Darcy–Carreau Model and Nonlinear Natural Convection for Pseudoplastic and Dilatant Fluids in Porous Media

Brandão, Pedro Vayssière; Ouarzazi, M. N.

doi:10.1007/s11242-020-01523-9

Cited by 6 publications

(4 citation statements)

References 25 publications

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“…In Equation (12), σ is the ratio between the average volumetric heat capacity of the porous medium and the volumetric heat capacity of the fluid; α and χ are the average thermal diffusivity and the average thermal conductivity of the saturated porous medium, respectively.…”

Section: Governing Equationsmentioning

confidence: 99%

“…The Darcy-Bénard instability for saturating fluids with a non-Newtonian rheology has been investigated with reference to viscoelastic fluids [4][5][6], to fluids with yield-stress [7] and to purely viscous fluids [8][9][10][11][12][13][14]. In particular, Barletta and Nield [8], Alves and Barletta [9], Celli et al [10] and Petrolo et al [11] discuss the onset of the Darcy-Bénard instability in a porous medium by considering the power-law model.…”

Section: Introductionmentioning

confidence: 99%

“…A more sophisticated model, i.e. Carreau-Yasuda, is employed by Brandão and Ouarzazi [12] and by Brandão et al [13] to model purely viscous, non-Newtonian flow in porous media.…”

Section: Introductionmentioning

confidence: 99%

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Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

Brandão

Celli

Barletta

2021

Fluids

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The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non–Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid.

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Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

Brandão

Celli

Barletta

2021

Fluids

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“…Other 16 surveys relative to this area of research are provided by Straughan [2], Barletta [3]. Except The Darcy-Bénard instability for saturating fluids with a non-Newtonian rheology 21 has been investigated with reference to viscoelastic fluids [4][5][6], to fluids with yield-stress 22 [7] and to purely viscous fluids [8][9][10][11][12][13][14].…”

Section: Introduction 12mentioning

confidence: 99%

Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

Brandão¹,

Celli²,

Barletta³

2021

Preprint

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The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non-Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid.

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Darcy–Carreau–Yasuda rheological model and onset of inelastic non-Newtonian mixed convection in porous media

et al. 2021

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An extension of Carreau and Carreau–Yasuda rheological models to porous media is proposed to study the onset of mixed convection of both pseudoplastic fluids (PF) and dilatant fluids (DF) in a porous layer heated from below in the presence of a horizontal throughflow. In comparison with Newtonian fluids, three more dimensionless parameters are introduced, namely, the Darcy–Weissenberg number Wi, the power–law index n, and the Yasuda parameter a. Temporal stability analysis of the basic state showed that in the absence of a throughflow (Wi = 0), the critical Rayleigh number and the critical wavenumber at the onset of convection are the same as for Newtonian fluids, namely, Rac=4π2 and kc=π, respectively. When the throughflow is added (Wi > 0), it is found that moving transverse rolls (stationary longitudinal rolls) are the dominant mode of the instability for PF (for DF). Furthermore, depending on Wi, two regimes of instability were identified. In the weakly non-Newtonian regime (i.e., Wi<Wit≈1), a destabilizing effect is observed for PF, while the reverse occurs for DF. These effects are more intense by reducing (increasing) the index n for PF (for DF). In this regime, a significant qualitative difference is found between the Darcy–Carreau model and the power–law model. However, in the strongly non-Newtonian regime, the two models lead to similar results. A mechanical energy budget analysis is performed to understand the physical effects of the interaction between the basic throughflow and the disturbances. It is also shown that the intrinsic macroscale properties of the porous medium may play a key role in the stabilizing/destabilizing effect. Finally, a comparison is made between the present theoretical predictions and recent mixed convection experiments in a Hele–Shaw cell.

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Darcy–Carreau Model and Nonlinear Natural Convection for Pseudoplastic and Dilatant Fluids in Porous Media

Cited by 6 publications

References 25 publications

Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

Darcy–Carreau–Yasuda rheological model and onset of inelastic non-Newtonian mixed convection in porous media

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