THERMAL SCIENCE

International Scientific Journal

THERMAL CONVECTION OF DUSTY COMPRESSIBLE RIVLIN-ERICKSEN VISCOELASTIC FLUID WITH HALL CURRENTS

ABSTRACT
An investigation is made on the effect of Hall currents and suspended particles on the hydromagnetic stability of a compressible, electrically conducting Rivlin-Ericksen elastico-viscous fluid. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant set of hydromagnetic equations. A dispersion relation governing the effects of viscoelasticity, magnetic field, Hall currents, compressibility and suspended particles is derived. For the stationary convection Rivlin-Ericksen fluid behaves like an ordinary Newtonian fluid due to the vanishing of the viscoelastic parameter. Compressibility and magnetic field are found to have a stabilizing effect on the system whereas Hall currents and suspended particles hasten the onset of thermal instability. These analytic results are confirmed numerically and the effects of various parameters on the stability parameter are depicted graphically. The critical Rayleigh numbers and the wavenumbers of the associated disturbances for the onset of instability as stationary convection are obtained and the behavior of various parameters on critical thermal Rayleigh numbers has been depicted graphically. It has been observed that oscillatory modes are introduced due to the presence of viscoelasticity, suspended particles and Hall currents which were not existing in the absence of these parameters.
KEYWORDS
PAPER SUBMITTED: 2011-01-28
PAPER REVISED: 2011-10-10
PAPER ACCEPTED: 2011-10-11
DOI REFERENCE: https://doi.org/10.2298/TSCI110128113G
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2012, VOLUME 16, ISSUE 1, PAGES [177 - 191]
REFERENCES
  1. Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York, 1981
  2. Sherman, A., Sutton, G.W., Magnetohydrodynamics, Northwestern University Press, Evanston, IL, 1962
  3. Gupta, A.S., Hall Effects on Thermal Instability, Rev. Roum. Math. Pures Appl., 12 (1967), pp. 665-677
  4. Sharma, K.C., Gupta, U., Finite Larmor Radius and Hall Effects on Thermosolutal Instability of a Rotating Plasma, Astrophysics and Space Science, 178 (1991), pp. 147-157
  5. Chandra, K., Instability of Fluids Heated from Below, Proc. Roy. Soc., London., A164 (1938), pp. 231- 242
  6. Scanlon, J.W., Segel, L.A., Some Effects of Suspended Particles on the Onset of Bénard Convection, Phys. Fluids, 16 (1973), pp. 1573-1578
  7. Sharma, R.C., Prakash, K., Dube, S.N., Effect of Suspended Particles on the Onset of Bénard Convection in Hydromagnetics, Acta Physica Hungarica, 40 (1976), pp. 3-10
  8. Palaniswamy, V.A., Purushotham, C.M., Stability of Shear Flow of Stratified Fluids with Fine Dust, Phys.Fluids, 22 (1981), pp. 1224-1229
  9. Sharma, R.C., Gupta, U., Thermal Instability of Compressible Fluids with Hall Currents and Suspended Particles in Porous Medium, Int.J. Eng. Sci., 31(7) (1993), pp. 1053-1060
  10. Spiegal, E.A., Veronis, G., On the Boussinesq Approximation for a Compressible Fluid, Astrophys. J., 131 (1960), pp. 442
  11. Sharma, R.C., Thermal Instability in Compressible Fluids in the Presence of Rotation and Magnetic Field, J. Math. Anal. Appl., 60 (1977), pp. 227-235
  12. Sharma, K.C., Gupta, U., Finite Larmor Radius Effect on Thermal Instability of a Compressible Rotating Plasma, Astrophysics and Space Science, 167 (1990), pp. 235-243
