On the stability of a steady convective flow due to nonlinear heat sources in a magnetic field

A. Kolyshkin, V. Koliškina
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引用次数: 3

Abstract

Consider a layer of a viscous incompressible fluid bounded by two vertical planes. There exists a steady flow in the vertical layer caused by internal heat generation. The heat sources are distributed within the fluid in accordance with the Arrhenius law. A magnetic field of constant strength is applied in the direction perpendicular to the planes. The flow is characterized by four dimensionless parameters: the Grashof number, the Prandtl number, the Hartmann number and the Frank-Kamenetsky parameter. This problem is important in applications such as biomass thermal conversion. The objective of the study is to determine the factors that enhance mixing and lead to more efficient energy conversion. The problem is described by a system of magnetohydrodynamic equations under the Boussinesq approximation. The nonlinear system of ordinary differential equations describing the steady flow is solved numerically. Linear stability of the steady flow is investigated using the method of normal modes. The corresponding linear stability problem is solved numerically by means of a collocation method. The solution is found for different values of the parameters characterizing the problem. It is found that the increase of the Frank-Kamenetsky parameter destabilizes the flow. On the other hand, the increase of the Hartmann number stabilizes the flow.
磁场中非线性热源引起的定常对流的稳定性
考虑一层由两个垂直平面包围的粘性不可压缩流体。由于内部产生热量,在垂直层存在稳定的流动。热源按照阿累尼乌斯定律分布在流体内部。在垂直于平面的方向上施加恒定强度的磁场。流动由四个无量纲参数表征:Grashof数、Prandtl数、Hartmann数和Frank-Kamenetsky参数。这个问题在生物质热转换等应用中很重要。研究的目的是确定增强混合和导致更有效的能量转换的因素。这个问题是用一个在布辛尼斯克近似下的磁流体动力学方程系统来描述的。对描述稳态流动的非线性常微分方程组进行了数值求解。用正态模态法研究了定常流动的线性稳定性。采用配点法对相应的线性稳定性问题进行了数值求解。对表征该问题的参数的不同值求出了解。结果表明,增大Frank-Kamenetsky参数会使流动失稳。另一方面,哈特曼数的增加使流动趋于稳定。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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