On the effect of porous thick horizontal partial partition attached to one of the active walls of a differentially heated square cavity
01 May 1994-International Journal of Numerical Methods for Heat & Fluid Flow (MCB UP Ltd)-Vol. 4, Iss: 5, pp 399-411
TL;DR: In this article, the effect of a horizontal partial porous partition on heat transfer and flow structure in a differentially heated square cavity is investigated, where the fluid flow is assumed to be governed by Navier-Stokes equations and fluid saturated porous media is governed by Darcy's equations.
Abstract: The effect of a horizontal partial porous partition on heat transfer and flow structure in a differentially heated square cavity is investigated. While the fluid flow is assumed to be governed by Navier—Stokes equations, fluid saturated porous media is assumed to be governed by Darcy’s equations. Standard Galerkin method of finite element formulation is applied for discretization of the system of equations. The non‐linearities in the discretized equations are treated with Newton‐Raphson scheme. The code developed is tested for validation for modified Rayleigh number Ra up to 400. The code is then applied to a differentially heated square cavity with a horizontal partial porous partition. While the thickness of the porous partition is found to have appreciable effect on heat transfer and flow field, width of the porous partition is found to have insignificant bearing on heat transfer except when the partition is very small and compatible to the thickness of the boundary layer developed. During the experime...
...read more
Citations
More filters
43 citations
TL;DR: In this article, a new lattice Boltzmann (LB) approach was developed to overcome the difficulty of conjugate problems on fluid-porous interfaces, which is validated by three benchmark tests.
Abstract: Conjugate natural convection heat transfer in an open-ended square cavity, which is partially filled with porous media, is a useful research prototype to deepen our insight into many important practical applications, such as solar energy collectors. But surprising, until now there is no open literature on it. In addition, for traditional numerical approaches, it is a great challenge to model conjugate problems on fluid-porous interfaces. In the present work, firstly we develop a new lattice Boltzmann (LB) approach to overcome such difficulty. The present LB model is validated by three benchmark tests. With the aid of this LB approach, we investigate the effects of thickness of porous layer, fluid-to-porous thermal conductivity ratio and permeability of porous layer on conjugate natural convection heat transfer in an open-ended porous-partially-filled square cavity, for the first time. It is found that these factors all influence the patterns of flow field and temperature field significantly. Especially, there exist some critical values. A small offset from them will cause a substantial change of heat and mass transfer. Sometimes the change trends are completely reversed. The present results may provide useful theoretical guides for the relevant practical applications.
22 citations
TL;DR: In this article, the authors provided a numerical study of conjugate heat transfer by mixed convection and conduction in a lid-driven enclosure with thick vertical porous layer, and the effect of the relevant parameters: Richardson number (Ri=0.1, 1, 10, 100) and thermal conductivity ratio (Rk = 0.
Abstract: Purpose – The purpose of this paper is to provide a numerical study of conjugate heat transfer by mixed convection and conduction in a lid-driven enclosure with thick vertical porous layer. The effect of the relevant parameters: Richardson number (Ri=0.1, 1, 10) and thermal conductivity ratio (Rk=0.1, 1, 10, 100) are investigated. Design/methodology/approach – The studied system is a two dimensional lid-driven enclosure with thick vertical porous layer. The left vertical wall of the enclosure is allowed to move in its own plane at a constant velocity. The enclosure is heated from the right vertical wall isothermally. The left and the right vertical walls are isothermal but temperature of the outside of the right vertical wall is higher than that of the left vertical wall. Horizontal walls are insulated. The governing equations are solved by finite volume method and the SIMPLE algorithm. Findings – From the finding results, it is observed that: for the two studied cases, heat transfer rate along the hot wa...
4 citations
References
More filters
TL;DR: In this paper, the authors used mesh refnement and extrapolation to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls.
