Hydromagnetic thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles in porous medium

Rana, G.C.; Jamwal, H.S.

doi:10.2478/sgem-2013-0038

Abstract

In this paper, the thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles (fine dust) in porous medium in hydromagnetics is considered. By applying normal mode analysis method, the dispersion relation has been derived and solved analytically. It is observed that the rotation, magnetic field, suspended particles and viscoelasticity introduce oscillatory modes. For stationary convection, Walters’ (Model B′) elastico-viscous fluid behaves like an ordinary Newtonian fluid and it is observed that rotation has stabilizing effect, suspended particles are found to have destabilizing effect on the system, whereas the medium permeability has stabilizing or destabilizing effect on the system under certain conditions. The magnetic field has destabilizing effect in the absence of rotation, whereas in the presence of rotation, magnetic field has stabilizing or destabilizing effect under certain conditions

References

[1] CHANDRASEKHAR S., Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York, 1981.
Search in Google Scholar
[2] CHANDRA K., Instability of fluids heated from below, Proc. Roy. Soc. London, 1938, A164, 231.10.1098/rspa.1938.0015
Search in Google Scholar
[3] BHATIA P.K., STEINER J.M., Thermal instability of fluid layer in Hydromagnetics, J. Math. Anal. Appl., 1973, 41, 271.10.1016/0022-247X(73)90201-1
Search in Google Scholar
[4] SHARMA R.C., Effect of rotation on thermal instability of a visco-elastic fluid, Acta Physica Hungarica, 1976, 40, 11-17.10.1007/BF03157148
Search in Google Scholar
[5] LAPWOOD E.R., Convection of a fluid in porous medium, Proc. Camb. Phil. Soc., 1948, 44, 508-519.10.1017/S030500410002452X
Search in Google Scholar
[6] WOODING R.A., Rayleigh instability of a thermal boundary layer in flow through a porous medium, J. Fluid Mech., 1960, 9, 183.10.1017/S0022112060001031
Search in Google Scholar
[7] SCANLON J.W., SEGEL L.A., Effect of suspended particles on the onset of Bénard convection, Physics Fluids, 1973, 16, 1573.
Search in Google Scholar
[8] SHARMA R.C., SUNIL, Thermal instability of an Oldroydian viscoelastic fluid with suspended particles in hydromagnetics in porous medium, J. Polymer Plastic Technology and Engineering, 1994, 33, 323.10.1080/03602559408013096
Search in Google Scholar
[9] WALTERS’ K., The solution of flow problems in the case of materials with memory, J. Mecanique, 1962, 1, 469.
Search in Google Scholar
[10] SPIEGAL E.A., VERONIS G, On Boussnesq approximation for compressible fluid, Astrophysics J., 1960, 131, 442.10.1086/146849
Search in Google Scholar
[11] SHARMA V., RANA G.C., 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., 2001, 26, 31.10.1515/JNETDY.2001.003
Search in Google Scholar
[12] SHARMA V., RANA G.C., Thermosolutal instability of a Walters’ ((Model B′) elastico-viscous rotating fluid in the presence of magnetic field and variable gravity field in porous medium, Proc. Nat. Acad. Sci. India, 2003, 73, 93.
Search in Google Scholar
[13] RANA G.C., KUMAR S., Thermal instability of a Rivlin-Ericksen elastico-viscous rotating fluid permeated with suspended particles and variable gravity field in porous medium, Studia Geotechnica et Mechanica, 2010, XXXII, 39.
Search in Google Scholar
[14] RANA G.C., KANGO S.K., Effect of rotation on thermal instability of compressible Walters’ (Model B′) fluid in porous medium, J. Adv. Res. Appl. Math., 2011, 3, 44. 10.5373/jaram.815.030211
Search in Google Scholar

Hydromagnetic thermal instability of compressible Walters’ (Model B′) rotating fluid permeated with suspended particles in porous medium

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