Entropy Generation During Natural Convection in a Porous Cavity: Effect of Thermal Boundary Conditions
02 Aug 2012-Numerical Heat Transfer Part A-applications (Taylor & Francis Group)-Vol. 62, Iss: 4, pp 336-364
TL;DR: In this article, the authors investigated the effect of different boundary conditions on entropy generation, and showed that the entropy generation rates are reduced in sinusoidal heating (case 2) when compared to that for uniform heating with a penalty on thermal mixing, and that there exists an intermediate Da for optimal values of entropy generation.
Abstract: Entropy generation plays a significant role in the overall efficiency of a given system, and a judicious choice of optimal boundary conditions can be made based on a knowledge of entropy generation. Five different boundary conditions are considered and their effect of the permeability of the porous medium, heat transfer regime (conduction and convection) on entropy generation due to heat transfer, and fluid friction irreversibilities are investigated in detail for molten metals (Pr = 0.026) and aqueous solutions (Pr = 10), with Darcy numbers (Da) between 10−5–10−3 and at a representative high Rayleigh number, Ra = 5 × 105. It is observed that the entropy generation rates are reduced in sinusoidal heating (case 2) when compared to that for uniform heating (case 1), with a penalty on thermal mixing. Finally, the analysis of total entropy generation due to variation in Da and thermal mixing and temperature uniformity indicates that, there exists an intermediate Da for optimal values of entropy generation, th...
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TL;DR: In this paper, a finite volume analysis is performed to investigate the effects of uniform heating of the bottom wall on natural convection in an isosceles triangular attic space filled with saturated porous medium.
Abstract: A finite volume analysis is performed to investigate the effects of uniform heating of the bottom wall on natural convection in an isosceles triangular attic space filled with saturated porous medium. The simulations are carried out over a wide range of parameters of Darcy number Da (10−6 ≤ Da ≤ 10−2), Rayleigh number Ra (101 ≤ Ra ≤ 108), and attic angle θ (10° ≤ θ ≤ 45°). Numerical results are presented in terms of stream functions, isotherms, velocity profiles, as well as local and average Nusselt numbers. The flow and heat transfer in the attic space are solely determined by the combined parameter DaRa when Da 10−4. When DaRa is smaller than a certain value (∼10), the heat transfer in the attic space is conduction-dominated and a simplified model is proposed to calculate the local and average Nusselt numbers. The analytical solutions agree well with the numerical simulations, especially when the attic angle is small. As DaRa in...
18 citations
TL;DR: In this article, entropy generation due to laminarnatural convection in a square inclined cavity is investigated by numerically solving the dimensionless mass, momentum and energy balance equations.
Abstract: The investigation of entropy generation of a system can provide very important information about the efficiency of a system, and can play a significant role in optimizing the conditions of the system. In the present study, Entropy generation due to laminarnatural convection in a square inclined cavity is investigated by numerically solving the dimensionless mass, momentum and energy balance equations. The cavity is bounded by two horizontal adiabatic walls and two vertical walls that are at different constant temperatures of which left wall is hot and right wall is cold. Five cases has been considered for which the inclination angles are 0°,15°,30°,45°and 60°.For each of the cases, convection and entropy generation characteristics have been described and analyzed in terms of distribution of isothermal lines, stream function, local entropy generation due to heat transfer and fluid friction and local Bejan number .It is found that with the increase of Rayleigh number, the total entropy generation due to fluid friction as well as total entropy generation increases and average Bejan number decreases. Also with the increase of inclination angle the total entropy generation due to fluid friction increases but total entropy generation due to heat transfer and average Bejan number decreases. The present results are compared with the previous reported solutions and excellent agreement is observed. The study is performed for Rayleigh number range, 10 3 5 , with airreversibility ratio of 10 -4 and Prandtl number0.71.
17 citations
TL;DR: In this paper, the problem of entropy generation in a semicircular porous cavity bounded by a solid wall of finite thickness and conductivity has been investigated numerically using finite difference method using the dimensionless stream function, vorticity, and temperature formulation.
Abstract: The problem of unsteady conjugate natural convection and entropy generation within a semicircular porous cavity bounded by solid wall of finite thickness and conductivity has been investigated numerically. The governing partial differential equations with the corresponding initial and boundary conditions have been solved by the finite difference method using the dimensionless stream function, vorticity, and temperature formulation. Numerical results for the isolines of the stream function, temperature, and the local entropy generation due to heat transfer and fluid friction as well as the average Nusselt and Bejan numbers, and the average total entropy generation and fluid flow rate have been analyzed for different values of the Rayleigh number, Darcy number, thermal conductivity ratio, and the dimensionless time. It has been found that low values of the temperature difference reflect the entropy generation, mainly in the upper corners of the cavity, while for high Rayleigh numbers, the entropy generation occurs also along the internal solid–porous interface. A growth of the thermal conductivity ratio leads to an increase in the average Bejan number and the average entropy generation due to a reduction of the heat loss inside the heat-conducting solid wall. [DOI: 10.1115/1.4038842]
17 citations
Cites background from "Entropy Generation During Natural C..."
...[29] numerically investigated the impact of thermal boundary conditions on the entropy generation during natural convection in a porous enclosure....
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TL;DR: In this article, the effect of Dam on entropy generation in porous square enclosures has been investigated using the penalty finite element method using the Darcy-Brinkman-Forchheimer model.
