Rayleigh–Bénard stability of a solidifying porous medium

Mackie, Calvin; Desai, Prateen V.; Meyers, Carolyn W.

doi:10.1016/s0017-9310(98)00361-5

Cited by 10 publications

(5 citation statements)

References 8 publications

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“…Equation 2.2 is the Darcy equation combined with the Bousinessq approximation. In the previous studies (Hwang 2001;Zhang and Nguyen 1999;Karcher and Müller 1995;Mackie et al 1999) ε(ρc) f /(ρc) e is assumed to be 1, that is, the effect of heat capacity of solid matrix is neglected. However, this simplification is valid when solid matrix is composed of low heat capacity material such as metal.…”

Section: Governing Equationsmentioning

confidence: 99%

“…This kind of study is useful in understanding solidification and therefore, the related hydrodynamic stability has attracted many researchers' interest (Hwang and Choi 2004;Mackie et al 1999;Karcher and Müller 1995;Zhang and Nguyen 1999;Zhang et al 1991;Beckermann and Viskanta 1988;Weaver and Viskanta 1986;Boger and Westwater 1967). The convective motion driven by buoyancy forces in the presence of solid components plays an important role in industrial applications, such as manufacturing of composite materials and purification of metals, as well as in a wide range of systems in nature, such as seasonal freezing and melting of soil, lakes, and rivers, artificial freezing of the ground as a construction technique for supporting poor soils, insulation of underground buildings, thermal energy storage in porous media, and storage of frozen foods.…”

Section: Introductionmentioning

confidence: 99%

“…Karcher and Müller (1995) and Mackie et al (1999) investigated the Rayleigh-Bénard stability problem on solidification of porous media. Previous studies (Zhang and Nguyen 1999;Karcher and Müller 1995) employed static assumption where the temporal growth rates of velocity and temperature disturbances are assumed to be zero.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Onset of Buoyancy-driven Instability in Porous Medium Solidified from Above

2008

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When a porous melt layer saturated by liquid is solidified from above, convection often sets in due to buoyancy forces. In this study, the onset of buoyancy-driven convection during time-dependent solidification is investigated by using the similarly transformed disturbance equations. The thermal disturbance distribution of the solid phase is approximated by the WKB method and effects of various parameters on the stability condition of the melt phase are analyzed theoretically. For the limiting case of λ → 0 and finite k r , the critical conditions approach asymptotically Ra * D,c = 25.89 and a * c = 1.80. This study presenting a constant-temperature cooling model predicts greater instability and gives more unstable results than those obtained from the constant solidification rate model.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Onset of Buoyancy-driven Instability in Porous Medium Solidified from Above

2008

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“…The hydrodynamic stability associated with melting or solidification has attracted many researchers' interests (Sparrow et al 1976;Gau and Viskanta 1985;Lowell 1985;Xhang and Nguyen 1991;Mackiea et al 1999;Nield and Bejan 1999;Hwang 2001;Govender and Vadasz 2002;Hwang and Choi 2004) because solid-liquid phase-change heat transfer occurring in saturated porous media is important in solving geophysical and engineering problems. However, due to the intrinsic complexities associated with the melting of solid or solidification of liquid in the presence of a nonmelting component, such as a solid matrix or soil, hydrodynamic stability during the melting of such mixtures has not been studied so much.…”

mentioning

confidence: 99%

“…Solid/liquid phase change in liquid-saturated porous medium has received considerably less attention. Previous studies (Mackiea et al 1999;Hwang 2001) examined coupled effects on stability arising from thermal convection and solidification of a single-component liquid in a porous medium. However, in these studies the temporal growth rate of velocity and temperature disturbances are ignored under static assumption.…”

mentioning

confidence: 99%

Onset of Buoyancy-driven Instability in Porous Media Melted from Below

Hong¹,

Kim

Choi

2006

Transp Porous Med

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When a nonhomogeneous solid is melting from below, convection may be induced in a thermally-unstable melt layer. In this study, the onset of buoyancydriven 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. Nomenclaturea Dimensionless wavenumber, a 2 x + a 2 y a * Modified dimensionless wave number, aδ a H Dimensionless wave number based on the melt thickness, a * λ c Specific heat J kg · K d Arbitrary length scale (m) g Gravitational acceleration vector m s 2 H Thickness of the melt layer (m)

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Convective instability in porous media during solidification

Hwang

2001

AIChE Journal

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In this study, the convective instability in porous media during solidification is analyzed using the linear stability thcory. The governing equation in the porous media is based on the Darcy's equation. The present predictions for the onset of convection recover the results of convective instability in packed beds with through flow for large Peclet number.Solidification of porous media has its applications in engineering practices with phase change, such as materials processing, thermal energy storage, and so on. When a pure melt in porous media is solidified from above, thermal convection can be induced by an unstable density profile in the porous media under a gravitational field. Convective instability problems during solidification of a liquid have been studied extensively, while those of porous media have received less attention. Recent studies (Karcher and Miiller, 1995: Mackie et al., 1999) investigated the Rayleigh-Benard stability problem with solidification of porous media. Smith (1988) examined the onset of convection driven by the thermal gradient under the solidifying interface during directional solidification of a pure liquid. whereas the present study is concerned with that of porous media. Governing equationsThe porous media saturated with a pure liquid is solidified downward in a semi-infinite region, as shown in Figure I . The coordinate system is attached to the planar interface that is moving at the constant velocity V,,. Under the assumption that the thermophysical properties of the liquid phase and the porous material. such as heat capacity and thermal conductivity, are the same, the governing equations are given as followsFor the solid luyer For thc porous niediuwhere 7 denotes the temperature, / the time, Z thc vertical coordinate, U the velocity. and P thc pressure. N denotes the thermal diffusivity, p the viscosity, K the permeability. p the density. ,G the thermal expansion coefficient, and g the gravity acceleration. The subscript S and L represent the solid and liquid quantitics, respectively. T,, denotes the reference temperature and e, the unit vector in the Z-direction. Equation 3 is the Darcy's equation, which is undcr the Boussincsq approximation. The density change in thc liquid can induce buoyancy-driven convection. In the present study. solidification shrinkage is neglected, and the densities of the

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Rayleigh–Bénard stability of a solidifying porous medium

Cited by 10 publications

References 8 publications

Onset of Buoyancy-driven Instability in Porous Medium Solidified from Above

Onset of Buoyancy-driven Instability in Porous Medium Solidified from Above

Onset of Buoyancy-driven Instability in Porous Media Melted from Below

Convective instability in porous media during solidification

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