An Analytical Study on Natural Convection in Isotropic and Anisotropic Porous Channels

Nilsen, Trygve; Storesletten, L.

doi:10.1115/1.2910390

Cited by 87 publications

(73 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Haugen and Tyvand [9] gave a mathematical analysis to confirm that only axisymmetric mode of convection is prevalent in slendercylinder limit for perfectly heat-conducting side wall. The smooth relation between Ra c and a was found by Nilsen and Storesletten [10] for thermal convection in a twodimensional box with conducting walls and also verified by Rees and Lage [11] for natural convection in a vertical porous insulation layer. The case at Bi=10 4 also presents a nearly smooth relation between Ra c and a because large Bi corresponding to perfectly heat-conducting case.…”

Section: Resultsmentioning

confidence: 70%

“…The eigenvalue problem for temperature perturbation composed of (18), (19), (10) and (22) is solved by using separation of variables. We assume two eigen-functions corresponding to the two Helmholtz equations in the form …”

Section: Methods Of Solutionmentioning

confidence: 99%

“…Heat conduction at the lateral walls usually takes away the heat and thus delays the onset of convection, leading to critical Rayleigh number Ra=4 2 . The analytical approaches con-firmed this argument, the readers are referred to Zebib [4], Kubitschek and Weidman [8], Haugen and Tyvand [9], Nilsen and Storesletten [10]. Incorporated with the curl of Darcy's law, the first boundary condition in (10) …”

Section: Problem Formulationmentioning

confidence: 99%

See 2 more Smart Citations

Onset of thermal convection of a fluid saturated porous medium in a vertical cylinder with mixed heating on lateral wall

Liu¹,

C²,

Chang³

2016

Fifth International Conference on Advances in Applied Science and Environmental Technology- ASET 2016

View full text Add to dashboard Cite

Abstract-In this paper we examine the thermal-convective stability of a fluid-saturated porous medium filled within a vertical cylindrical container heated from below. The upper and lower surfaces of the cylinder are impermeable and are kept at constant but different temperatures. The lateral sidewall is impermeable and subject to mixed heating which is characterized by the Biot number. The threshold of Rayleigh number, above which the small disturbance becomes unstable, is sought from the characteristic equation. Our results show that the preferred mode at onset is always axisymmetric for all aspect ratios when Biot number approaches infinitely, and it becomes non-monotonic variation with respect to aspect ratio when Biot number is finite.

show abstract

Section: Resultsmentioning

confidence: 70%

Section: Methods Of Solutionmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

See 1 more Smart Citation

Onset of thermal convection of a fluid saturated porous medium in a vertical cylinder with mixed heating on lateral wall

Liu¹,

C²,

Chang³

2016

Fifth International Conference on Advances in Applied Science and Environmental Technology- ASET 2016

View full text Add to dashboard Cite

show abstract

“…All the phenomena mentioned above are also realized in this problem, but our study is motivated mainly by nontrivial facts observed here and previously not yet 20 encountered in the problems of mathematical physics. This is the result of the action of cosymmetry.…”

Section: Introductionmentioning

confidence: 99%

Selection of steady regimes of a one-parameter family in the problem of plane convective flow through a porous medium

Говорухин¹,

Shevchenko²

2013

Fluid Dyn

View full text Add to dashboard Cite

We study convection in a two-dimensional container of porous material saturated with fluid and heated from below. This problem belongs to the class of dynamical systems with nontrivial cosymmetry. The cosymmetry gives rise to a hidden parameter in the system and continuous families of infinitely many equilibria, and leads to non-trivial bifurcations. In this article we present our numerical studies that demonstrate nonlinear phenomena resulting from the existence of cosymmetry. We give a comprehensive picture of different bifurcations which occur in cosymmetric dynamical systems and in the convection problem. It includes internal and external (as an invariant set) bifurcations of one-parameter families of equilibria, as well as bifurcations leading to periodic, quasiperiodic and chaotic behaviour. The existence of infinite number of stable steady-state regimes begs the important question as to which of them can realize in physical experiments. In the paper, this question (known as the selection problem) is studied in detail. In particular, we show that the selection scenarios strongly depend on the initial temperature distribution of the fluid. method, and numerical methods used to analyse cosymmetric systems are also described.

show abstract

“…Furthermore, the condition of a finite lateral width of the channel was analysed as well. The case of a horizontal porous channel with rectangular cross-section was studied by Sutton (1970), Beck (1972), and further explored by Nilsen and Storesletten (1990).…”

Section: Introductionmentioning

confidence: 99%

Convective Instability in a Horizontal Porous Channel with Permeable and Conducting Side Boundaries

2013

View full text Add to dashboard Cite

The stability analysis of the motionless state of a horizontal porous channel with rectangular cross-section and saturated by a fluid is developed. The heating from below is modelled by a uniform flux, while the top wall is assumed to be isothermal. The side boundaries are considered as permeable and perfectly conducting. The linear stability of the basic state is studied for the normal mode perturbations. The principle of exchange of stabilities is proved, so that only stationary normal modes need to be considered in the stability analysis. The eigenvalue problem for the neutral stability condition is solved analytically, and a closed-form dispersion relation is obtained for the neutral stability. The Darcy-Rayleigh number is expressed as an implicit function of the longitudinal wave number and of the aspect ratio. The critical wave number and the critical Darcy-Rayleigh number are evaluated for different aspect ratios. The preferred modes under critical conditions are detected. It is found that the selected patterns of instability at the critical Rayleigh number are two-dimensional, for slender or square cross-sections of the channel. On the other hand, instability is three dimensional when the critical width-to-height ratio, 1.350517, is exceeded. Eventually, the effects of a finite longitudinal length of the channel are discussed.

show abstract

An Analytical Study on Natural Convection in Isotropic and Anisotropic Porous Channels

Cited by 87 publications

References 0 publications

Onset of thermal convection of a fluid saturated porous medium in a vertical cylinder with mixed heating on lateral wall

Onset of thermal convection of a fluid saturated porous medium in a vertical cylinder with mixed heating on lateral wall

Selection of steady regimes of a one-parameter family in the problem of plane convective flow through a porous medium

Convective Instability in a Horizontal Porous Channel with Permeable and Conducting Side Boundaries

Contact Info

Product

Resources

About