A numerical study of natural convection in a vertical, annular, porous layer

Hickox, C. E.; Gartling, D. K.

doi:10.1016/0017-9310(85)90196-6

Cited by 37 publications

(19 citation statements)

References 8 publications

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“…For an annuli whose inner wall is heated at constant temperature and outer wall is isothermally cooled, the top and bottom being insulated (82,83,84,85), heat transfer results have been obtained for a wide range 119 of Rayleigh numbers, aspect (height to gap width) ratios, A, and radius ratios, C. Results obtained through a numerical study show that the curvature effects are significant, and completely disturb the centrosymmetrical nature found in the vertical cavity case (Figure 26). Though the effect of the Rayleigh number and the aspect ratio are qualitatively similar to what has been observed for the vertical cavity, the correlations for the average Nusselt number requires modification in order to include the influence of the curvature C.…”

Section: Vertical Porous Layersmentioning

confidence: 99%

Natural Convection in Porous Media

Bories

1987

Advances in Transport Phenomena in Porous Media

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When the temperature of the saturating fluid phase in a porous medium is not uniform, some flows induced by buoyancy effects may occur. Commonly called free or natural convective movements, these flows depend on density differences due to temperature gradients and boundary conditions. Generally speaking, convective movements which tend to homogenize the whole fluid volume where they take place have two main effects: produce a non-uniform insitu temperature distribu~ tion characterized by hot and cold zones, and increase the overall heat transfer.Due to its numerous applications in geophysics and energyrelated engineering problems, natural convection ili porous media has been receiving increased interest over the last few decades (1,2).In this review, we deal mainly with the presentation of fundamental results obtained through the ~tudy of this phenomena in dispersed saturated porous media. Beginning with the formulation of basic equations and boundary conditions, we then successively review:-first, the results concerning natural convection in homogeneous isotropic porous layers of wide lateral extent in horizontal or inclined positions, -second, the studies on natural convection in confined porous media, i.e., when the lateral extent of the layer is of the same order of magnitude so that the thickness and the lateral thermal boundary effects are taken into account, -and finally, the problems related to natural convection in more complex configurations, such as anisotropic porous layers or porous layers saturated by a fluid of non-constant properties.80

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Section: Vertical Porous Layersmentioning

confidence: 99%

Natural Convection in Porous Media

Bories

1987

Advances in Transport Phenomena in Porous Media

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“…To verify the accuracy of the numerical method, its results are compared with results presented in four other papers. The first comparison is with numerical results from Hickox and Gartling [2] and Prasad and Kulacki [3], where radius ratio R* = 1, Rayleigh number Ra = 100, Forchheimer number Fc = 0, Darcy number Da = 0, and where the aspect ratio AR ranges from 2 to 8 (shown as Table 2). Moreover, the second comparison is with experimental data of Prasad et al [4] and numerical results of Marpu [5] for radius ratio R*= 4.338, aspect ratio AR = 1, Prandtl number Pr = 7, Forchheimer number Fc = 0.003 69, Darcy number Da = 0.000 123, and Rayleigh numbers Ra in the range 2 000-6 309 (shown in Table 3).…”

Section: Resultsmentioning

confidence: 99%

“…Using finite element technique and an approximate method, Hickox and Gartling [2] analyzed the natural convection flow arising in a vertical annular space insulated at the top and bottom and subjected to uniform but different temperatures of the inside and outside vertical walls. Using a finite difference method, Prasad and Kulacki [3] have obtained heat transfer results for a wide range of Rayleigh numbers, aspect ratios and radii ratios.…”

Section: Nomenclaturementioning

confidence: 99%

Maximum density effects on natural convection in a vertical annulus filled with a non-Darcy porous medium

Char

Lee

1998

Acta Mechanica

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This article numerically studies the problem of natural convection in a porous medium saturated with cold water, under density inversion, within a vertical annulus. In modeling the flow in the porous medium the non-Darcy effects, which include the Forchheimer inertia and Brinkman viscous effects are taken into account. The governing equations are solved numerically by the finite difference method using the modified strongly implicit procedure. The effects of the inversion parameter Theta(m), radius ratio R*, aspect ratio AR, Forchheimer inertia parameter Fc/Pr, and Darcy number parameter Da on the heat transfer and fluid flow characteristics are discussed in detail. Results show that both the inversion parameter and radius ratio have a significant influence on the flow structure and heat transfer rate in the annulus. It is also found that the mean Nusselt number decreases as the Forchheimer inertia parameter or the Darcy number increases. Moreover, the results obtained here are also compared and favorably agree with numerical results and with experimental data

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“…Among these studies, a special interest has been devoted to internal buoyant flows in annular and circular cavities with either closed or open ends. Havstad and Burns (1982), Hickox and Gartling (1985), Prasad andKulacki (1984, 1985), and Prasad (1986) have analyzed the natural convection in a vertical annulus with an isothermal inner wall. The outer wall has been assumed as isothermally cooled and the top and bottom walls are insulated.…”

Section: Introductionmentioning

confidence: 99%

Buoyant Flow with Viscous Heating in a Vertical Circular Duct Filled with a Porous Medium

et al. 2007

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Combined, forced, and free flow in a vertical circular duct filled with a porous medium is investigated according to the Darcy-Boussinesq model. The effect of viscous dissipation is taken into account. It is shown that a thermal boundary condition compatible with fully developed and axisymmetric flow is either a linearly varying wall temperature in the axial direction or, only in the case of uniform velocity profile, an axial linear-exponential wall temperature change. The case of a linearly varying wall temperature corresponds to a uniform wall heat flux and includes the uniform wall temperature as a special case. A general analytical solution procedure is performed, by expressing the seepage velocity profile as a power series with respect to the radial coordinate. It is shown that, for a fixed thermal boundary condition, i.e., for a prescribed slope of the wall temperature, and for a given flow rate, there exist two solutions of the governing balance equations provided that the flow rate is lower than a maximum value. When the maximum value is reached, the dual solutions coincide. When the flow rate is higher than its maximum, no axisymmetric solutions exist.

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A numerical study of natural convection in a vertical, annular, porous layer

Cited by 37 publications

References 8 publications

Natural Convection in Porous Media

Natural Convection in Porous Media

Maximum density effects on natural convection in a vertical annulus filled with a non-Darcy porous medium

Buoyant Flow with Viscous Heating in a Vertical Circular Duct Filled with a Porous Medium

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