Journal ArticleDOI
Onset of thermal convection in a vertical porous cylinder with conducting wall
Kjetil B. Haugen,Peder A. Tyvand +1 more
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In this article, the onset of Rayleigh-Benard convection in a finite circular porous cylinder with vertical axis is investigated analytically, where the cylinder is heated from below, and its top and bottom are assumed impermeable and perfectly heat-conducting.Abstract:
The onset of Rayleigh–Benard convection in a finite circular porous cylinder with vertical axis is investigated analytically. The cylinder is heated from below, and its top and bottom are assumed impermeable and perfectly heat-conducting. The impermeable sidewall of the cylinder is assumed to be heat-conducting so that the temperature perturbation there is zero. The eigenvalue problem is split into two different Helmholtz equations. The resulting eigenmode is expressed in terms of Bessel functions. The preferred mode at the onset of convection is found to be axisymmetric. The critical Rayleigh number is a smooth function of the aspect ratio of the cylinder, in contrast to the standard case of an insulating sidewall.read more
Citations
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Ritz solution of the Helmholtz equation in a stadium-shaped domain with zero normal derivatives – applications to fluid sloshing and thermo-convective stability
TL;DR: In this paper, the eigenvalues and eigenfunctions of the Helmholtz equation with Neumann conditions were obtained for the stadium-shaped domain using the variational Ritz method.
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Onset of Convection in a Porous Rectangle with Buoyancy Along an Open Sidewall
Heidi S. Nygård,Peder A. Tyvand +1 more
TL;DR: In this article, the onset of thermal convection in a two-dimensional porous box is investigated analytically, where one of the two lateral boundaries is in contact with a hydrostatic reservoir, where the saturating fluid can flow freely in and out.
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Onset of Convection in a Triangular Porous Prism with Robin-Type Thermal Wall Condition
TL;DR: In this paper, the authors investigated a peculiar case of thermal convection in a vertical porous prism with impermeable and partially conducting walls, which results in a non-normal-mode behavior in the horizontal cross-sectional plane.
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Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries
TL;DR: In this article, the onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically, and the critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse.
Journal ArticleDOI
Eddy Heat Conduction and Nonlinear Stability of a Darcy Lapwood System Analysed by the Finite Spectral Method
TL;DR: A finite Fourier transform is used to perform both linear and nonlinear stability analyses of a Darcy-Lapwood system of convective rolls, producing an eddy heat conduction coefficient where a Nu-RaL relationship is found.
References
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Book
Convection in Porous Media
Donald A. Nield,Adrian Bejan +1 more
TL;DR: In this paper, an introduction to convection in porous media assumes the reader is familiar with basic fluid mechanics and heat transfer, going on to cover insulation of buildings, energy storage and recovery, geothermal reservoirs, nuclear waste disposal, chemical reactor engineering and the storage of heat-generating materials like grain and coal.
Journal ArticleDOI
Convection of a fluid in a porous medium
TL;DR: In this article, it was shown that under certain conditions convective flow may occur in fluid which permeates a porous stratum and is subject to a vertical temperature gradient, on the assumption that the flow obeys Darcy's law.
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Convection Currents in a Porous Medium
C. W. Horton,F. T. Rogers +1 more
TL;DR: In this paper, it was shown that the minimum temperature gradient for which convection can occur is approximately 4π2h2μ/kgρ0α D2, where h2 is the thermal diffusivity, g is the acceleration of gravity, μ is the viscosity, k is the permeability, α is the coefficient of cubical expansion, ρ 0 is the density at zero temperature, and D is the thickness of the layer; this exceeds the limiting gradient found by Rayleigh for a simple fluid by a factor of 16D2/27π2
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Onset of Thermohaline Convection in a Porous Medium
TL;DR: In this article, the problem of the onset of convection, induced by buoyancy effects resulting from vertical thermal and solute concentration gradients, in a horizontal layer of a saturated porous medium, is treated by linear perturbation analysis.