caa a22 4500 463163532 CHVBK 20180406164755.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s11242-006-9003-5 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9003-5 Govender Saneshan School of Mechanical Engineering, University of Kwa-Zulu Natal, King George V Avenue, 4041, Durban, South Africa aut Coriolis Effect on the Stability of Centrifugally Driven Convection in a Rotating Anisotropic Porous Layer Subjected to Gravity [Elektronische Daten] [Saneshan Govender] We investigate natural convection in a fluid saturated rotating anisotropic porous layer subjected to centrifugal gravitational and Coriolis body forces. The Darcy model (including the centrifugal, gravitational and Coriolis terms; and permeability anisotropy effects) and a modified energy equation (including the effects of thermal anisotropy) is used in the current analysis. The linear stability theory is used to evaluate the critical Rayleigh number for the onset of convection in the presence of thermal and mechanical anisotropy. It is shown that the preferred solution comprises roll cells aligned parallel to the vertical z-axis. As a result, it is found that the Coriolis acceleration (or Taylor number) and the gravitational term play no role in the stability of convection. Springer Science+Business Media, B.V., 2006 Mechanical anisotropy nationallicence Thermal anisotropy nationallicence Rotation nationallicence Centrifugal Rayleigh number nationallicence Gravitational Rayleigh number nationallicence Taylor number nationallicence Latin Symbols nationallicence a k : Coefficients in Galerkin expansion nationallicence g * : Acceleration due to gravity nationallicence H * : Height of the porous layer nationallicence $$\boldsymbol{\hat {e}}_x$$ : Unit vector in the x-direction nationallicence $$\boldsymbol{\hat {e}}_y$$ : Unit vector in the y-direction nationallicence $$\boldsymbol{\hat {e}}_z$$ : Unit vector in the z-direction nationallicence k : Permeability tensor nationallicence k * x , k * y , k * z : Characteristic permeabilities in the x-, y- and z- directions nationallicence L * : Length of the porous layer nationallicence p : Reduced pressure nationallicence R g : Scaled gravitational Rayleigh number, Ra g / π2 nationallicence R ω : Scaled centrifugal Rayleigh number, Ra ω/ π2 nationallicence Ra g : Gravitational Rayleigh number, β* ΔTk * x g * L */ κ* x ν* nationallicence Ra ω : Centrifugal Rayleigh number, $$\beta_{\ast} \Delta Tk_{\ast x} \omega_{\ast} ^{2} L_{\ast}^{2} \left/ \kappa_{\ast x} \nu _{\ast}\right.$$ nationallicence s : Wave number, $$\sqrt {s_y^2 +s_z^2} $$ nationallicence s y : y-component of wavenumber nationallicence s z : z-component of wavenumber nationallicence t : Time nationallicence T : Dimensionless temperature, (T * −T C)/ (T H −T C) nationallicence T C : Temperature at cold wall nationallicence T H : Temperature at hot wall nationallicence Ta : Taylor number, defined as (2 ω* k * x / ν* ϕ *.) nationallicence u : Horizontal x-component of the filtration velocity nationallicence v : Horizontal y-component of filtration velocity nationallicence w : Vertical component of filtration velocity nationallicence W * : Width of porous layer nationallicence V : Dimensionless filtration velocity vector, $$u\hat {e}_x +v\hat {e}_y+w\hat {e}_z$$ nationallicence X : Space vector, $$x\hat {e}_x +y\hat {e}_y +z\hat {e}_z$$ nationallicence x : Horizontal length co-ordinate nationallicence y : Horizontal width co-ordinate nationallicence z : Vertical co-ordinate nationallicence Greek Symbols nationallicence α : Scaled wavenumber, ξ s 2/ π2 nationallicence β* : thermal expansion coefficient nationallicence η : κ* y / κ * x .=κ * z / κ* x nationallicence ϕ* : Porosity nationallicence κ* : Fluid thermal diffusivity nationallicence φ : Parameter, η/ ξ nationallicence μ* : Fluid dynamic viscosity nationallicence ν* : Fluid kinematic viscosity nationallicence θ : Galerkin function nationallicence ρ* : Fluid density nationallicence ω* : Angular velocity nationallicence ξ : k * y / k * x .=k * z / k * x nationallicence Subscripts nationallicence * : Dimensional quantities nationallicence B : Basic flow quantities nationallicence C : Associated with cold wall nationallicence H : Associated with hot wall nationallicence cr : Critical values nationallicence Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 219-227 0169-3913 67:2<219 2007 67 11242 https://doi.org/10.1007/s11242-006-9003-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9003-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Govender Saneshan School of Mechanical Engineering, University of Kwa-Zulu Natal, King George V Avenue, 4041, Durban, South Africa aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 219-227 0169-3913 67:2<219 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer