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On the Effects of Magnetic Field and Temperature-Dependent Viscosity on the Onset Magnetoconvection for General Boundary Conditions


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1 Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla (H.P.)-171005, India
     

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In the present paper, the problem of thermal instability of an electrically conducting fluid layer heated from below and permeated with a uniform vertical magnetic field is studied for all combinations of rigid and dynamically free boundary conditions. The effect of temperature-dependent viscosity on the onset of hydromagnetic thermal convection is investigated both analytically and numerically. The validity of the principle of exchange of stabilities for this general problem has been investigated using the Pellew and Southwell’s method and a sufficient condition for the validity of this principle is also derived. The values of the Rayleigh numbers for each case of boundary combinations are obtained numerically using Galerkin technique. Further, the effect of temperature-dependent viscosity on the onset of stationary convection and consequently on the celebrated ∏2 Q-law of Chandrasekhar for each case of boundary combinations is computed numerically. It is observed that the temperature-dependent viscosity also has the inhibiting effect on the onset of convection as that of magnetic field and the ∏2 Q -law is also valid for this problem.
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  • On the Effects of Magnetic Field and Temperature-Dependent Viscosity on the Onset Magnetoconvection for General Boundary Conditions

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Authors

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

Abstract


In the present paper, the problem of thermal instability of an electrically conducting fluid layer heated from below and permeated with a uniform vertical magnetic field is studied for all combinations of rigid and dynamically free boundary conditions. The effect of temperature-dependent viscosity on the onset of hydromagnetic thermal convection is investigated both analytically and numerically. The validity of the principle of exchange of stabilities for this general problem has been investigated using the Pellew and Southwell’s method and a sufficient condition for the validity of this principle is also derived. The values of the Rayleigh numbers for each case of boundary combinations are obtained numerically using Galerkin technique. Further, the effect of temperature-dependent viscosity on the onset of stationary convection and consequently on the celebrated ∏2 Q-law of Chandrasekhar for each case of boundary combinations is computed numerically. It is observed that the temperature-dependent viscosity also has the inhibiting effect on the onset of convection as that of magnetic field and the ∏2 Q -law is also valid for this problem.

References