Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review

Al-Sumaily, Gazy F.; Ezzi, Amged Al; Dhahad, Hayder A.; Thompson, Mark C.; Yusaf, Talal

doi:10.3390/en14238114

Cited by 13 publications

(7 citation statements)

References 58 publications

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“…The LTE assumption is checked using difference in the average temperatures of solid and fluid phases, which is calculated by using the correlation [7,51,52]…”

Section: T D T Da Amentioning

confidence: 99%

Flow Characterization in Triply-Periodic-Minimal-Surface (TPMS) based Porous Geometries: Part 2 – Heat Transfer

Rathore

Mehta

Kumar

et al. 2023

Preprint

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A complex heat transfer takes place between the solid matrix and the fluid within its pores and generally two types of assumptions are widely used for macro-scale modelling of heat transfer: local thermal equilibrium (LTE) when the solid and fluid phases are at the same temperature, and local thermal non-equilibrium (LTNE) when the solid and fluid phases are at different temperatures. A direct numerical simulation has been performed for heat transfer in Triply-Periodic-Minimal-Surface (TPMS) lattices, with identical void fraction and unit-cell size, but different geometrical shape, namely Diamond, I-WP, Primitive, and Gyroid. Further, each lattice derived into three different types of porous structures by designing second sub-volume as solid (Type 1), fluid (Type 2), and microporous zones (Type 3). The heat transfer in the hydrodynamically and thermally developed flow in a square mini-channel filled with these porous inserts for a range of Reynolds number \(0.01<Re<100\) and \(Pr=7\) is investigated. The temperature distributions, solid and fluid Nusselt numbers on the external walls and also heat transfer coefficient (pore-scale) in the internal walls, and quantitative departure from local thermal equilibrium (LTE) assumption for twelve different porous media are compared, and the effect of porous morphology, effective porosity, and flow rate on them are examined. Out of twelve porous media, the maximum and minimum effective Nusselt number on the external walls are obtained for Primitive lattice of Type 3 and Type 2 as 407.7 and 6.2, respectively. Similarly, pore-scale Nusselt number (on the internal walls) has maximum and minimum lattice of Type 1 and Type 3 as 64.2 and 7.6, respectively. As a general observation, the percentage deviation from LTE assumption is found to be maximum for Type 1 and 3 lattices, and minimum for Type 2 lattices throughout the range of flow rate. Primitive lattice with Type 1 treatment shows maximum deviation from LTE assumption, whereas Gyroid lattice of Type 2 treatment shows the minimum deviation.

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“…The LTE assumption is checked using difference in the average temperatures of solid and fluid phases, which is calculated by using the correlation [7,51,52]…”

Section: T D T Da Amentioning

confidence: 99%

Flow Characterization in Triply-Periodic-Minimal-Surface (TPMS) based Porous Geometries: Part 2 – Heat Transfer

Rathore

Mehta

Kumar

et al. 2023

Preprint

View full text Add to dashboard Cite

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“…The numerical solutions proposed for the eigenvalue problem Eqs (17) are based on the two combined procedures carried out between the Runge-Kutta solver and the finding-root algorithm of the shooting method. To apply both of them, we need to switch Eqs (17) into an initial value problem by providing other boundary conditions to Eq. (17d),…”

Section: Numerical Solutionsmentioning

confidence: 99%

“…However, the feature of the LTE is not always true as we can encounter in some cases a disparity in the thermal conductivity or/and a weakness in the heat transfer coefficient, which can yield a relaxation of the local thermal equilibrium regime. From a practical standpoint, the local thermal non-equilibrium (LTNE) model has a vital effect on the cooling process of countless engineering devices [10,17]. On the other hand, the approach of the LTNE can highlight difficulties in the modelling of thermal boundaries, especially in the case of isoflux [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Effects of Neumann and Robin boundaries on the thermal instability

Lagziri

Fakiri

Bouardi

2023

IRASE

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The thermo convective instability of the Darcy-Benard problem (DB) using Robin (third-kind) thermal conditions is investigated here. We consider a viscous Newtonian fluid saturating a porous layer in which the layer is sandwiched between two impermeable boundaries. The upper and the lower walls are modelled in the form of the Neumann (second-kind) and the Robin (third-kind) thermal conditions, respectively. The difference in the temperature distribution between both phases allows the lack of a local thermal equilibrium model to be present. As a consequence, the third kind of thermal condition brings about one extra dimensionless parameter of the Biot number to the usual one of the inter-heat transfer coefficient and the thermal conductivity ratio. The normal modes method adopted in a linear stability analysis gives rise to perturbed governing equations. The eigenvalue problem is handled numerically as a result of the perturbed governing equations leading to the marginal stability condition.

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“…Generally, the accuracy of the LTNE model is considered higher than the LTE model. However, when the effect of heat convection is powerful enough, the temperature difference between the solid and fluid phases can be ignored, and the LTE model is considered quick and accurate [27]. From Li's study, which is based on the LTNE model [14], fluid and solid temperatures are almost equal in the bristle pack, and the temperature fields of the fluid and solid phases are very similar.…”

Section: Numerical Simulation Of the Cfd Modelmentioning

confidence: 99%

Temperature Field and Performance Analysis of Brush Seals Based on FEA-CFD and the Porous Medium of Anisotropic Heat Transfer Models

Song,

Liu,

Sun

et al. 2023

Energies

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A brush seal is a type of contact sealing technology that generates a great amount of heat during operations. The heat can affect the seal’s performance and lifespan. To study the brush seals’ temperature distribution, a new model considering the anisotropic heat transfer effect is established in this paper. The friction heat effect at the bristles’ tip is studied. The temperature field and leakage rates are obtained by using combined finite element analysis (FEA)-computational fluid dynamics (CFD) analysis and the anisotropic heat transfer theory. The influence of operating and structural parameters on the temperature field and the sealing properties of the brush seal are investigated. It is shown that the value of the rotation rate and the interference can cause the temperature of the brush seal to increase. The pressure difference enhances the convective heat transfer from the brush seals. While the temperature at the bristles’ tip increases, the radial average temperature of the bristles decreases significantly. In the case of a small pressure difference, the fence’s height can increase the windward area, leading to stiff bristles and resulting in a temperature increase at the bristles’ tip; however, the effective flow area increases, resulting in an acceleration of the radial temperature’s decrease. To summarize, the porous medium model of anisotropic heat transfer provides a new method for studying brush seals, and it can reflect the temperature distribution and leakage performance of brush seals.

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Legitimacy of the Local Thermal Equilibrium Hypothesis in Porous Media: A Comprehensive Review

Cited by 13 publications

References 58 publications

Flow Characterization in Triply-Periodic-Minimal-Surface (TPMS) based Porous Geometries: Part 2 – Heat Transfer

Flow Characterization in Triply-Periodic-Minimal-Surface (TPMS) based Porous Geometries: Part 2 – Heat Transfer

Effects of Neumann and Robin boundaries on the thermal instability

Temperature Field and Performance Analysis of Brush Seals Based on FEA-CFD and the Porous Medium of Anisotropic Heat Transfer Models

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