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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
12 May 2023-Energies
TL;DR: In this paper , the authors studied the effect of Rayleigh number, Hartmann number and magnetic field inclination on the average Nusselt number and the entropy generation of the semicircular cavity.
Abstract: To study the natural convection and entropy generation of a semicircular cavity containing a heat source under the magnetic field, based on the single-phase lattice Boltzmann method, a closed cavity model with a heat source in the upper semicircular (Case 1) and lower semicircular cavity (Case 2) is proposed. The cavity is filled with CuO-H2O nanofluid, and the hot heat source is placed in the center of the cavity. The effects of Rayleigh number, Hartmann number and magnetic field inclination on the average Nusselt number and the entropy generation of the semicircular cavity are studied. The results show that the increase in the Rayleigh number can promote the heat transfer performance and entropy generation of nanofluids. When the Hartmann number is less than 30, the increasing function of the Hartmann number at the time of total entropy generation reaches its maximum when the Hartmann number reaches 30. As the Hartmann number increases, the total entropy generation is the decreasing function of the Hartmann number. The larger the Hartmann number, the greater the influence of the magnetic field angle system. Under the same Hartman number, with the increase in the Rayleigh number, the flow function of Case 2 increases by 29% compared with that of Case 1. The average Nusselt number of heat source surfaces in Case 2 increases by 5.77% compared with Case 1.
Book ChapterDOI
08 May 2020
TL;DR: In this paper, the effect of three different thermal boundary conditions on fluid flow, entropy generation and heat transfer is analyzed for natural convection in a closed square porous cavity using the generalized lattice Boltzmann method (based on Brinkman-Forchheimer-extended Darcy model) to simulate the flow through the porous medium.
Abstract: The effect of three different thermal boundary conditions on fluid flow, entropy generation and heat transfer is analyzed for natural convection in a closed square porous cavity. The generalized lattice Boltzmann method (based on Brinkman–Forchheimer-extended Darcy model) is used to simulate the flow through the porous medium. The three different cooling arrangements are made at the vertical walls of the cavity via uniform, sinusoidal and linear temperature distributions while maintaining the bottom wall uniformly heated and the top wall thermally insulated. The comparison is carried out with existing published results to lend legitimacy to the findings. Numerical simulations are carried out for the range of Rayleigh number (Ra) from 103 to 105 and Darcy number (Da) from 10−1 to 10−5 with porosity (e) at 0.5. The volume fractions (\(\phi\)) of Cu nanoparticles in water are varied from 0 to 5% to check the influence of nanofluid on the enhancement of heat transfer efficiency. The entropy generation minimization (EGM) approach, based on heat transfer rate and entropy generation, is implemented in order to make a judicious choice of boundary condition in terms of energy efficiency. The results indicate that the selection of optimum boundary condition depends on the values of Ra and Da.
Journal ArticleDOI
TL;DR: In this paper, the steady flow of a reactive variable viscous fluid in a porous cylindrical pipe was examined and a regular perturbation technique was employed to obtain an approximate solution of the resulting dimensionless nonlinear equations.
Abstract: Studies of mass transfer in a porous medium are of interest to researchers as a result of its various uses in different fields of engineering practices. This work examined the steady flow of a reactive variable viscous fluid in a porous cylindrical pipe. Dimensionless variables were used to dimensionalize the governing equations. A regular perturbation technique was employed to obtain an approximate solution of the resulting dimensionless non-linear equations. Numerical simulation was done to get the threshold values for the flow parameters under consideration. The effects of viscous heating and permeability parameters on the steady flow were studied and reported.

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

  • ...Ever since the pioneering work of Darcy on flow through porous beds which resulted in the identification of permeability as the property of porous media, there has been tremendous interest in the study of flow through porous media which occur widely in nature and industry [9]....

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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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