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首页> 外文期刊>International Journal of Heat and Mass Transfer >Natural convection in a shallow cavity filled with a micropolar fluid
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Natural convection in a shallow cavity filled with a micropolar fluid

机译：充满微极性流体的浅腔中的自然对流

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摘要

This paper reports an analytical and numerical study of natural convection in a shallow rectangular cavity filled with a micropolar fluid. Neumann boundary conditions for temperature are applied to the horizontal walls of the enclosure, while the two vertical ones are assumed insulated. The governing parameters for the problem are the thermal Rayleigh number, Ra, the Prandtl number, Pr, the aspect ratio of the cavity, A and various material parameter of the fluid. For convection in an infinite layer (A 》 1), analytical solutions for the stream function temperature and angular velocity are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy equation. The critical Rayleigh numbers for the onset of supercritical convection are predicted explicitly by the present model. Furthermore, a linear stability analysis is conducted yielding numerically the critical Rayleigh numbers for the onset of motion. Also, results are obtained from the analytical model for finite-amplitude convection for which the flow and heat transfer are presented in terms of the governing parameters of the prob-rnlem. Numerical solutions of the full governing equations are obtained for a wide range of the governing parameters. A good agreement is observed between the analytical model and the numerical simulations. The influence of the material parameters on the flow and heat transfer is demonstrated to be significant.
机译：本文报道了一个充满微极性流体的浅矩形腔内自然对流的分析和数值研究。将温度的诺伊曼边界条件应用于外壳的水平壁，而假定将两个垂直壁都绝缘。该问题的主要控制参数是热瑞利数Ra，普朗特数Pr，腔体的长径比A和流体的各种材料参数。对于无限层中的对流（A》 1），使用腔体核心区域的平行流近似和能量方程的积分形式，获得了流函数温度和角速度的解析解。本模型明确预测了超临界对流发生的临界瑞利数。此外，进行了线性稳定性分析，得出了运动开始时的临界瑞利数。同样，从有限振幅对流分析模型中获得了结果，对于该模型，流动和传热是根据问题的控制参数来表示的。对于宽范围的控制参数，可以获得完整控制方程的数值解。在分析模型和数值模拟之间观察到良好的一致性。材料参数对流动和传热的影响被证明是显着的。

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