Instability of MHD Fluid Flow through a Horizontal Porous Media in the Presence of Transverse Magnetic Field - A Linear Stability Analysis

M. Basavaraj
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引用次数: 3

Abstract

The study was to conduct a stability analysis of pressure driven ow of an electrically conducting fluid through a horizontal porous channel in the presence of a transverse magnetic field. We employed the Brinkman-extended Darcy model with fluid viscosity is different from effective viscosity. In deriving the equations governing the stability, a simplication is made using the fact that the magnetic Prandtl number Pr m for most of the electrically conducting fluids is assumed to be small. Using the Chebyshev collocation method, the critical Reynolds number Re c , the critical wave number α c and the critical wave speed c c are computed for various values of the parameters present in the problem. The neutral curves are drawn in the (Re, α)- plane for various values of the non-dimensional parameters present in the problem. This study also tells how the combined effect of the magnetic field strength and the porosity of the porous media to delay the onset of instability compare to their presence in isolation. In the absence of some parameters, the results obtained are compared with the existed results to check the accuracy and validity of the present study. An excellent agreement is observed with the existed results.
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横向磁场作用下MHD流体在水平多孔介质中的不稳定性——线性稳定性分析
该研究旨在对存在横向磁场的情况下,导电流体通过水平多孔通道的压力驱动流动进行稳定性分析。我们采用了Brinkman扩展Darcy模型,其中流体粘度不同于有效粘度。在推导控制稳定性的方程时,利用假设大多数导电流体的磁普朗特数Pr m较小的事实进行了简化。使用切比雪夫配置法,计算了问题中存在的各种参数值的临界雷诺数Re c、临界波数αc和临界波速c c。对于问题中存在的各种无量纲参数值,在(Re,α)-平面中绘制中性曲线。这项研究还告诉了磁场强度和多孔介质孔隙度的综合效应如何延迟不稳定性的开始,与单独存在的情况相比。在没有某些参数的情况下,将获得的结果与现有结果进行比较,以验证本研究的准确性和有效性。观察到与现有结果非常一致。
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来源期刊
Journal of the Indian Mathematical Society
Journal of the Indian Mathematical Society Mathematics-Mathematics (all)
CiteScore
0.50
自引率
0.00%
发文量
32
期刊介绍: The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.
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