In this work, secondary convection regimes in a. fluid with a. viscosity linearly dependent on temperature, enclosed between two vertical parallel planes heated to different temperatures, are studied. The boundaries of the layer were considered hard and perfectly heat-conducting. The problem was solved numerically by the finite difference method. Calculations were carried out for Prandtl numbers equal to one and twenty. In the first case, in a. fluid with constant viscosity, the loss of stability of the main flow is related to the development of hydrodynamic perturbations, which comprise motionless vortices at the boundary of the counter flows. In the second case, the instability of the main flow is caused by oscillatory perturbations, which comprise thermal waves. Dependences of the Nus-selt number on the Grashof number and data on the structure of the secondary flows are obtained. It is found that, if the Prandtl number is equal to unity, the Nusselt number monotonically increases with the Grashof number and, near the instability threshold of the main flow, it increases according to the root law; i.e., the secondary flow arises softly. The secondary structures look like drifting vortices at the boundary of counter flows, which, after a. transient process, leads to the establishment of steady oscillations of the heat flux. At a. Prandtl number of twenty, the relationship of the Nusselt number with the Grashof number is nonmonotonic; the curve contains sections in which the Nusselt number is equal to unity and sections in which the Nusselt number increases/decreases with increasing Grashof number. This behavior is explained by the fact that, for the Prandtl number equal to twenty, there are two instability modes; oscillatory and monotonic, and the region of increasing oscillatory perturbations with a. fixed wavenumber is bounded both above and below.

中文翻译：

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平面垂直层中粘度随温度变化的流体中的二次对流机制

在这项工作中，a 中的二次对流机制。流体 a. 研究了粘度与温度呈线性关系，封闭在两个加热到不同温度的垂直平行平面之间。该层的边界被认为是坚硬且完美的导热。该问题通过有限差分法进行数值求解。对等于 1 和 20 的普朗特数进行计算。在第一种情况下，在 a. 对于具有恒定粘度的流体，主流稳定性的丧失与流体动力扰动的发展有关，其中包括逆流边界处的静止涡流。在第二种情况下，主流的不稳定性是由包含热波的振荡扰动引起的。获得了 Nus-selt 数对 Grashof 数的依赖性和二次流结构的数据。发现，如果普朗特数等于1，则努塞尔数随格拉肖夫数单调增加，在主流不稳定阈值附近，按根定律增加；即，二次流柔和地产生。二级结构看起来像逆流边界处的漂移涡流，在 a. 瞬态过程，导致建立热通量的稳定振荡。在一个。二十的普朗特数，努塞尔数与格拉肖夫数的关系是非单调的；该曲线包含 Nusselt 数等于 1 的部分和 Nusselt 数随 Grashof 数增加而增加/减少的部分。这种行为的解释是，对于等于 20 的普朗特数，有两种不稳定模式；振荡和单调，以及随着 a 增加振荡扰动的区域。固定波数上下都有界。