Abstract: Computational studies on entropy generation during laminar mixed convection in porous square enclosures have been carried out based on Darcy–Brinkman–Forchheimer model using the penalty finite element method. Finite element simulations are performed for the isothermally hot bottom wall, adiabatic top wall, and isothermally cold side walls (case 1) or linearly heated side walls (case 2) or linearly heated left wall with isothermally cold right wall (case 3) for a wide range of modified Darcy numbers (10−5 ≤ Dam ≤ 10−2), Grashof numbers (Gr = 103 − 105), and modified Prandtl numbers (Prm = 0.026 and 7.2). Further, the effects of Dam on the total entropy generation (Stotal), average Bejan number (Beav), and average Nusselt number are discussed. It is found that Re = 100 is preferred over Re = 1 based on larger heat transfer rate with minimum entropy generation for Prm = 0.026 and 7.2, 10−5 ≤ Dam ≤ 10−2 at Gr = 105 for all the cases.
14 citations
Cites methods from "Entropy Generation During Natural C..."
...[28] performed entropy generation analysis in porous square cavities with various thermal boundary conditions....
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References
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Book•
01 Jan 1992TL;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.
Abstract: This 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. Geophysical applications range from the flow of groundwater around hot intrusions to the stability of snow against avalanches. The book is intended to be used as a reference, a tutorial work or a textbook for graduates.
5,570 citations
"Entropy Generation During Natural C..." refers background in this paper
...An extensive review of literature on porous media may be found in earlier works [ 8 ]....
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Book•
01 Jan 1984
TL;DR: Second-order Differential Equations in One Dimension: Finite Element Models (FEM) as discussed by the authors is a generalization of the second-order differential equation in two dimensions.
Abstract: 1 Introduction 2 Mathematical Preliminaries, Integral Formulations, and Variational Methods 3 Second-order Differential Equations in One Dimension: Finite Element Models 4 Second-order Differential Equations in One Dimension: Applications 5 Beams and Frames 6 Eigenvalue and Time-Dependent Problems 7 Computer Implementation 8 Single-Variable Problems in Two Dimensions 9 Interpolation Functions, Numerical Integration, and Modeling Considerations 10 Flows of Viscous Incompressible Fluids 11 Plane Elasticity 12 Bending of Elastic Plates 13 Computer Implementation of Two-Dimensional Problems 14 Prelude to Advanced Topics
3,043 citations
01 Jan 1997
TL;DR: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems and discusses the main points in the application to electromagnetic design, including formulation and implementation.
Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.
1,820 citations
"Entropy Generation During Natural C..." refers background or methods in this paper
...(5), (9), and (10)] with boundary conditions is solved by using the Galerkin finite element method [41]....
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...(12) and (13), the second term containing the penalty parameter (c) are evaluated with two point Gaussian quadrature (reduced integration penalty formulation, [41])....
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TL;DR: Entropy generation minimization (finite time thermodynamics, or thermodynamic optimization) is the method that combines into simple models the most basic concepts of heat transfer, fluid mechanics, and thermodynamics as mentioned in this paper.
Abstract: Entropy generation minimization (finite time thermodynamics, or thermodynamic optimization) is the method that combines into simple models the most basic concepts of heat transfer, fluid mechanics, and thermodynamics. These simple models are used in the optimization of real (irreversible) devices and processes, subject to finite‐size and finite‐time constraints. The review traces the development and adoption of the method in several sectors of mainstream thermal engineering and science: cryogenics, heat transfer, education, storage systems, solar power plants, nuclear and fossil power plants, and refrigerators. Emphasis is placed on the fundamental and technological importance of the optimization method and its results, the pedagogical merits of the method, and the chronological development of the field.
1,516 citations
"Entropy Generation During Natural C..." refers background in this paper
...The main idea behind thermodynamic optimization is to relate degree of thermodynamic non-ideality of the design to the physical characteristics of the system, such as finite dimensions, shapes, materials, finite speeds, and finite-time of intervals of operation and vary one or more physical characteristics to optimize the design characterized by minimum entropy generation subject to finite-size and finite-constraints [22, 23]....
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TL;DR: In this article, the effects of a solid boundary and the inertial forces on flow and heat transfer in porous media were analyzed, and a new concept of the momentum boundary layer central to the numerical routine was presented.
Abstract: The present work analyzes the effects of a solid boundary and the inertial forces on flow and heat transfer in porous media. Specific attention is given to flow through a porous medium in the vicinity of an impermeable boundary. The local volume-averaging technique has been utilized to establish the governing equations, along with an indication of physical limitations and assumptions made in the course of this development. A numerical scheme for the governing equations has been developed to investigate the velocity and temperature fields inside a porous medium near an impermeable boundary, and a new concept of the momentum boundary layer central to the numerical routine is presented. The boundary and inertial effects are characterized in terms of three dimensionless groups, and these effects are shown to be more pronounced in highly permeable media, high Prandtl-number fluids, large pressure gradients, and in the region close to the leading edge of the flow boundary layer.
1,427 citations
"Entropy Generation During Natural C..." refers methods in this paper
...Under these assumptions and following Vafai and Tien [37] with Forchheimer inertia term being neglected, the governing equations for steady two-dimensional natural convection flow in a porous square cavity using conservation of mass, momentum, and energy may be written with the following dimensionless variables or numbers:...
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...The momentum transfer in porous medium is based on generalized non-Darcy model proposed by Vafai and Tien [37]....
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...Under these assumptions and following Vafai and Tien [37] with Forchheimer inertia term being neglected, the governing equations for steady two-dimensional natural convection flow in a porous square cavity using conservation of mass, momentum, and energy may be written with the following dimensionless variables or numbers: X ¼ x L ; Y ¼ y L ; U ¼ uL a ; V ¼ vL a ; h ¼ T Tc Th Tc P ¼ pL 2 qa2 ; Pr ¼ n a ; Da ¼ K L2 ; Ra ¼ gbðTh TcÞL 3Pr n2 ð1Þ as qU qX þ qV qY ¼ 0 ð2Þ U qU qX þ V qU qY ¼ qP qX þ Pr q 2U qX 2 þ q 2U qY 2 !...
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