two different magnitudes of the viscoelastic relaxation time, the critical Rayleigh number, wavenumber and frequency of oscillation are plotted against log X for different magnitudes of D and the heat flux relaxation time.

中文翻译：

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粘弹性 Cattaneo-Christov 流体的自然对流由具有有限热导率的厚壁界定

研究了具有 Cattaneo-Christov 热通量本构方程的麦克斯韦粘弹性流体在两个具有有限热导率的厚壁之间的线性自然对流。粘弹性流体和热通量具有不同的弛豫时间。主要兴趣在于不同厚度比的临界曲线丁和热导率比X. 在日志的中间范围X临界曲线的稳定取决于问题的其他参数。据透露，对于某些普朗特数，小的临界曲线仍然较高X大而低X. 但是，增加普朗特数会逆转此行为。结果表明，当热通量弛豫时间增加时，这对临界曲线的顺序具有重要影响。根据普朗特数，此弛豫时间的增加可能会降低（不稳定）临界曲线，直到达到最小值，之后曲线再次开始增加（稳定）。对于粘弹性弛豫时间的两个不同大小，临界瑞利数、波数和振荡频率根据对数绘制X对于不同的量级丁和热流弛豫时间。