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首页> 外文期刊>International Journal of Heat and Mass Transfer >Finite amplitude cellular convection under the influence of a vertical magnetic field
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Finite amplitude cellular convection under the influence of a vertical magnetic field

机译：垂直磁场影响下的有限振幅细胞对流

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摘要

At the onset of stationary convection, the effect of a vertical magnetic field on the heat transfer of Rayleigh-Benard convection for an electrically conducting fluid is studied. The nonlinear governing equations describing the motion, temperature and magnetic fields are expanded as the sequence of non-homogeneous linear equations, which depend on the solutions of the linear stability problem. Infinite number of steady state with finite amplitude solutions are obtained for the stress-free boundary conditions. The perturbation method proposed by Kuo (1961) is used for the first time to highlight the heat transfer features of magnetoconvection. An explicit expression at the onset of convection in terms of parameters of the system is obtained. The dependence of heat transfer rate on Rayleigh number (R), Chandrasekhar number, thermal and magnetic Prandtl numbers is extensively examined until sixth order using an expansion of R as proposed by Kuo (1961). The results show that the magnetic field dampens the heat flow for stationary convection, i.e., the onset of convection shifts to higher values of R as the vertical magnetic field increases. Under the uniform magnetic field, heat flow gets enhanced as the thermal Prandtl number increases, whereas heat flow diminishes for the increase in magnetic Prandtl number. The results of flow field and heat transfer characteristics are depicted in the form of streamlines and isotherms, respectively. The presence of magnetic field changes the flow structure of streamlines from unicellular to multicellular patterns. This is due to the magnetic susceptibility of colder fluid flow towards the magnetic field. The flow field is analyzed with respect to the topological invariant relation. To trace the path of convective heat transport, the concept of Heatfunction has been employed. This methodology explains the comprehensive interpretation of energy distribution in terms of heatlines.
机译：在静止对流开始时，研究了垂直磁场对导电流体瑞利-贝纳德对流传热的影响。描述运动，温度和磁场的非线性控制方程扩展为非齐次线性方程的序列，这取决于线性稳定性问题的解。对于无应力边界条件，获得了具有有限振幅解的无限数量的稳态。 Kuo（1961）提出的微扰方法首次用于强调磁对流的传热特性。获得了对流开始时根据系统参数的明确表达式。传热率对瑞利数（R），钱德拉塞卡尔数，热磁和普朗特数的依赖性得到了广泛的研究，直到使用Kuo（1961）提出的R的扩展达到六阶为止。结果表明，磁场抑制了固定对流的热流，即，随着垂直磁场的增加，对流的开始移动到较高的R值。在均匀磁场下，热量随Prandtl数的增加而增加，而热量随Prandtl数的增加而减小。流场和传热特性的结果分别以流线和等温线的形式描述。磁场的存在将流线的流动结构从单细胞模式改变为多细胞模式。这是由于较冷的流体流向磁场的磁化率。针对拓扑不变关系分析了流场。为了追踪对流热传递的路径，已经采用了热功能的概念。该方法论根据热线解释了能量分布的综合解释。

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