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...
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44 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.
33 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...
6 citations
TL;DR: In this paper , the authors presented the numerical analysis of exergy transfer and irreversibility through the discrete filling of high-porosity aluminum metal foams inside the horizontal pipe.
Abstract:
Purpose
This study aims to present the numerical analysis of exergy transfer and irreversibility through the discrete filling of high-porosity aluminum metal foams inside the horizontal pipe.
Design/methodology/approach
In this study, the heater is embedded on the pipe’s circumference and is assigned with known heat input. To enhance the heat transfer, metal foam of 10 pores per inch with porosity 0.95 is filled into the pipe. In filling, two kinds of arrangements are made, in the first arrangement, the metal foam is filled adjacent to the inner wall of the pipe [Model (1)–(3)], and in the second arrangement, the foam is located at the center of the pipe [Models (4)–(6)]. So, six different models are examined in this research for a fluid velocity ranging from 0.7 to7 m/s under turbulent flow conditions. Darcy Extended Forchheimer is combined with local thermal non-equilibrium models for forecasting the flow and heat transfer features via metal foams.
Findings
The numerical methodology implemented in this study is confirmed by comparing the outcomes with the experimental outcomes accessible in the literature and found a fairly good agreement between them. The application of the second law of thermodynamics via metal foams is the novelty of current investigation. The evaluation of thermodynamic performance includes the parameters such as mean exergy-based Nusselt number (Nue), rate of irreversibility, irreversibility distribution ratio (IDR), merit function (MF) and non-dimensional exergy destruction (I*). In all the phases, Models (1)–(3) exhibit better performance than Models (4)–(6).
Practical implications
The present study helps to enhance the heat transfer performance with the introduction of metal foams and reveals the importance of available energy (exergy) in the system which helps in arriving at optimum design criteria for the thermal system.
Originality/value
The uniqueness of this study is to analyze the impact of discrete metal foam filling on exergy and irreversibility in a pipe under turbulent flow conditions.
References
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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.
2,529 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.
681 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.
327 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
248 citations
TL;DR: In this paper, a numerical and experimental study of natural convection in a vertical rectangular fluid enclosure that is partially filled with a fluid-saturated porous medium is reported. But the authors did not consider the effect of the porous layer geometry on the degree of penetration of fluid into the medium.
Abstract: A numerical and experimental study is reported of natural convection in a vertical rectangular fluid enclosure that is partially filled with a fluid-saturated porous medium. Velocities, stresses, temperatures, and heat fluxes are assumed to be continuous across the fluid/porous-medium interface, and the conservation equations for the fluid and the porous regions are combined into a single set of equations for numerical solution. Thermocouples as well as a Mach-Zehnder interferometer are used to measure temperature distributions and infer fluid flow patterns within the fluid and the porous medium. For various test cells, porous-layer configurations and fluid-solid combinations, the model predictions show excellent agreement with the experimental measurements. It is found that the intensity of natural convection is always much stronger in the fluid regions, while the amount of fluid penetrating into the porous medium increases with increasing Darcy and Rayleigh numbers. The degree of penetration of fluid into the porous medium depends strongly on the porous-layer geometry and is less for a horizontal porous layer occupying the lower half of the test cell. If penetration takes place, the flow patterns in the fluid regions are significantly altered and the streamlines show cusps at the fluid/porous-medium interfaces. For a high effective-thermal-conductivity porous medium, natural convection in the medium is suppressed, while the isotherms bend sharply at the fluid/porous-medium interface.
166 citations