caa a22 4500 463163524 CHVBK 20180406164754.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s11242-006-9027-x doi (NATIONALLICENCE)springer-10.1007/s11242-006-9027-x Bhadauria B. Department of Mathematics and Statistics, Jai Narain Vyas University, 342005, Jodhpur, India aut Fluid convection in a rotating porous layer under modulated temperature on the boundaries [Elektronische Daten] [B. Bhadauria] The linear stability of thermal convection in a rotating horizontal layer of fluid-saturated porous medium, confined between two rigid boundaries, is studied for temperature modulation, using Brinkman's model. In addition to a steady temperature difference between the walls of the porous layer, a time-dependent periodic perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The combined effect of rotation, permeability and modulation of walls' temperature on the stability of flow through porous medium has been investigated using Galerkin method and Floquet theory. The critical Rayleigh number is calculated as function of amplitude and frequency of modulation, Taylor number, porous parameter and Prandtl number. It is found that both, rotation and permeability are having stabilizing influence on the onset of thermal instability. Further it is also found that it is possible to advance or delay the onset of convection by proper tuning of the frequency of modulation of the walls' temperature. Springer Science+Business Media B.V., 2006 Thermal convection nationallicence Modulation nationallicence Rayleigh number nationallicence Porous medium nationallicence Rotation nationallicence Galerkin method nationallicence a : Horizontal wave number $$\left({a_x^2 +a_y^2}\right)^{1/2}$$ nationallicence a c : Critical wave number nationallicence d : Depth of the porous layer nationallicence g : Gravitational acceleration nationallicence k : Permeability of the porous medium nationallicence κf : Thermal conductivity of the fluid nationallicence κs : Thermal conductivity of the solid nationallicence κ m : δκf +(1−δ)κs, effective thermal conductivity of porous media nationallicence p : Pressure nationallicence P l : Porous parameter, k/d 2 nationallicence P r : Prandtl number, ν /κ nationallicence R : Thermal Rayleigh number, $$\frac{\alpha g\Delta Td^3}{\nu \kappa}$$ nationallicence Ω : Angular velocity vector (0, 0, Ω) nationallicence T : Taylor number 4Ω2 d 4/ν2 nationallicence R c : Critical Rayleigh number nationallicence T : Temperature nationallicence θ : Perturbed temperature nationallicence Δ T : Temperature difference between the walls nationallicence V : Mean filter velocity, (u, v, w) nationallicence x , y , z : Space coordinates nationallicence (ρ c p )f : Heat capacity of the fluid nationallicence (ρ c p )s : Heat capacity of the solid nationallicence (ρ c p ) m : δ(ρ c p )f +(1−δ)(ρ c p )s relative heat capacity of the porous medium nationallicence T S ( z ) : Steady temperature field nationallicence To(z, t) : Oscillating temperature field nationallicence Greek symbols nationallicence ζ : Z-component of vorticity nationallicence α : Coefficient of thermal expansion nationallicence $$\varepsilon$$ : Amplitude of modulation nationallicence δ : Porosity nationallicence γ : Heat capacity ratio, (ρ c p ) m /(ρ c p )f nationallicence κ : Effective thermal diffusivity, κ m /(ρ c p )f nationallicence μ : Coefficient of viscosity nationallicence ν : Kinematic viscosity,μ/ρ R nationallicence ρ : Density nationallicence ω : Modulation frequency nationallicence $$\phi$$ : Phase angle nationallicence Other symbols nationallicence $$\nabla_1^2$$ : $$\frac{\partial^2}{\partial x^2}+ \frac{\partial^2}{\partial y^2}$$ nationallicence $${\nabla}^{2}$$ : $$\nabla_1^2 +\frac{\partial^2}{\partial z^2}$$ nationallicence D : $$\frac{\partial} {\partial z}$$ nationallicence Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 297-315 0169-3913 67:2<297 2007 67 11242 https://doi.org/10.1007/s11242-006-9027-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9027-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bhadauria B. Department of Mathematics and Statistics, Jai Narain Vyas University, 342005, Jodhpur, India aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 297-315 0169-3913 67:2<297 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer