Solid-Liquid Phase Change in Porous Media: Solution by Boundary Integral Method

Purpose The purpose of this study is to investigate the applicability of volume average which is extensively used for analyzing the heat and fluid flow (both for single-phase and solid/liquid-phase change) in a closed cell porous medium numerically. Design/methodology/approach Heat conduction equations for the solid frame and fluid (or phase change material) are solved for pore scale and volume average approaches. The study mainly focuses on the effect of porosity and the number of porous media unit cell on the agreement between the results of the pore scale and volume average approaches. Findings It is observed for the lowest porosity values such as 0.3 and the number of porous media unit cell as 4 in heat transfer direction, the results between two approaches may be questionable for the single-phase fluid. By increasing the number of porous media unit cell in heat transfer direction, the agreement between two approaches becomes better. In general, for high porosity values (such as 0.9) the agreement between the results of two approaches is in the acceptable range both for single-phase and solid/liquid-phase change. Two charts on the applicability of volume average method for single-phase and solid/liquid-phase change are presented. Originality/value The authors’ literature survey shows that it is the first time the applicability of volume average which is extensively used for analyzing the heat and fluid flow in a closed cell porous medium is investigated numerically.

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Boundary Integral Method for Porous Media

Boundary Element Methods ◽

10.1007/978-3-662-11270-0_21 ◽

1981 ◽

pp. 325-334 ◽

Cited By ~ 8

Author(s):

M. Predeleanu

Keyword(s):

Porous Media ◽

Integral Method ◽

Boundary Integral ◽

Boundary Integral Method

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A boundary integral method for contaminant transport in two adjacent porous media

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000006214 ◽

1989 ◽

Vol 30 (3) ◽

pp. 251-267 ◽

Cited By ~ 3

Author(s):

K. A. Landman

Keyword(s):

Integral Equation ◽

Porous Media ◽

Contaminant Transport ◽

Integral Method ◽

Boundary Integral ◽

Boundary Integral Method ◽

Contaminant Concentration ◽

Two Dimensional ◽

Initial Concentration ◽

Media Systems

AbstractThe problem of transient two-dimensional transport by diffusion and advection of a decaying contaminant in two adjacent porous media is solved using a boundary-integral method. The method requires the construction of appropriate Green's functions. Application of Green's theorem in the plane then yields representations for the contaminant concentration in both regions in terms of an integral of the initial concentration over the region's interior and integrals along the boundaries of known quantities and the unknown interfacial flux between the two adjacent media. This flux is given by a first-kind integral equation, which can be solved numerically by a discretisation technique. Examples of contaminant transport in fractured porous media systems are presented.

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