Thermal convection in a rotating viscoelastic fluid saturated porous layer

Abstract Linear and nonlinear stability of a rotating viscoelastic fluid saturated porous layer heated from below is studied analytically. The modified Darcy–Oldroyd model that includes the time derivative and Coriolis terms is employed as a momentum equation. The onset criterion for both stationary and oscillatory convection is derived as a function of Taylor number, Darcy–Prandtl number and viscoelastic parameters. There is a competition between the processes of rotation, viscous relaxation and thermal diffusion that causes the convection to set in through oscillatory mode rather than stationary. The rotation inhibits the onset of convection in both stationary and oscillatory modes. The stress relaxation parameter destabilizes the system towards the oscillatory mode, while the strain retardation parameter enhances the stability. The effect of Darcy–Prandtl number on the stability of the system is also investigated. The nonlinear theory is based on the truncated representation of Fourier series method. The effect of rotation, stress relaxation and strain-retardation time and also the Darcy–Prandtl number on the transient heat transfer is presented graphically.

[1]  S. Govender.  Oscillatory convection induced by gravity and centrifugal forces in a rotating porous layer distant from the axis of rotation , 2003 .

[2]  E. Koschmieder,et al.  Bénard cells and Taylor vortices , 1993 .

[3]  M. Mamou,et al.  Thermosolutal bifurcation phenomena in porous enclosures subject to vertical temperature and concentration gradients , 1999, Journal of Fluid Mechanics.

[4]  V. Bertola,et al.  Thermal instability of viscoelastic fluids in horizontal porous layers as initial value problem , 2006 .

[5]  A. Bejan,et al.  Convection in Porous Media , 1992 .

[6]  C. W. Horton,et al.  Convection Currents in a Porous Medium , 1945 .

[7]  M. S. Malashetty,et al.  Convective Instability of Oldroyd-B Fluid Saturated Porous Layer Heated from Below using a Thermal Non-equilibrium Model , 2006 .

[8]  J. Jou,et al.  Thermal convection in a porous medium subject to transient heating and rotation , 1987 .

[9]  L. Tam,et al.  Chaotic convection of viscoelastic fluids in porous media , 2008 .

[10]  Jacob Bear,et al.  Transport Phenomena in Porous Media , 1998 .

[11]  G. Vaidyanathan,et al.  On setting up of convection currents in a rotating porous medium under the influence of variable viscosity , 1983 .

[12]  Hsien-Keng Chen,et al.  A unified system describing dynamics of chaotic convection , 2009 .

[13]  B. Straughan.  A sharp nonlinear stability threshold in rotating porous convection , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[14]  P. Vadasz.  Coriolis effect on gravity-driven convection in a rotating porous layer heated from below , 1998, Journal of Fluid Mechanics.

[15]  E. R. Lapwood.  Convection of a fluid in a porous medium , 1948, Mathematical Proceedings of the Cambridge Philosophical Society.

[16]  S. Rosenblat.  Thermal convection in a viscoelastic liquid , 1986 .

[17]  Peter Vadasz,et al.  Emerging topics in heat and mass transfer in porous media : from bioengineering and microelectronics to nanotechnology , 2008 .

[18]  G. Lebon,et al.  Thermal instability of a rotating saturated porous medium heated from below and submitted to rotation , 2002 .

[19]  S. Govender.  Coriolis Effect on the Linear Stability of Convection in a Porous Layer Placed Far Away from the Axis of Rotation , 2003 .

[20]  P. Kaloni,et al.  Nonlinear stability problem of a rotating porous layer , 1995 .

[21]  D. Nield.  The limitations of the Brinkman-Forchheimer equation in modeling flow in a saturated porous medium and at an interface , 1991 .

[22]  M. S. Malashetty,et al.  The effect of rotation on the onset of convection in a horizontal anisotropic porous layer , 2007 .

[23]  Min Chan Kim,et al.  Thermal instability of viscoelastic fluids in porous media , 2003 .

[24]  B. Straughan.  Global nonlinear stability in porous convection with a thermal non-equilibrium model , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[25]  E. Palm,et al.  Thermal convection in a rotating porous layer , 1984 .

[26]  R. Khayat,et al.  Finite-amplitude Rayleigh–Bénard convection and pattern selection for viscoelastic fluids , 2005, Journal of Fluid Mechanics.