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Journal ArticleDOI

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...
Citations
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Journal ArticleDOI
TL;DR: In this article, a numerical study of heat transfer and entropy generation of a magneto-hydrodynamic (MHD) nanofluid flow inside an enclosure filled with a fluid saturated porous medium is presented.

76 citations

Journal ArticleDOI
TL;DR: In this paper, a detailed review of works on the entropy generation analysis during natural convection in various enclosures and processes involving different practical applications is presented, where the mathematical formulations of the fundamental governing equations for natural convections followed by the equations of entropy generation are presented.
Abstract: The entropy generation minimization (EGM) technique is an important tool for the optimization of the thermal systems via the analysis of the associated irreversibilities measured by the entropy generation. This article presents a detailed review of works on the entropy generation analysis during natural convection in various enclosures and processes involving different practical applications. The mathematical formulations of the fundamental governing equations for natural convection followed by the equations of the entropy generation are presented. The calculation procedure of the entropy generation for various test cases is reported briefly with the finite difference and finite volume techniques for some test cases and the detailed discussion of the evaluation of the entropy generation via the finite element method is addressed. Further, the problem formulation and results in terms of the entropy generation are discussed for natural convection in enclosures of various shapes (square/rectangular, trapezoidal, triangular, parallellogrammic/rhombic, curved/wavy). The brief discussion on the entropy generation analysis during various practical applications is also addressed. Overall, the minimum entropy generation vs enhanced heat transfer rate is the main issue in all the case studies with various enclosures involving a number of practical applications to achieve the optimal configuration with the high energy efficiency. The need of the renewable energy is increasing day by day. Thus, the conversion of the renewable energy to a useful form is one of the most challenging processes and natural convection plays an important role in the conversion. The loss of the available energy via the entropy production during natural convection is highly important for the design of suitable energy systems. This review article further provides basis for future research on the entropy generation analysis during natural convection in order to improve the energy efficiency which may be applicable for various renewable energy systems.

63 citations

Journal ArticleDOI
TL;DR: In this article, the natural convection heat transfer and entropy generation characteristics inside a two-dimensional porous quadrantal enclosure heated nonuniformly from the bottom of the enclosure were studied.
Abstract: In this work, we study numerically the natural convection heat transfer and entropy generation characteristics inside a two-dimensional porous quadrantal enclosure heated nonuniformly from the bott...

61 citations

Journal ArticleDOI
TL;DR: In this paper, the thermal aspects of a differentially heated porous square enclosure in the presence of an adiabatic block of different block sizes utilizing Darcy-Rayleigh number in the range of 1-10,000 with Darcy number was investigated.
Abstract: The present work investigates the thermal aspects of a differentially heated porous square enclosure in the presence of an adiabatic block of different block sizes utilizing Darcy–Rayleigh number in the range of 1–10,000 with Darcy number $$10^{-2}$$ – $$10^{-6}$$ . Heatlines and Nusselt number, streamlines, and entropy generation are used for the analysis of heat transfer, flow circulation, and irreversibility production in the enclosure. The study reveals that the presence of an adiabatic block affects the heat transfer process severely, and three different zones of heat transfer are identified. These are namely the zone of heat transfer augmentation, the zone of heat transfer augmentation along with entropy generation reduction, and the zone of both heat transfer and entropy generation reduction. It is also found that the presence of an adiabatic block can enhance heat transfer up to a certain critical block size; thereafter, further increasing in block size reduces the heat transfer rate. An optimal block size where the heat transfer enhancement is maximum is observed to be smaller than the critical block size. The study demonstrates the analyses of heat transfer and entropy generation for a better thermal design of a system. This study is also extended for higher Prandtl number fluids.

47 citations


Cites background or methods from "Entropy Generation During Natural C..."

  • ...The effects of thermal boundary conditions on entropy generation characteristics in a porous enclosure were analyzed by Basak et al. (2012) and Zahmatkesh (2008)....

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  • ...Entropy generation characteristics in the absence of a block in a porous enclosure undergoing natural convection were addressed by (Baytaş 2000; Zahmatkesh 2008; Kaluri and Basak 2011; Basak et al. 2012; Mchirgui et al. 2013)....

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  • ...…as 1 by (Poulikakos 1986; Chen et al. 2009; Varol 2011; Chandra and Satyamurty 2011; Sathiyamoorthy and Narshimman 2011; Tasnim et al. 2013) and high porosity )1~( media by (Prasad and Kulacki 1984; Poulikakos 1986; Sivasankaran et al. 2011; Basak et al. 2006; Basak et al. 2012; Umavathi 2013)....

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Journal ArticleDOI
TL;DR: In this article, a finite volume-based three-dimensional numerical simulation on natural convection and entropy generation in a cubical cavity filled with a nanofluid of aluminum oxide-water is presented by vorticity-vector potential formalism.
Abstract: A finite volume-based three-dimensional numerical simulation on natural convection and entropy generation in a cubical cavity filled with a nanofluid of aluminum oxide–water is presented by vorticity–vector potential formalism. The blocks are adiabatic and the vertical walls are differentially heated unidirectionally. The variables considered are Ra, volumetric fraction of aluminum oxide particles, and block size. The results for fluid flow with a single-phase model are elucidated with iso-surfaces of temperature, Nusselt number, and Bejan number. The local entropy generated was due to friction surges when the volumetric fraction of nanoparticles was increased. The average Nusselt number rose with the increase in Ra and volumetric fraction of solid particles and declined with the increase in block size.

43 citations


Cites background from "Entropy Generation During Natural C..."

  • ...[24] showed that an intermediate Da exists for optimum value of entropy generation by natural convection with porous media....

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References
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Book
01 Jan 1992
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.
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

Book ChapterDOI
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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Journal ArticleDOI
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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Journal ArticleDOI
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.

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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