Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation

Storesletten, L.; Rees, D. Andrew S.

doi:10.3390/fluids4020075

Cited by 30 publications

(16 citation statements)

References 30 publications

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“…Moreover, anisotropy is a characteristic of artificial porous materials like pelleting used in the chemical engineering process, fiber material used in insulating purpose and in the phase change materials on natural convection. The effect of anisotropy on thermal convection in porous media has gained prime importance in the literature and has been studied extensively 13‐19 . A detailed account on this topic can be found in the book by Nield and Bejan 20 …”

Section: Introductionmentioning

confidence: 99%

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

2020

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By adopting a perturbation method and a local thermal nonequilibrium model, nonlinear thermal convection in an anisotropic porous layer saturated by an elasticoviscous fluid is investigated. An elasticoviscous fluid is modeled by a modified Darcy-Oldroyd-B model, and the fluid and solid phase temperatures are represented using a two-field model for the heat transport equation. Anisotropy in permeability and fluid and solid thermal conductivities are considered. A cubic Landau equation is derived separately to study the stability of bifurcating solution of both stationary and oscillatory convection, and the results of linear instability theory are delineated. The boundary between stationary and oscillatory convection is demarcated by identifying codimensiontwo points in the viscoelastic parameters plane. It is found that the subcritical instability is not possible, and the linear instability analysis itself completely captures the behavior of the onset of convection. Heat transfer is obtained in terms of Nusselt number, and the effect of governing parameters on the same is discussed. The results of the Maxwell fluid are obtained as a particular case from the present study. K E Y W O R D S cubic Landau equation, heat transport, local thermal nonequilibrium, nonlinear convection, Oldroyd-B fluid, porous layer

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Section: Introductionmentioning

confidence: 99%

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

2020

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“…Linear stability was applied in the studies. New study from Storesletten and Rees [8] investigated the combination of both effects which is internal heat generation and inclination anisotropy for instability linear.…”

Section: Introductionmentioning

confidence: 99%

Stability Convection in a Couple Stress Fluid Saturated in an Anisotropic Porous Medium with Internal Heating Effect

Mokhtar

Senu

Isa

2020

ARFMTS

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Internal heating effect with stability convection in a couple stress fluid saturated in an anisotropic porous medium has been studied numerically using linear stability analysis. The presence of internal heating on couple stress fluid in an anisotropic porous medium heated from below has been verified. The momentum equation and Boussinesq approximation is used for the density variation in the porous medium. By using Chebyshev Tau method numerically, the eigenvalue problems of the perturbed state were obtained from a normal mode analysis. The effect of the Rayleigh number, internal heat source and anisotropy parameter has been shown graphically. The critical Rayleigh number also has been obtained and plotted on the system. From the result, it is found that the mechanical anisotropy parameter and internal heating effect destabilized the system while couple stress fluid and thermal anisotropy parameter help in stabilizing the system.

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“…Other works including internal heat generation in porous media with anisotropy are presented in [25,26]. Research specifically involving the effects of gravity modulation and internal heat generation in porous media are presented in [25][26][27][28]. Readers are also referred to two important books [29,30] for further review/reading.…”

Section: Introductionmentioning

confidence: 99%

Vadasz Number Effects on Convection in a Horizontal Porous Layer Subjected to Internal Heat Generation and G-Jitter

Govender

2020

Fluids

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Flow and heat transfer in a horizontal porous layer subjected to internal heat generation and g-jitter is considered for the Dirichlet thermal boundary condition. A linear stability analysis is used to determine the convection threshold in terms of the critical Rayleigh number. For the low amplitude, high frequency approximation, the results show that vibration has a stabilizing effect on the onset of convection when the porous layer is heated from below. When the porous layer is cooled from below and heated from above, the vibration has a destabilizing effect in the presence of internal heat generation. It is also demonstrated that when the top and bottoms walls are cooled and rigid/impermeable, the critical Rayleigh number is infinitely large and conduction is the only possible mode of heat transfer. The impact of increasing the Vadasz number is to stabilize the convection, in addition to reducing the transition point from synchronous to subharmonic solutions.

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Onset of Convection in an Inclined Anisotropic Porous Layer with Internal Heat Generation

Cited by 30 publications

References 30 publications

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

Nonlinear convection in an elasticoviscous fluid‐saturated anisotropic porous layer using a local thermal nonequilibrium model

Stability Convection in a Couple Stress Fluid Saturated in an Anisotropic Porous Medium with Internal Heating Effect

Vadasz Number Effects on Convection in a Horizontal Porous Layer Subjected to Internal Heat Generation and G-Jitter

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