caa a22 4500 463163559 CHVBK 20180406164755.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s11242-006-9001-7 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9001-7 The onset of convection in a viscoelastic liquid saturated anisotropic porous layer [Elektronische Daten] [M. Malashetty, Mahantesh Swamy] The linear stability of a viscoelastic liquid saturated horizontal anisotropic porous layer heated from below and cooled from above is investigated by considering the Oldroyd type liquid. A generalized Darcy model, which takes into account the viscoelastic properties, the mechanical and thermal anisotropy is employed as momentum equation. The critical Rayleigh number, wavenumber, for stationary and oscillatory states and frequency of oscillation are determined analytically. It is shown that oscillatory instabilities can set in before stationary modes are exhibited. The effect of the viscoelastic parameter, the mechanical and thermal anisotropy parameters and specific heat ratio on the linear stability of the system is analyzed and presented graphically. Springer Science+Business Media B.V, 2006 Stationary/oscillatory convection nationallicence Mechanical/thermal anisotropy nationallicence Viscoelastic liquid nationallicence a : wavenumber, $$\sqrt{l^2+m^2} $$ nationallicence d : height of the fluid layer nationallicence D : thermal diffusivity tensor, D x (ii+jj )+D z (kk ) nationallicence g : gravitational acceleration, (0,0,−g ) nationallicence K : permeability tensor, K x −1 (ii+jj )+K z −1 (kk ) nationallicence p : pressure nationallicence q : velocity vector (u,v,w ) nationallicence R D : Darcy-Rayleigh number, β gΔTd K z / ν D z nationallicence T : temperature nationallicence Δ T : temperature difference between the walls nationallicence t : time nationallicence x , y , z : space coordinates nationallicence Greek symbols nationallicence β : thermal expansion coefficient nationallicence γ : ratio of specific heats (ρc) m / (ρc) f nationallicence $$\varepsilon $$ : porosity nationallicence η : thermal anisotropy parameter, D x / D z nationallicence $${\overline{\lambda}}_{1} $$ : stress relaxation time nationallicence λ 1 : dimensionless stress relaxation time, $$D_{z} {\overline{\lambda}}_{1} \big/ d^{2}$$ nationallicence $$\overline{\lambda} _2 $$ : strain retardation time nationallicence λ 2 : dimensionless strain retardation time, $$D_{z} \overline{\lambda}_{2} \big/ d^{2}$$ nationallicence μ : dynamic viscosity nationallicence ν : kinematic viscosity,μ / ρ 0 nationallicence Θ : dimensionless amplitude of temperature perturbation nationallicence ρ : density nationallicence σ : growth rate nationallicence ξ : mechanical anisotropy parameter, K x / K z nationallicence ψ : stream function nationallicence Ψ : dimensionless amplitude of stream function nationallicence ω : frequency nationallicence Subscripts nationallicence b : basic state nationallicence c : critical nationallicence 0 : reference value nationallicence Superscripts nationallicence * : dimensionless quantity nationallicence / : perturbed quantity nationallicence Osc : oscillatory nationallicence S : stationary nationallicence Malashetty M. Department of Mathematics, Gulbarga University, Jnana Ganga, 585 106, Gulbarga, India aut Swamy Mahantesh Department of Mathematics, Gulbarga University, Jnana Ganga, 585 106, Gulbarga, India aut Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 203-218 0169-3913 67:2<203 2007 67 11242 https://doi.org/10.1007/s11242-006-9001-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9001-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Malashetty M. Department of Mathematics, Gulbarga University, Jnana Ganga, 585 106, Gulbarga, India aut NATIONALLICENCE 700 1- Swamy Mahantesh Department of Mathematics, Gulbarga University, Jnana Ganga, 585 106, Gulbarga, India aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 203-218 0169-3913 67:2<203 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer