Rotating Rayleigh Bernard Convection with Variable Diffusive Coefficient

(*) Corresponding author

Authors' affiliations

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


The problem of rotating natural convective flow about the vertical axis, with variable viscosity confined between the two horizontal plates, is investigated via linear stability analysis. The transformed governing equations are solved numerically by using the Galerkin method. The computed results are compared for special cases with the results of earlier research by Chandrasekhar and Stengel et al., and are found to be in good agreement. We studied both stationary convection and oscillatory convection. The threshold values of Rayleigh number and wavenumber are computed and presented for various boundary conditions viz. rigid-rigid, rigid-free, free-rigid and free-free, and for different values of physical parameters viz. Taylor number Ta, viscosity ratio c and Prandtl number Pr. For rigid-rigid boundary conditions we studied the effect of c, Ta and Pr on the vertical velocity and temperature eigenfunctions at the onset. It is observed that the rotation rate stabilizes the dynamical system. The occurrence of the co-dimension two bifurcation point (CTP) is shown for various boundary conditions
Copyright © 2013 Praise Worthy Prize - All rights reserved.


Variable Viscosity; Coriolis Force; Exponential Fluid; Galerkin Method

Full Text:



Alloui Z, Vasseur P, (2011). Onset of Bénard–Marangoni convection in a micropolar fluid. Int. J. Heat Mass Tran. 54: 2765-2773.

Alonso A, Net M, Mercader I, Knobloch E, (1999). Onset of convection in a rotating annulus with radial gravity and heating. Fluid Dynamics Res. 24: 133-145.

Awang Kechil S, Hashim I, (2009). Oscillatory Marangoni convection in variable-viscosity fluid layer: The effect of thermal feedback control, Int. J. Thermal Sci. 48: 1102-1107.

Booker JR, (1976). Thermal convection with strongly temperature dependent viscosity. J. Fluid Mech. 76: 741-754.

Booker JR, Stengel KC (1978). Further thoughts on convective heat transport in variable viscosity fluids. J. Fluid Mech. 86: 289-291.

Busse FH, (1967). The stability of finite amplitude cellular convection and its relation to an extremum principle. J. Fluid Mech. 30(4): 625-649.

Busse FH, Heikes KE, (1980). Convection in a rotating layer: a simple case of turbulence. Science 208:173.

Chandrashekar S, (1961). Hydrodynamic and Hydromagnatic stability. Oxford: Clarendon.

Chatterjee S, Basak T, Das SK, (2008). Onset of natural convection in a rotating fluid layer with non-uniform volumetric heat sources. Int. J. Thermal Sci. 47: 730-741.

Clever RM, Busse FH, (1979). Nonlinear properties of convection rolls in a horizontal layer rotating about a vertical axis. J. Fluid Mech. 94: 609-627.

Clune T, Knobloch E, (1993). Pattern selection in rotating convection with experimental boundary conditions. Phys. Rev. E., 47: 2536-2550.

Jakins DR , (1987). Rolls versus squares in thermal convection of fluids with temperature dependent viscosity. J. Fluid Mech., 178: 491-506.

Knobloch E, (1998). Rotating convection : Recent developments. Int. J. Engg. Sci., 36: 1421-1450.

Knobloch E, Silber M, (1990). Travelling wave convection in a rotating layer. Geophys. Astrophys. Fluid Dyn. 51: 195-209.

Küppers G, Lortz D, (1969). Transition for laminar convection to thermal turbulence in rotating fluid layer. J. Fluid Mech. 35: 609-620.

Malashetty MS, Swamy MS, Sidram W, (2010). Thermal convection in a rotating viscoelastic fluid saturated porous layer. Int. J Heat Mass Trans. 53 : 5747-5756.

Niemela JJ, Donnelly RJ, (1986). Direct transition to turbulence in rotating Bénard convection, Phys. Rev. Lett. 57: (1986), pp.2524-2527.

Prabhamani R. Patil, Vaidyanathan G, (1983). On setting up of convection currents in a rotating porous medium under the influence of variable viscosity, Int. J. Eng. Sci. 21: 123-130.

Rajagopal KR, Saccomandi G, Vergori L, (2009). Stability Analysis of the Rayleigh-Bénard convection for a fluid with temperature and pressure dependent viscosity. ZAMP, 60: 739-755.

Schluter S, Lortz D, Busse FH, (1965). On the stability of steady finite amplitude convection. J. Fluid Mech. 23(1): 129-144.

Stengel KC, (1977). Onset of convection in a variable viscosity fluid, M.Sc. Thesis, University of Washington.

Stengel KC, Oliver DS, Booker JR, (1982). Onset of convection in a variable viscosity fluid. J. Fluid Mech. 120: 411-431.

Sekhar GN, Jayalatha G, (2010). Elastic Effects on Rayleigh-Bénard convection in liquids with temperature dependent viscosity. Int. J. Ther. Sci. 49: 67-75.

Schubert G, Turcotte DL, Oslon P, (2004). Mantle convection in the Earth and Planets, Taylor and Francis. New York (Chapters 5, 9, 13).

Tagare SG, Benerji Babu A, Rameshwar Y, (2008). Rayleigh-Bénard convection in rotating fluids. Int. J. Heat Mass Trans. 51: 1168-1178.

Thanham S, Chen CF, (1986). Stability analysis on the convection of a variable viscosity fluid in an infinite vertical slot. Phys. Fluids. 29: 1367-1373.

Torrence KE, Turcotte DL, (1971). Thermal convection with large viscosity variation. J. Fluid Mech. 47: 113-125.

Vadasz P, (1998). Coriolis effect on gravity-driven convection in a rotating porous layer heated from below, J. Fluid Mech. 376: 351-375.

Vanishree RK, Siddheshwar PG, (2010). Effect of rotation on thermal convection in an anisotropic porous medium with temperature dependent viscosity. Transp Porous Med. 81: 73-87.

Yen-Ming Chen and Arne J, Pearlstein, (1988). Onset of convection in variable viscosity fluids: assessment of approximate viscosity-temperature relations. Phys. Fluids. 31: 1380-1386.

Sammouda M, Gueraoui K, Driouich M, El Hammoumi A, Iben Brahim A, The Variable Porosity Effect on the Natural Convection in a non-Darcy Porous Media, (2011) International Review on Modelling and Simulations (IREMOS), 4 (5), pp. 2701-2707.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2024 Praise Worthy Prize