  13. Sharma, R.C., Sunil, Thermal Instability of Compressible Finite-Larmor-Radius Hall Plasma in Porous Medium, Journal of Plasma Physics, 55(1) (1996), pp. 35-45
  14. Oldroyd, J.G., Non-Newtonian Effects in Steady Motion of Some Idealized Elastico-viscous Liquids, Proc. Roy. Soc. (London), A245 (1958), pp. 278
  15. Bhatia, P.K., Steiner, J.M., Convective Instability in a Rotating Viscoelastic Fluid Layer, Z. Angew. Math. Mech., 52 (1972), pp. 321-327
  16. Sharma, R.C., Effect of Rotation on Thermal Instability of a Viscoelastic Fluid, Acta Physica Hungrica, 40 (1976), pp. 11-17
  17. Rivlin, R.S., Ericksen, J.L., Stress Deformation Relations for Isotropic Materials, J. Rat. Mech. Anal., 4 (1955), pp. 323-329
  18. Sharma, R.C., Kumar, P., Thermal Instability of Rivlin-Erickson Elastico-viscous Fluid in Presence of Uniform Rotation, Z.Naturforch., 51(a) (1997), pp. 821-824
  19. Sharma, R.C., Kumar, P., Thermal Instability of Rivlin-Ericksen Elastico-viscous Fluid in Hydromagnetics, Z.Naturforch., 52(a) (1997), pp. 369-371
  20. Prakash, K., Kumar, N., Thermal Instability in Rivlin-Ericksen Elastico-viscous Fluid in the Presence of Finite Larmor Radius and Variable Gravity in Porous Medium, The Physical Society of Japan, 68 (1999), pp. 1168-1172
  21. Kumar, P., Mohan, H., Lal, R., Effect of Magnetic Field on Thermal Instability of a Rotating Rivlin-Ericksen Viscoelastic Fluid, Int J. Math. and Math. Sc., 28042 (2006), pp. 1-10
  22. Gupta, U., Sharma, G., On Rivlin-Ericksen elastico-viscous fluid heated and soluted from below in the presence of compressibility, rotation and Hall currents, Journal of Applied Mathematics and Computing, 25(1-2) (2007), pp. 66
  23. Gupta, U., Sharma, G., Thermosolutal instability of a compressible Rivlin-Ericksen fluid in the presence of rotation and Hall currents saturating a porous medium, Applied Mathematics and Computation, 196(1) (2008), pp. 158-173
  24. Gupta, U., Kumar, V., Thermosolutal Instability of a Compressible Rotating Walters' (Model B¢) Elastico-viscous Fluid in the Presence of Hall Currents, Chemical Engineering Communications, 197(9) (2010), pp. 1225-1239
  25. Kolsi, L., Abidi, A., Borjini, M.N., Ben Aïssia, H., The Effect of an External Magnetic Field on the Entropy Generation in Three-Dimensional Natural Convection, Thermal Science, 14(2) (2010), pp. 341-352
  26. Savić, S.R. Obrović, B.Z. Despotović, M.R. Gordić, D., The Influence of the Magnetic Field on the Ionized Gas Flow Adjacent to the Porous Wall, Thermal Science, 14(Suppl.) (2010), pp. S183-S196
  27. Gupta, U., Aggarwal, P., Thermal Instability of Compressible Walters' (Model B) Fluid in the Presence of Hall Currents and Suspended Particles, Thermal Science, 15(2) (2011), pp. 487-500
  28. Sharma, R.C., Aggarwal, A.K., Effect of Compressibility and Suspended Particles on Thermal Convection in a Walters' Elastico-Viscous Fluid in Hydromagnetics, Int. J of Applied Mechanics and Engineering, 11(2) (2006), pp. 391-399
  29. Sharma, R.C., Sunil, Chand, S., Hall Effect on Thermal Instability of Rivlin-Ericksen Fluid, Indian J. of pure Appl. Math., 31 (1) (2000), pp. 49-59
  30. Kumar, P., Singh, G.J., Lal, R., Thermal Instability of Walters B¢ Viscoelastic Fluid Permeated with Suspended Particles in Hydromagnetics in Porous Medium, Thermal Science, 8(1) (2004), pp. 51-61

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