caa a22 4500 463162692 CHVBK 20180406164752.0 cr unu---uuuuu 170326e20071101xx s 000 0 eng 10.1007/s11242-006-9095-y doi (NATIONALLICENCE)springer-10.1007/s11242-006-9095-y Bhadauria B. Department of Mathematics and Statistics, Faculty of Sciences, Jai Narain Vyas University, 342005, Jodhpur, India aut Double diffusive convection in a porous medium with modulated temperature on the boundaries [Elektronische Daten] [B. Bhadauria] The effect of temperature modulation on the onset of double diffusive convection in a sparsely packed porous medium is studied by making linear stability analysis, and using Brinkman-Forchheimer extended Darcy model. The temperature field between the walls of the porous layer consists of a steady part and a time dependent periodic part that oscillates with time. Only infinitesimal disturbances are considered. The effect of permeability and thermal modulation on the onset of double diffusive convection has been studied using Galerkin method and Floquet theory. The critical Rayleigh number is calculated as a function of frequency and amplitude of modulation, Vadasz number, Darcy number, diffusivity ratio, and solute Rayleigh number. Stabilizing and destabilizing effects of modulation on the onset of double diffusive convection have been obtained. The effects of other parameters are also discussed on the stability of the system. Some results as the particular cases of the present study have also been obtained. Also the results corresponding to the Brinkman model and Darcy model have been compared. Springer Science+Business Media, Inc., 2007 Double diffusive convection nationallicence Thermal modulation nationallicence Darcy Rayleigh number nationallicence Porous medium 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 V : Mean filter velocity, (u, v, w) nationallicence p : Pressure nationallicence S : Solute concentration nationallicence T : Temperature nationallicence θ : Perturbed temperature nationallicence Δ S : Salinity difference between the walls nationallicence Δ T : Temperature difference between the walls nationallicence D a : Darcy number, k/d 2 nationallicence P r : Prandtl number, ν /κ T nationallicence R a : Darcy Rayleigh number, $$\frac{\alpha g \Delta T k d}{\nu \kappa _T }$$ nationallicence $$R_a^O $$ : Oscillatory Rayleigh number nationallicence R ac : Critical Rayleigh number nationallicence R S : Solute Rayleigh number, $$\frac{\beta \,g\,\Delta S\,k\,d}{\nu \kappa _S }$$ nationallicence $$R_S^\ast $$ : Crossover solute Rayleigh number nationallicence x , y , z : Space coordinates nationallicence Other symbols nationallicence $$\nabla _1^2 $$ : $$\frac{\partial ^2}{\partial x^2}+\frac{\partial ^2}{\partial y^2}$$ nationallicence ∇ 2 : $$\nabla _1^2 +\frac{\partial ^2}{\partial z^2}$$ nationallicence D : $$\frac{\partial }{\partial z}$$ nationallicence Greek symbols nationallicence α : Coefficient of thermal expansion nationallicence β : Coefficient of solute expansion nationallicence $$\varepsilon$$ : Amplitude of modulation nationallicence γ : Heat capacity ratio (ρc p ) m /(ρc p ) f nationallicence δ : Porosity nationallicence K f : Thermal conductivity of the fluid nationallicence K SO : Thermal conductivity of the solid nationallicence K m : Effective thermal conductivity of Porous media,δK f +(1−δ )K SO nationallicence κ T : Effective thermal diffusivity, K m /(ρc p ) f nationallicence κ S : Solute diffusivity nationallicence μ : coefficient of viscosity nationallicence ν : Kinematic viscosityμ /ρR nationallicence ρ : Density nationallicence ω : Modulation frequency nationallicence $$\phi $$ : Phase angle nationallicence σ : Growth rate (a complex number) nationallicence τ : Diffusivity ratio, κ S /κ T nationallicence Subscripts nationallicence b : Basic state nationallicence c : Critical nationallicence f : Fluid nationallicence R : Reference value nationallicence Superscript nationallicence / : Perturbed state nationallicence Transport in Porous Media Springer Netherlands 70/2(2007-11-01), 191-211 0169-3913 70:2<191 2007 70 11242 https://doi.org/10.1007/s11242-006-9095-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9095-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bhadauria B. Department of Mathematics and Statistics, Faculty of Sciences, Jai Narain Vyas University, 342005, Jodhpur, India aut NATIONALLICENCE 773 0- Transport in Porous Media Springer Netherlands 70/2(2007-11-01), 191-211 0169-3913 70:2<191 2007 70 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer