ABSTRACT The effects of electric field and non-uniform basic temperature gradient on the onset of Rayleigh-Bénard convection in a micropolar fluid are studied using the Galerkin technique. The eigenvalues are obtained for free-free, rigid-free and rigid-rigid velocity boundary combinations and for isothermal and/or adiabatic temperature boundaries. The microrotation is assumed to vanish at the boundaries. A linear stability analysis is performed. The influence of various micropolar fluid parameters and electric Rayleigh number on the onset of convection has been analyzed. One linear and five non-uniform temperature profiles are considered and their comparative influence on onset is discussed.
Cite this paper
S. Pranesh and R. Baby, "Effect of Non-Uniform Temperature Gradient on the Onset of Rayleigh-Bénard Electro Convection in a Micropolar Fluid," Applied Mathematics, Vol. 3 No. 5, 2012, pp. 442-450. doi: 10.4236/am.2012.35067.
 P. H. Roberts, “Electrodynamic Convection,” Quarterly Journal of Mechanics and Applied Mathematics, Vol. 22, No. 2, 1969, pp. 211-220. doi:10.1093/qjmam/22.2.211
 T. Maekawa, K. Abe and I. Tanasawa, “Onset of Natural Convection under an Electric Field,” International Journal of Heat and Mass Transfer, Vol. 35, 1992, pp. 613621.
 M. I. Char and K. T. Chiang, “Boundary Effects on the Bénard-Marangoni Instability under the Electric Field,” Applied Scientific Research, Vol. 52, No. 4, 1994, pp. 331-354. doi:10.1007/BF00936836
 A. Douiebe, M. Hannaoui, G. Lebon, A. Benaboud and A. Khmou, “Effects of a.c. Electric Field and Rotation on Bénard-Marangoni Convection,” Flow, Turbulence and Combustion, Vol. 67, No. 3, 2001, pp. 185-204.
 M. F. El-Sayed, “Onset of Electroconvective Instability of Oldroydian Viscoelastic Liquid Layer in Brinkman Porous Medium,” Archive of Applied Mechanics, Vol. 78, No. 3, 2008, pp. 211-224.
 N. Rudraiah and M. S. Gayathri, “Effect of Thermal Modulation on the Onset of Electrothermoconvection in a Dielectric Fluid Saturated Porous Medium,” Journal of Heat Transfer, Vol. 131, No. 10, 2009, p. 101009.
 K. Hemalatha and I. S. Shivakumara, “Thermo Convective Instability in a Heat Generating Dielectric Fluid Layer under Alternating Current Electric Field,” Carmelight, Vol. 7, 2010, pp. 125-136.
 A. C. Eringen, “Theory of Micropolar Fluids,” International Journal of Engineering Science, Vol. 16, 1966, p. 1.
 G. Lukaszewicz, “Micropolar Fluid Theory and Applications,” Birkhauser, Boston, 1999.
 B. Datta and V. U. K. Sastry, “Thermal Instability of a Horizontal Layer of Micropolar Fluid Heated from Below,” International Journal of Engineering Science, Vol. 14, No. 7, 1976, pp. 631-637.
 G. Ahmadi, “Stability of a Micropolar Fluid Layer Heated from Below,” International Journal of Engineering Science, Vol. 14, No. 7, 1976, pp. 81-89.
 S. P. Bhattacharyya and S. K. Jena, “On the Stability of Hot Layer of Micropolar Fluid,” International Journal of Engineering Science, Vol. 21, No. 9, 1983, pp. 1019-1024.
 P. G. Siddheshwar and S. Pranesh, “Magnetoconvection in a Micropolar Fluid,” International Journal of Engineering Science, Vol. 36, No. 10, 1998, pp. 1173-1181.
 P. G. Siddheshwar and S. Pranesh, “Effects of a NonUniform Basic Temperature Gradient on Rayleigh-Bénard Convection in a Micropolar Fluid,” International Journal of Engineering Science, Vol. 36, No. 11, 1998, pp. 1183-1196. doi:10.1016/S0020-7225(98)00015-9
 P. G. Siddheshwar and S. Pranesh, “Effects of Non-Uniform Temperature Gradients and Magnetic Field on the Onset of Convection in Fluids with Suspended Particles under Microgravity Conditions,” Indian Journal of Engineering and Materials Sciences, Vol. 8, No. 77, 2001, pp. 83.
 P. G. Siddheshwar and S. Pranesh, “Magnetoconvection in Fluids with Suspended Particles under 1g and mg,” International Journal of Aerospace Science and Technology, Vol. 6, No. 2, 2001, pp. 105-114.
 P. G. Siddheshwar and S. Pranesh, “Linear and Weakly Non-Linear Analyses of Convection in a Micropolar Fluid,” Hydrodynamics VI-Theory and Applications, 2005, pp. 487-493.
 S. Pranesh and R. V. Kiran, “Study of Rayleigh Bénard Magneto Convection in a Micropolar Fluid with Maxwell-Cattaneo Law,” Applied Mathematics, Vol. 1, 2010, pp. 467-480.
 S. Chandrasekhar, “Hydrodynamic and Hydromagnetic Stability,” Clarendon Press, Oxford, 1961.
 R. J. Turnbull, “Electro Convective Instability with a Stabilizing Temperature Gradient, I. Theory,” Physics of Fluids, Vol. 11, No. 12, 1968, pp. 2588-2596.