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On π2 Q-Law in Magnetoconvection Problem for General Nature of Boundaries Using Galerkin Method


Affiliations
1 Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla (H.P.)-171005, India
2 Govt. College, Sanjauli, Shimla (H.P.)-171006, India
     

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Chandrasekhar proved his famous -law of stationary convection in magnetoconvection problem for the case of both dynamically free boundaries. For the other two cases of boundary conditions, namely; both rigid boundaries and combinations of rigid and dynamically free boundaries he, on the basis of numerical computations, conjectured that the same law must hold true. In the present paper, we have reinvestigated the onset of thermal instability in an electrically conducting fluid layer heated from below in the presence of a uniform magnetic field. In the present analysis the validity of -law for general nature of bounding surfaces is proved using the Galerkin technique. The obtained results are in good agreement with the numerical results of Chandrasekhar and thus validate his claim.
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  • On π2 Q-Law in Magnetoconvection Problem for General Nature of Boundaries Using Galerkin Method

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Authors

Joginder Singh Dhiman
Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla (H.P.)-171005, India
Vijay Kumar
Govt. College, Sanjauli, Shimla (H.P.)-171006, India

Abstract


Chandrasekhar proved his famous -law of stationary convection in magnetoconvection problem for the case of both dynamically free boundaries. For the other two cases of boundary conditions, namely; both rigid boundaries and combinations of rigid and dynamically free boundaries he, on the basis of numerical computations, conjectured that the same law must hold true. In the present paper, we have reinvestigated the onset of thermal instability in an electrically conducting fluid layer heated from below in the presence of a uniform magnetic field. In the present analysis the validity of -law for general nature of bounding surfaces is proved using the Galerkin technique. The obtained results are in good agreement with the numerical results of Chandrasekhar and thus validate his claim.