Natural convection between two horizontal coaxial cylinders

Passerini, Arianna; Růžička, Michael; Thäter, Gudrun

doi:10.1002/zamm.200800222

Cited by 14 publications

(18 citation statements)

References 25 publications

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“…In 2004, Passerini et al [12] performed a theoretical investigation about the free convection in horizontal concentric cylinders. They showed that, for su ciently small Rayleigh numbers, a steady stable solution can be obtained.…”

Section: Literature Surveymentioning

confidence: 99%

Combination of projection and Galerkin finite element methods to solve the problem of free convection in enclosures with complex geometries

Zendehbudi

2017

Scientia Iranica

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Abstract. In the present work, a numerical method for solving the problem of free convection in enclosures with complex geometries is developed. This development is executed by the combination of projection and Galerkin nite-element methods. Ninenode (quadratic) quadrilateral elements are used to generate the grid for the eld of the problem. The results show that the convergence of this method is acceptable while there is no necessity to use upwind schemes. Increasing the numbers of nodes and decreasing the time increment yield a more accurate solution. The advantages of this numerical method are the ability to model any complex geometry and no necessity to use upwind schemes.

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Section: Literature Surveymentioning

confidence: 99%

Combination of projection and Galerkin finite element methods to solve the problem of free convection in enclosures with complex geometries

Zendehbudi

2017

Scientia Iranica

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“…This means that even the most simplified model problem for natural convection in horizontal annuli has not been solved analytically. Thus, in the domains we are considering, the analytical study of the dynamical system is still in an initial phase (see [19]). …”

Section: Mathematical Modelmentioning

confidence: 99%

“…In [19] it is shown that for sufficiently small Ra a solution can always be found for system (3)(4)(5). However, a simpler system would be easier to handle.…”

Section: Mathematical Modelmentioning

confidence: 99%

Natural convection in horizontal annuli: a lower bound for the energy

2007

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We study natural convection in the gap between two infinitely\ud long horizontal coaxial cylindrical surfaces, each of which is\ud maintained at constant temperature. If the inverse relative gap\ud width $\cA$ is large,\ud relevant steady convective flow and considerable heat transfer\ud are observed, even for extremely small Rayleigh numbers $\Ra$. A lower\ud bound for the norm of the velocity and of the temperature is\ud rigorously found by studying an approximation problem, which is a\ud good model in the parameter range where steady stable flow\ud occurs. The lower bound depends on $\cA$ only, and is an\ud increasing function of $\cA$. This means that the bound can be\ud arbitrarily increased via the geometry only - no matter how small\ud the temperature difference is, and independently of the Prandtl\ud number $\Pr$

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“…In the geometry given here, some theoretical properties of Boussinesq's system can be found in Ferrario et al (2010) and Passerini et al (2009). On the other hand, a comprehensive review of the available experimental data and numerical results for heat transfer in a horizontal circular annulus has been presented by Teerstra and Yovanovich (1998).…”

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confidence: 92%

“…In the light of Kuehn and Goldstein (1976), Passerini et al (2009) and Powe et al (1969) what should be expected for small Ra and any A is a steady unicellular flow (see, e.g. Fig.…”

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confidence: 95%

Natural convection in horizontal annuli: evaluation of the error for two approximations

2011

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We consider convection inside annuli, driven by a uniform temperature gap on the boundaries and gravitation as outer force. It takes place for any Rayleigh number while steady convective motions are observed only for small ones (but any Prandtl number and gap width). We provide estimates for the relative error of two popular approximations to the full Navier–Stokes–Fourier equations. For this we propose a new method. In particular we have to derive a lower bound for the norm of the velocity and the temperature both for steady nonlinear coupled and decoupled approximations in two space dimensions

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Natural convection between two horizontal coaxial cylinders

Cited by 14 publications

References 25 publications

Combination of projection and Galerkin finite element methods to solve the problem of free convection in enclosures with complex geometries

Combination of projection and Galerkin finite element methods to solve the problem of free convection in enclosures with complex geometries

Natural convection in horizontal annuli: a lower bound for the energy

Natural convection in horizontal annuli: evaluation of the error for two approximations

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