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首页> 外文期刊>International Journal of Heat and Mass Transfer >Critical role of Prandtl number on multiple steady states during natural convection in square enclosures: Analysis of heat transfer rates, flow and thermal maps
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Critical role of Prandtl number on multiple steady states during natural convection in square enclosures: Analysis of heat transfer rates, flow and thermal maps

机译：Prandtl号码在方形围栏自然对流期间普朗特数在多个稳态的关键作用：传热速率，流量和热贴图分析

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摘要

The effect of Prandtl number (Pr) on the multiplicity of the steady states (flow and temperature maps) is investigated for the natural convection of Newtonian fluids within a square enclosure involving hot bottom wall, cold side walls and adiabatic top wall. The analysis is based on the steady state governing equations, which are solved by penalty Galerkin finite element method and Newton-Raphson solution scheme. A novel perturbation technique has been developed, which is applied in conjunction with an in-house continuation scheme for the initiation of various symmetric as well as asymmetric steady states. The current computation strategy involving perturbation and continuation schemes leads to a rich bifurcation diagram in the parameter space of Pr (0.01 ≤ Pr ≤10) for Ra (Rayleigh number) = 10~6. It is found that the occurrence of multiple steady states depends on Pr. Only one symmetric solution is obtained in the high-Pr regime (Pr > 0.42), while a highly populated bifurcation diagram consisting of 6 symmetric branches, 18 asymmetric branches and 4 isolas is obtained in the low-Pr regime (especially for Pr approx< 0.05). The solution branches correspond to a wide spectrum of flow structures involving single cell, multiple cells, reverse-cells, corner-cells, horizontally stacked cells, vertically stacked cells etc., which are reported for the first time. These flow structures result in a wide range of Nusselt numbers (average heat transfer rates) at a given Pr. especially for the low-Pr fluids (such as liquid metals). The flow structures are critically analyzed in terms of the location of the flow intensification and its impact on the overall heat transfer rates. It has been shown that the overall heat transfer rates for the low-Pr fluids can be significantly enhanced (80 -100% in few cases) based on corner-cells or single cell driven flow.
机译：研究了Prandtl号码（PR）对稳定状态（流量和温度图）的多重性的影响，用于涉及热底壁，冷侧壁和绝热顶壁的方形外壳内的牛顿流体的自然对流。该分析基于稳态控制方程，由惩罚Galerkin有限元方法和Newton-Raphson解决方案解决。已经开发了一种新的扰动技术，其与内部延续方案一起应用，用于启动各种对称以及不对称稳态。涉及扰动和连续方案的当前计算策略导致Pr（0.01≤Pr≤10）的富分叉图，用于RA（瑞利数）= 10〜6。发现多个稳态的发生取决于Pr。在高PR结果（PR> 0.42）中仅获得一个对称溶液，而在低PR结果中获得由6个对称分支，18个不对称分支和4个米兰组成的高度填充的分叉图（特别是对于PR约< 0.05）。溶液分支对应于涉及单个电池，多个小区，反向单元，角电池，水平堆叠的单元，垂直堆叠的电池等的宽频谱结构。这些流动结构导致给定PR的宽范围的露珠数（平均传热速率）。特别是对于低PR流体（例如液体金属）。在流动强化的位置和对整体传热速率的影响方面，流动结构受到严格分析。已经表明，基于角电池或单电池驱动流动，可以显着提高低PR流体的总传热速率（在少数情况下80 -100％）。

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