Abstract: Details are given of the computational method used to obtain an accurate solution of the equations describing two-dimensional natural convection in a square cavity with differentially heated side walls. Second-order, central difference approximations were used. Mesh refnement and extrapolation led to solutions for 103⩽Ra⩽10 6 which are believed to be accurate to better than 1 per cent at the highest Rayleigh number and down to one-tenth of that at the lowest value.
2,342 citations
TL;DR: In this paper, the authors discuss the mathematical formulation of convective heat transfer in geothermal systems and the prediction of reservoir behavior under production can be obtained by idealizing it as a saturated porous medium.
Abstract: Publisher Summary This chapter discusses the mathematical formulation of the problems of convective heat transfer in geothermal systems. Geothermal reservoirs may have numerous near-vertical faults and relatively impermeable intrusive interspersed in the aquifers. Both theoretical and experimental investigations of heat transfer in geothermal systems are reviewed. A qualitative understanding of the large-scale convection processes in a geothermal reservoir and the prediction of reservoir behavior under production can be obtained by idealizing it as a saturated porous medium. The identification of a viable geothermal reservoir and the estimation of its capacity remain major problems in the utilization of geothermal resources. Thermal anomalies in geothermal areas can be detected by surface manifestations, aerial infrared surveys, geochemical analyses, or exploratory drillings. Many of the analyses are applicable to a wide range of engineering problems whenever they can be idealized as convection in a porous medium. These include the problems of the secondary recovery of oil by thermal methods, the use of fibrous materials for thermal insulations, the design of aquifers as an energy storage system, and the deposition of mineral ore in the subsurface formation. Results from short-duration well testing are used to determine reservoir characteristics.
663 citations
TL;DR: In this paper, the Darcy-Rayleigh number R and the cavity aspect ratio A were used to obtain the approximate solutions for shallow cavities, A → 0, by using matched asymptotic expansions up to O(A6R4).
Abstract: Convection in a porous cavity driven by heating in the horizontal is analysed by a number of different techniques which yield a fairly complete description of the two-dimensional solutions. The solutions are governed by two dimensionless parameters: the Darcy-Rayleigh number R and the cavity aspect ratio A. We first find solutions valid for shallow cavities, A → 0, by using matched asymptotic expansions. These solutions are given up to O(A6R4). For A fixed, we find regular expansions in R by semi-numerical techniques, up to O(R30) in some cases. Series-improvement techniques then enable us to cover the range 0 ≤ R ≤ ∞. A limited result regarding bifurcations is noted. Finally, for R → ∞ with A fixed, we propose a self-consistent boundary-layer theory which extends previous approximate work. The results obtained by these different methods of solution are in good agreement with each other and with experiments.
313 citations
TL;DR: In this paper, a modelisation of l'ecoulement dans la couche poreuse a l'aide de l'equation de Darcy et endue par Brinkman et Forchheimer is presented.
Abstract: Etude numerique et experimentale. Modelisation de l'ecoulement dans la couche poreuse a l'aide de l'equation de Darcy etendue par Brinkman et Forchheimer. Verification experimentale sur des ecoulements d'eau et de glycerine dans un milieu constitue de billes de verre
228 citations
TL;DR: In this paper, numerical methods are used to solve the field equations for heat transfer in a porous medium filled with gas and bounded by plane rectangular surfaces at different temperatures, and the relative increases in heat transfer rate, corresponding to natural convection, are obtained as functions of 3-dimensional parameters: the Darcy number Da, the Rayleigh number Ra and a geometric aspect ratio L/D.
Abstract: Numerical methods are used to solve the field equations for heat transfer in a porous medium filled with gas and bounded by plane rectangular surfaces at different temperatures. The results are presented in terms of theoretical streamlines and isotherms. From these the relative increases in heat transfer rate, corresponding to natural convection, are obtained as functions of 3- dimensionless parameters: the Darcy number Da, the Rayleigh number Ra, and a geometric aspect ratio L/D. A possible correlation using the lumped parameter Da Ra is proposed for Da Ra greater than about 40. (33 refs.)
152 citations