caa a22 4500 463163591 CHVBK 20180406164755.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s11242-006-9004-4 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9004-4 Onset of Buoyancy-driven Instability in Porous Media Melted from Below [Elektronische Daten] [Joung Hong, Min Kim, Chang Choi] When a nonhomogeneous solid is melting from below, convection may be induced in a thermally-unstable melt layer. In this study, the onset of buoyancy-driven convection during time-dependent melting is investigated by using similarly transformed disturbance equations. The critical Darcy-Rayleigh numbers based on the melt-layer thickness, Ra H,c, are found numerically for various conditions. For small superheats, the present predictions show that Ra H,c is located between 27.1 and 4π 2 and it approaches the well-known results of the original Horton-Rogers-Lapwood problem. However, for high superheats, it is dependent on the phase change rate λ and the relation of Ra H,c λ =25.89 is shown. Springer Science+Business Media B.V., 2006 Buoyancy-driven convection nationallicence Melting nationallicence Porous medium nationallicence Stefan problem nationallicence Similarity transform nationallicence a : Dimensionless wavenumber, $$\sqrt {a_x^2 +a_y^2}$$ nationallicence a * : Modified dimensionless wave number, aδ nationallicence a H : Dimensionless wave number based on the melt thickness, a * λ nationallicence c : Specific heat (J/(kg · K)) nationallicence d : Arbitrary length scale (m) nationallicence g : Gravitational acceleration vector (m/s 2) nationallicence H : Thickness of the melt layer (m) nationallicence h : Dimensionless thickness of the melt layer, H/d nationallicence K : Permeability (m 2) nationallicence k : Thermal conductivity, (W / (m · K)) nationallicence k r : Thermal conductivity ratio,k S/k L nationallicence L : Latent heat of melting (J / kg) nationallicence P : Pressure (Pa) nationallicence Ra D : Darcy-Rayleigh number, $$\varepsilon ( ( \rho c )_f / ( \rho c )_s) g \beta K \Delta Td/ \alpha_{\rm L} \nu$$ nationallicence Ra * : Modified Darcy-Rayleigh number, Ra D δ nationallicence Ra H : Darcy-Rayleigh number based on the melt thickness, Ra * λ nationallicence St : Stefan number, L / [c (T A−T M) ] nationallicence T : Temperature (K) nationallicence t : Time (s) nationallicence U : velocity vector (m/s) nationallicence w : Dimensionless vertical velocity component nationallicence ( x , y , z ) : Dimensionless Cartesian coordinates nationallicence Greek letters nationallicence α : Thermal diffusivity (m 2/s) nationallicence α r : Thermal diffusivity ratio, α S α L nationallicence β : Thermal expansion coefficient (K−1) nationallicence δ : Dimensionless depth, $$\sqrt {4\tau }$$ nationallicence $$\varepsilon$$ : Porosity nationallicence θ : dimensionless temperature, (T−T A )/(T A −T M ) nationallicence λ : Phase change rate nationallicence μ : Viscosity (Pas) nationallicence ρ : Density (kg / m 3) nationallicence τ : Dimensionless time, αL t/ d 2 nationallicence ζ : Similarity variable, z / δ nationallicence Subscripts nationallicence c : Critical state nationallicence e : Effective values nationallicence f : Fluid phase nationallicence L : Liquid phase nationallicence S : Solid phase nationallicence s : Solid matrix nationallicence 0 : Basic quantity nationallicence 1 : Perturbed quantity nationallicence Hong Joung ARC Center, Korea University, 136-701, Seoul, Korea aut Kim Min Department of Chemical Engineering, Cheju National University, 690-756, Cheju, Korea aut Choi Chang School of Chemical and Biological Engineering, Seoul National University, 151-744, Seoul, Korea aut Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 229-241 0169-3913 67:2<229 2007 67 11242 https://doi.org/10.1007/s11242-006-9004-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9004-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hong Joung ARC Center, Korea University, 136-701, Seoul, Korea aut NATIONALLICENCE 700 1- Kim Min Department of Chemical Engineering, Cheju National University, 690-756, Cheju, Korea aut NATIONALLICENCE 700 1- Choi Chang School of Chemical and Biological Engineering, Seoul National University, 151-744, Seoul, Korea aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/2(2007-03-01), 229-241 0169-3913 67:2<229 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer