Two-medium treatment of heat transfer in porous media: numerical results for effective properties

Quintard, Michel; Kaviany, Massoud; Whitaker, Stephen

doi:10.1016/s0309-1708(96)00024-3

Cited by 212 publications

(147 citation statements)

References 39 publications

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“…In that case two energy equations are set-up and solved, one for each phase. In models like this there is a need for exchange terms between the phases that are modelled either empirically [3] or by using constitutive equations [9,36].…”

Section: Heat Transfermentioning

confidence: 99%

Modelling heat transfer during flow through a random packed bed of spheres

et al. 2017

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Heat transfer in a random packed bed of monosized iron ore pellets is modelled with both a discrete three-dimensional system of spheres and a continuous Computational Fluid Dynamics (CFD) model. Results show a good agreement between the two models for average values over a cross section of the bed for an even temperature profiles at the inlet. The advantage with the discrete model is that it captures local effects such as decreased heat transfer in sections with low speed. The disadvantage is that it is computationally heavy for larger systems of pellets. If averaged values are sufficient, the CFD model is an attractive alternative that is easy to couple to the physics up-and downstream the packed bed. The good agreement between the discrete and continuous model furthermore indicates that the discrete model may be used also on non-Stokian flow in the transitional region between laminar and turbulent flow, as turbulent effects show little influence of the overall heat transfer rates in the continuous model.

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Section: Heat Transfermentioning

confidence: 99%

Modelling heat transfer during flow through a random packed bed of spheres

et al. 2017

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“…(1) and (2) involves posing and formally solving associated closure problems, so that the temperature deviations for both phases can be expressed in terms of the average temperatures [2,4], i.e., …”

Section: Averagingmentioning

confidence: 99%

One-Domain Approach for Heat Transfer At The Fluid-Porous Medium Inter-Region

Aguilar-Madera¹,

Valdés‐Parada²,

Goyeau³

et al. 2010

AIP Conference Proceedings

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:The modeling of transport phenomena in the zone of rapid changes between a fluid and a porous medium (i.e., the interregion) can be carried out using two distinctive approaches. The first one, generally called the one-domain approach, describes transport phenomena in the whole fluid-porous system using averaged macroscopic conservation equations including spatially dependent effective properties. These coefficients reduce to their respective constant values in the homogeneous fluid and porous regions of the system. As an alternative, the two-domain approach uses the transport equations with constant coefficients in the entire domain of each region, including the zone of drastic changes. To overcome this approximation, jump conditions are introduced but their derivation requires the knowledge of the corresponding one-domain approach model. This work deals with the derivation of the governing macroscale equations for convective heat transfer in the inter-region using a volume averaging procedure. Under a one-domain formulation, local thermal equilibrium (TE) and non-local thermal equilibrium (NTE) models are explored. In both cases, the associated closure problems are derived and solved numerically. This allows the computation of the spatial variations of the associated effective transfer properties in the inter-region. Comparisons of the temperature fields obtained with direct numerical simulations evidence that the TE model is good enough for describing the abrupt heat transfer variations in the interregion under certain conditions.

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“…where K eff,f and K eff,s are the effective conductivity tensors for the fluid and solid phases, respectively, given by Kuwahara and Nakayama (1996) [42] and Quintard et al (1997) [10], this can be accomplished for the thermal dispersion and local conduction tensors, K disp and K f,s , by making use of a unit cell subjected to periodic boundary conditions for the flow together with an imposed linear temperature gradient on the porous medium. The dispersion and conduction tensors are then obtained directly from the distributed results within the unit cell by making use of Eqs.…”

Section: Macroscopic Two-energy Equation Modelingmentioning

confidence: 99%

“…This model greatly simplifies theoretical and numerical research but the assumption of local thermal equilibrium between the fluid and the solid is inadequate for a number of practical problems [7][8][9]. As a result, in recent years more attention has been paid to the local thermal nonequilibrium model, both theoretically and numerically [10,11]. …”

mentioning

confidence: 99%

Interfacial Heat Transport in Highly Permeable Media: A Finite Volume Approach

Lemos

Saito

2008

Cellular and Porous Materials

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The transport of heat inside highly permeable media has attracted the attention of scientists and engineers due to its many engineering applications. Such applications can be found in solar energy receiver devices, heat exchangers, porous combustors, grain drying equipment, heat sink units, energy recovery systems, etc. In many of these modern engineering systems the use of cellular and metallic porous foams brings the advantages of having large specific heat transfer areas, or the interfacial transport area per unit volume is large when compared with other heat-capturing devices. More realistic modeling of transport processes in such media is then essential for the reliable design and analysis of high-efficiency engineering systems.Motivated by the wide spectrum of practical engineering applications, macroscopic transport modeling of incompressible flows in porous media has been developed over the last few decades, mostly based on the volume-average methodology for either heat [1] or mass transfer [2,3]. Classic books by Bear (1972) [4], Nield and Bejan (1992) [5] and Ingham and Pop (1998) [6], to mention a few, also document forced convection and related models for heat transport in porous media.From the point of view of energy transfer between phases, namely the cellular material phase and the working fluid, there are basically two different models commonly found in the literature: (a) a local thermal equilibrium model and (b) a two-energy equation or thermal nonequilibrium model. The first one assumes that the bulk solid temperature does not differ much from the average value of the fluid temperature; thus local thermal equilibrium between the fluid and the solid phase is assumed. This model greatly simplifies theoretical and numerical research but the assumption of local thermal equilibrium between the fluid and the solid is inadequate for a number of practical problems [7][8][9]. As a result, in recent years more attention has been paid to the local thermal nonequilibrium model, both theoretically and numerically [10,11].

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Two-medium treatment of heat transfer in porous media: numerical results for effective properties

Cited by 212 publications

References 39 publications

Modelling heat transfer during flow through a random packed bed of spheres

Modelling heat transfer during flow through a random packed bed of spheres

One-Domain Approach for Heat Transfer At The Fluid-Porous Medium Inter-Region

Interfacial Heat Transport in Highly Permeable Media: A Finite Volume Approach

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