Effect of hall currents on thermal instability of dusty couple stress fluid

Open access

Abstract

In this paper, effect of Hall currents on the thermal instability of couple-stress fluid permeated with dust particles has been considered. Following the linearized stability theory and normal mode analysis, the dispersion relation is obtained. For the case of stationary convection, dust particles and Hall currents are found to have destabilizing effect while couple stresses have stabilizing effect on the system. Magnetic field induced by Hall currents has stabilizing/destabilizing effect under certain conditions. It is found that due to the presence of Hall currents (hence magnetic field), oscillatory modes are produced which were non-existent in their absence.

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

[2] Chandra K.: Instability of fluid heated from below. Proc. Roy. Soc. London. 164(A) (1938), 231–258.

[3] Sharma R.C.: Thermal instability in compressible fluids in the presence of rotation and magnetic field. J. Math. Anal. Appl. 60(1977), 1, 227–235.

[4] Scanlon J.W., Segel L.A.: Some effects of suspended particles on the onset of Bénard convection. Phys. Fluids. 16(1973), 10, 573–578.

[5] Stokes V.K.: Couple-stresses in fluids. Phys. Fluids. 9(1966), 9, 1709–1715.

[6] Walicki E., Walicka A.: Inertia effecting the squeeze film of a couple-stress fluid in biological bearings. Int. J. Appl. Mech. Engg. 4(1999), 2, 363–373.

[7] Goel A.K., Agrawal S.C., Agrawal G.S.: Hydromagnetic stability of an unbounded couple-stress binary fluid mixture having temperature and concentration gradients with rotation. Indian J. Pure Appl. Math. 30(1999), 10, 991–1001.

[8] Sharma R.C., Sharma S.: On couple stress fluid heated from below in porous medium. Indian J. Phys. 75B(2001), 59–61.

[9] Sharma R.C., Sharma S.: On electrically conducting couple stress fluid heated from below in porous medium in presence of uniform horizontal magnetic field. Int. J. Appl. Mech. Engg. 6(2001), 2, 251–263.

[10] Sharma R.C., Thakur D.: On couple stress fluid heated from below in porous medium in hydromagnetics. Czech. J. Phys. 50(2000), 6, 753–758.

[11] Rathod V.P., Thippeswami G.: Gravity flow of pulsatile blood through closed rectangular inclined channel with micro-organisms. Math. Educ. 33(1999), 1, 40–49.

[12] Sunil, Sharma R.C., Chandel R.S.: Effect of suspended particles on couple stress fluid heated and soluted from below in porous medium. J. Porous Media 7(2004), 1, 9–18.

[13] Sharma R.C., Sharma M.: Effect of suspended particles on couple stress fluid heated from below in the presence of rotation and magnetic field. Indian J. Pure Appl. Math. 35(2004), 8, 973–989.

[14] Gupta A.S.: Hall effects on thermal instability. Rev. Roum. Math. Pure Appl. 12(1967), 665–677.

[15] Singh V., Dixit S.: Hall effect on thermal instability of compressible couple stress fluid in presence of suspended particles. Int. J. Math. Arch. 3(2012), 4, 1701–1711.

[16] Kumar V., Kumar S.: On a couple stress fluid heated from below in hydromagnetics. Appl. Appl. Math. Inter. J. 5(2010), 10, 1529–1542.

[17] Aggarwal A.K., Makhija S.: Combined effect of magnetic field and rotation on couple-stress fluid heated from below in the presence of suspended particles. Int. J. Appl. Mech. Engg. 16(2011), 4, 931–942.

[18] Aggarwal A.K., Verma A.: Effect of suspended particles, magnetic field and rotation on the thermal stability of a ferromagnetic fluid. Int J. Appl. Mech. Engg. 17(2012), 4, 1109–1122.

[19] Sharma R.C., Aggarwal A.K.: Effect of compressibility and suspended particles on thermal convection in a Walters’ B’ elastico-viscous fluid in hydromagnetics. Int J. Appl. Mech. Engg. 11(2006), 2, 391–399.

[20] Postrzednik S.: Influence of the heat transfer on the specific thermal capacity of the flowing compressible fluid. Arch. Thermodyn. 25(2004), 2, 95–106.

[21] Rup K., Nering K.: Unsteady natural convection in micropolar nanofluids. Arch. Thermodyn. 35(2015), 3, 155–170, DOI: 10.2478/aoter-2014-0027.

Archives of Thermodynamics

The Journal of Committee on Thermodynamics and Combustion of Polish Academy of Sciences

Journal Information


CiteScore 2016: 0.54

SCImago Journal Rank (SJR) 2016: 0.319
Source Normalized Impact per Paper (SNIP) 2016: 0.598

Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 44 44 16
PDF Downloads 16 16 8