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On the Behaviour of Hot Fluids in the Presence of Magnetic Field


Affiliations
1 Department of Mathematics, Himachal Pradesh University, Shimla-171005, India
2 Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-171005, India
3 Department of Mathematics, University Institute of Engineering and Technology, PU, Chandigarh, India
     

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In his masterly contributions to the theory of magnetohydrodynamic thermal convection (or magnetoconvection) Chandrasekhar (1952, 1961) laid down the guiding principles of the subject matter of the following conjectural assertions of which the first two were obtained by making use of the method of Pellew and Southwell (1940) while the rest were speculated through an extremely simple solution of the governing equations that fails to satisfy any plausible set of boundary conditions on the magnetic field (except in the case of the (vi) for which the latter part of the remark does not apply) and pertains, according to him, to the case of dynamically free boundaries which occurs only in real physical situations. These assertions are:

(i) The method of Pellew and South well (1940) is not quite strong enough to establish the validity or otherwise of the principle of exchange of stabilities for the problem.

(ii) There exists a parameter regime for the problem defined by the Chandrasekhar number Q remaining less than or equal to some fixed value Q􀀂 (σ , σ􀀂) in which the total kinetic energy associated with a marginal or unstable disturbance exceeds its total magnetic energy and as a consequence the principle of exchange of stabilities is valid for the problem in this parameter regime.


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  • On the Behaviour of Hot Fluids in the Presence of Magnetic Field

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Authors

Mihir B. Banerjee
Department of Mathematics, Himachal Pradesh University, Shimla-171005, India
J. R. Gupta
Department of Mathematics, Himachal Pradesh University, Shimla-171005, India
R. G. Shandil
Department of Mathematics, Himachal Pradesh University, Shimla-171005, India
Joginder S. Dhiman
Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-171005, India
Vinay Kanwar
Department of Mathematics, University Institute of Engineering and Technology, PU, Chandigarh, India

Abstract


In his masterly contributions to the theory of magnetohydrodynamic thermal convection (or magnetoconvection) Chandrasekhar (1952, 1961) laid down the guiding principles of the subject matter of the following conjectural assertions of which the first two were obtained by making use of the method of Pellew and Southwell (1940) while the rest were speculated through an extremely simple solution of the governing equations that fails to satisfy any plausible set of boundary conditions on the magnetic field (except in the case of the (vi) for which the latter part of the remark does not apply) and pertains, according to him, to the case of dynamically free boundaries which occurs only in real physical situations. These assertions are:

(i) The method of Pellew and South well (1940) is not quite strong enough to establish the validity or otherwise of the principle of exchange of stabilities for the problem.

(ii) There exists a parameter regime for the problem defined by the Chandrasekhar number Q remaining less than or equal to some fixed value Q􀀂 (σ , σ􀀂) in which the total kinetic energy associated with a marginal or unstable disturbance exceeds its total magnetic energy and as a consequence the principle of exchange of stabilities is valid for the problem in this parameter regime.