The onset of thermal convection in couple-stress fluid in hydromagnetics saturating a porous medium

Open access

Abstract

In this paper, the effect of magnetic field on thermal convection in couple-stress fluid saturating a porous medium is considered. By applying linear stability theory and the normal mode analysis method, a mathematical theorem is derived which states that the viscoelastic thermal convection at marginal state, cannot manifest as stationary convection if the thermal Rayleigh number R, the medium permeability parameter Pι the couple-stress parameter F and the Chandrasekher number Q, satisfy the inequality

the result clearly establishes the stabilizing character of couple-stress parameter and magnetic field whereas destabilizing character of medium permeability.

References

  • [1] S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York, 1981.

  • [2] E.R. Lapwood, “Convection of a fluid in porous medium”, Proc. Camb. Phil. Soc. 44, 508-519 (1948).

  • [3] R.A. Wooding, “Rayleigh instability of a thermal boundary layer in flow through a porous medium”, J. Fluid Mech. 9, 183-192 (1960).

  • [4] V.K. Stokes, “Couple-stress in fluids”, Phys. Fluids 9, 1709-1715 (1966).

  • [5] E. Walicki and A. Walicka, “Inertial effect in the squeeze film of couple-stress fluids in biological bearings”, Int. J. Appl. Mech. Engg. 4, 363-373 (1999).

  • [6] R.C. Sharma and K.D. Thakur, “Couple-stress fluid heated from below in hydromagnetics”, Czech. J. Phys. 50, 753-758 (2000).

  • [7] D. Ingham and L. Pop, Transport Phenomena in Porous Media, Elsevier, New York, 1981.

  • [8] D.A. Nield and A. Bejan, Convection in Porous Medium, Springer, New York, 2006.

  • [9] K. Vafai, and H.A. Hadim, Hand Book of Porous Media, M. Decker, New York, 2000.

  • [10] V. Sharma and G.C. Rana, “Thermal instability of a Walters’ (model B′) elastico-viscous fluid in the presence of variable gravity field and rotation in porous medium”, J. Non-Equilib. Thermodyn. 26, 31-40 (2001).

  • [11] G.C. Rana, V. Sharma, and S. Kumar, “Stability of incompressible Rivlin-Ericksen elastico-viscous superposed fluids in the presence of Uniform horizontal magnetic field in porous medium”, J. Appl. Math. and Fluid Mech. 2, 41-47 (2011).

  • [12] V. Kumar, “Stability of stratified couple-stress dusty fluid in the presence of magnetic field through porous medium”, Appl. And Appl. Math. 6, 510-521 (2011).

  • [13] G.C. Rana and V. Sharma, “Hydromagnetic thermosolutal instability of compressible Walters’ (model) rotating fluid permeated with suspended particles in porous medium”, Int. J. Multiphysics 5, 325-338 (2011).

Bulletin of the Polish Academy of Sciences Technical Sciences

The Journal of Polish Academy of Sciences

Journal Information


IMPACT FACTOR 2016: 1.156
5-year IMPACT FACTOR: 1.238

CiteScore 2016: 1.50

SCImago Journal Rank (SJR) 2016: 0.457
Source Normalized Impact per Paper (SNIP) 2016: 1.239

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 18 18 13
PDF Downloads 4 4 2