Linear and non-linear magnetoconvection in a porous medium

Rudraiah, N. (1984) Linear and non-linear magnetoconvection in a porous medium Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 93 (2-3). pp. 117-135. ISSN 0253-4142

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Official URL: http://www.ias.ac.in/j_archive/mathsci/93/2/117-13...

Related URL: http://dx.doi.org/10.1007/BF02840655

Abstract

Linear and non-linear magnetoconvection in a sparsely packed porous medium with an imposed vertical magnetic field is studied. In the case of linear theory the conditions for direct and oscillatory modes are obtained using the normal modes. Conditions for simple and Hopf-bifurcations are also given. Using the theory of self-adjoint operator the variation of critical eigenvalue with physical parameters and boundary conditions is studied. In the case of non-linear theory the subcritical instabilities for disturbances of finite amplitude is discussed in detail using a truncated representation of the Fourier expansion. The formal eigenfunction expansion procedure in the Fourier expansion based on the eigenfunctions of the corresponding linear stability problem is justified by proving a completeness theorem for a general class of non-self-adjoint eigenvalue problems. It is found that heat transport increases with an increase in Rayleigh number, ratio of thermal diffusivity to magnetic diffusivity and porous parameter but decreases with an increase in Chandrasekhar number.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
ID Code:47474
Deposited On:11 Jul 2011 13:58
Last Modified:18 May 2016 03:07

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