Research Journal of Science and Technology

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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


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

   Subscribe/Renew Journal


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.
Subscription Login to verify subscription
User
Notifications
Font Size


  • Banerjee, M. B., Gupta, J. R., Shandil, R. G. and Jamwal, H.S. (1989): Settlement of the long Standing Controversy in Magnetothermoconvection in favour of S. Chandrasekhar, J. Math. Anal. Appl., 144, 356.

  • Banerjee, M. B., Shandil, R.G. and Kumar, R. (1995) : On Chandrasekhar’s . –Law, J. Math. Anal. Appl., 191, 460.

  • Banerjee, M.B. and Bhowmick, S.K. (1992): Salvaging the Thompson-Chandrasekhar Criterion: A tribute to S. Chandrasekhar, J. Math. Anal. Appl., 167, 57-65.

  • Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Amen. House London, E.C.4, 1961.

  • Dhiman, J. S. and Kumar Vijay, (2012): On 2 p Q -Law in Magnetoconvection Problem for General Nature of Boundaries Using Galerkin Method, Research J. Engineering and Technology, 3(2), (2012), 186.

  • Finlayson, B.A. (1972): ‘The Method of Weighted Residuals and Variational Principles’; Academic Press, New York.

  • Gupta, J.R. and Kaushal, M.B. (1988): Rotatory hydromagnetic double-diffusive convection with viscosity variation, J. Math Phys. Sci., 22 (3), 301.

  • Jeffreys, H., Some Cases of Instability in Fluids Motions, Proc. Roy. Soc. London, 1928, A118, 195.

  • Kumar, Vijay (2012): A Study of Some Convective Stability Problems with Variable Viscosity, Ph.D. thesis (supervised by J.S. Dhiman), submitted to Himachal Pradesh University, Shimla.

  • Low, A. R, On the Criterion for Stability of a Layer of Viscous Fluid Heated From Below, Proc. Roy. Soc. London, 1929, A125, 180.

  • Pellew, A. and Southwell, R.V., On Maintained Convective Motion in a Fluid Heated From Below, Proc. Roy. Soc. London, 1940, A 176, 312.

  • Straughan, B., Sharp Global Non-Linear Stability for Temperature Dependent Viscosity, Proc. Roy. Soc. London, 2002, A 458, 1773.


Abstract Views: 726

PDF Views: 0




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

Abstract Views: 726  |  PDF Views: 0

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