caa a22 4500 463163435 CHVBK 20180406164754.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s11242-006-9034-y doi (NATIONALLICENCE)springer-10.1007/s11242-006-9034-y Govender Saneshan School of Mechanical Engineering, University of Natal, King George V Avenue, 4041, Durban, South Africa aut Linear stability of solutal convection in solidifying mushy layers: permeable mush-melt interface [Elektronische Daten] [Saneshan Govender] The linear stability theory is used to investigate analytically the effect of a permeable mush-melt boundary condition on the stability of solutal convection in a mushy layer of homogenous permeability at the near eutectic (solid) limit. The results clearly show that, in contrast to the impermeable mush-melt interface boundary condition, the application of the permeable mush-melt interface boundary condition destabilizes the convection in a mushy layer. Springer Science+Business Media B.V, 2006 Mushy layers nationallicence Solutal convection nationallicence Rayleigh number nationallicence Solidification nationallicence Latin Symbols nationallicence g * : Acceleration due to gravity nationallicence H * : Height of the mushy layer nationallicence K * : Permeability function nationallicence C : Mixture composition nationallicence c p : Specific heat of fluid nationallicence $$\hat{\varvec{e}}_z$$ : Unit vector in the z-direction nationallicence h fs : Latent heat of fluid nationallicence k 0 : Characteristic permeability nationallicence L : Length of the mushy layer nationallicence p : Reduced pressure nationallicence R : Rescaled mushy layer Rayleigh number, $$\sqrt{\delta Ra_{\rm m}}$$ nationallicence Ra m : Mushy layer Rayleigh number, β* ΔCg * k 0/ (ν * V f *) nationallicence s x : X-component of wavenumber nationallicence s y : Y-component of wavenumber nationallicence St : Reciprocal of Stefan number, h fs / c p ΔT nationallicence t : Time nationallicence T : Dimensionless temperature, (T * −T L) / (T L −T E) nationallicence u : Horizontal x-component of the filtration velocity nationallicence V : Dimensionless filtration velocity vector, $$u\hat{e}_x +v\hat{e}_y +w\hat{e}_z $$ nationallicence v : Horizontal y-component of filtration velocity nationallicence V f * : Velocity of solidifying front nationallicence w : Vertical component of filtration velocity 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, s 2 / π 2 nationallicence β C : Solutal expansion coefficient nationallicence β T : Thermal expansion coefficient nationallicence δ : Dimensionless depth of mushy layer nationallicence ɛ : Convection amplitude nationallicence $$\phi$$ : Porosity nationallicence $$\varphi$$ : Solid fraction = 1- $$\phi $$ nationallicence κ : Thermal diffusivity of liquid nationallicence μ : Dynamic viscosity of the fluid nationallicence ν : Kinematic viscosity nationallicence $$\Pi (\varphi)$$ : Dimensionless retardability function, k 0/ K * nationallicence $$\rho$$ : Fluid density nationallicence Γ : Slope of liquidus line nationallicence $$\psi _{mk}$$ : Kronecker delta notation nationallicence Superscripts nationallicence * : Dimensional quantities nationallicence Subscripts nationallicence 0 : Simplified parameters nationallicence B : Basic flow quantities nationallicence c : Characteristic values nationallicence cr : Critical values nationallicence E : Eutectic conditions nationallicence l : Liquid conditions nationallicence m : Mush conditions nationallicence S : Solid conditions nationallicence st : Stationary conditions nationallicence ∞ : Far field conditions nationallicence Over nationallicence − : Rescaled quantities nationallicence ~ : Unscaled quantities nationallicence Transport in Porous Media Kluwer Academic Publishers 67/3(2007-04-01), 431-439 0169-3913 67:3<431 2007 67 11242 https://doi.org/10.1007/s11242-006-9034-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9034-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Govender Saneshan School of Mechanical Engineering, University of Natal, King George V Avenue, 4041, Durban, South Africa aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/3(2007-04-01), 431-439 0169-3913 67:3<431 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer