Linear and weakly nonlinear magnetoconvection in a porous medium with a thermal nonequilibrium model

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• 作者：I. S. Shivakumara ; A. L. Mamatha ; M. Ravisha
• 关键词：Convection ; Local thermal nonequilibrium ; Magnetic field ; Porous medium
• 刊名：Afrika Matematika
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：27
• 期：7-8
• 页码：1111-1137
• 全文大小：1,201 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics Education
  Applications of Mathematics
  History of Mathematics
  Mathematics
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：2190-7668
• 卷排序：27

文摘

Two-dimensional magnetoconvection in a layer of Brinkman porous medium with local thermal nonequilibrium (LTNE) model is investigated by performing both linear and weakly nonlinear stability analyses. Condition for the occurrence of stationary and oscillatory convection is obtained in the case of linear stability analysis. It is observed that the presence of magnetic field is to introduce oscillatory convection once the Chandrasekhar number exceeds a threshold value if the ratio of the magnetic diffusivity to the thermal diffusivity is sufficiently small. Besides, asymptotic solutions for both small and large values of the inter-phase heat transfer coefficient are presented for the steady case. A weakly nonlinear stability analysis is performed by constructing a system of nonlinear autonomous ordinary differential equations. It is observed that subcritical steady convection is possible for certain choices of physical parameters. Heat transport is calculated in terms of Nusselt number. Increasing the value of Chandrasekhar number, inter-phase heat transfer coefficient and the inverse Darcy number is to decrease the heat transport, while increasing the ratio of the magnetic diffusivity to the thermal diffusivity and the porosity modified conductivity ratio shows an opposite kind of behavior on the heat transfer.